Chapter 11 discusses the importance of developing whole-number place-value concepts. Students just starting out in school hold absolutely no concept of the placement of number value. Having subbed in pre-K, I have gotten to see first hand that drill and practice on this begins on the very first day that a child enters a classroom! My intern classroom places straws in a ones place until they reach ten, then they rubber band them together and place them in a tens spot and so on. They also make it a point to talk about the value of zero and on every school that ends in zero they get a special visit from "zero-the-hero". Its a fun way to get the kids interested in place value! Recently, I got the privilege of introducing "hundreds" to the class. We estimated how many pumpkin seeds were in our pumpkin and then counted ten separate cups of ten seeds each and dumped them into one hundreds cup. The kids loved it! I really enjoyed the other ideas and resources the text gave.
Chapter 12 discussed developing strategies for whole-number computation. Being in kindergarten I haven't got to see whole lot of this during my internship yet. However, I subbed whenever I can and get to see it then. I enjoyed the section on student-invented strategies for addition and subtraction. I personally think it is fine for students to explore other ways in which to solve the problem as long as they are doing the math and figuring it out. One day when I was subbing in 2nd grade i got to introduce doing a +9 shortcut in which you add 10 to the number and then subtract one. Apparently many of the students were struggling with adding nine but after teaching this short cut they seemed to do much better with it! I think that all students really need to be successful with whole-number computation is options. They need to know if they don't understand it one way, that its okay to try to work it another way and figure out what works for them!
Chapter 13 talked about using computational estimation with whole numbers. It told us that there are three times of estimation- measurement (determining measurement without making an exact measurement), quantity (approximating the number of items in a collection), and computational (determining a number that is an approximation of a computation that we cannot or do not wish to determine exactly). It is very important for students to learn estimation and rounding in order to do a quick guess in their head and to be able to check their actual answer.
The concept of whole number place value is being taught at younger and younger ages. I do not remember being taught this concept until about 3rd grade (which was many many years ago). Now the students are immersed into this concept the second they walk into the school doors. I see the teachers beginning to use the same terminology more now which I think enables students to make a connection between grade level learning. The use of base ten blocks or cubes is ideal for teaching this concept in the early stages. The literature connection at the end of the chapter gives some wonderful resources for integrating across curriculum line. Chapter 12 is about developing whole number computation sense. I think this starts with number sense. Giving students the tools to understand whole numbers is the beginning of understanding computation. When a student invents a strategy and can explain it to the teacher then this is a way of having the student teach the class a new of computing numbers. Teachers should encourage the invention of new strategies. Some may say, "Whatever works for the student." The teacher should of course give the standard means of computing the answers but when a student comes up with a different way then this should be a praise worthy moment. Again, this chapter has some wonderful resources for integrating literature and technology into math lessons. Chapter 13 is all about using computational estimation with whole numbers. This is a concept I had a hard time fully understanding when I was a student. I always blamed it on my brain. I just thought my brain did not work that way and could not understand this concept. Now I think it was the way the concept was taught to me. The chapter says that "estimation is a suitable approximation for an exact number." I was never given the reason behind estimating. Why do we estimate? How is estimation used in real life? These are questions I would like to answer for the students I teach. Giving students the reason for doing math is the beginning of students grasping the concept. The suggestions for teaching computational estimation in this chapter are easy to understand and will be useful in the classroom.
Comment for Kristle C: Zero the hero is so fun to teach. I learned about this strategy in a K classroom and found that the students really looked forward to another visit from Zero. The plus 10 strategy for the 9's is a great way to learn both 10's and 9's all in one fell swoop. Good suggestion. Chapter 13 had the most useful information for me because this is a concept that I want to make sure my students understand and fully grasp. I took away many good strategies and learning lessons from this chapter.
Do you have any epiphanies after the reading or discussions? Any questions or concerns as you prepare to become a teacher of mathematics? Be sure to post one comment AND respond to at least one other person. Chapter 11 was very informative, as usual. It is hard for me to remember precisely when or why numerical connections were made. I am certain from the time I was in third grade we never used manipulatives, and I can understand now where most of my frustration in mathematics can be attributed to. I think that early on I never really had a firm understanding of why- things were always just taught to me ‘because that the way it is’, and I guess I had a hard time accepting that. Reading in this chapter about the importance of developing whole number and place value concepts has reinforced most of what we have been presented throughout this book. Hands on activities cement knowledge and build more connections within a childs' knowledge base, that knowledge becomes more meaningful and more useful to a child as they encounter more complex mathematics. They are not simply ‘going through the motions’ but rather they are actively aware of the computations they are performing and understand why they are using the methods that they are using. Chapter 12 focused on whole number computation. I personally found the suggestions within this chapter to be very useful. I liked that they spent a bit of time devoted to student invented strategies for working with whole number computations. As we have been discussing in class, there is no one way to ‘do’ math, and all approaches should be examined for their usefulness. I may not understand and do things in the same manner as you, but as long as I arrive at the same conclusion consistently my answer is still correct. I think I found this chapter to be so helpful because I am currently in a first grade classroom where a number of students are struggling with subtraction; I think that many of the suggestions in this chapter might help them understand. Chapter 23 was about computational estimation. I think that estimation can be a difficult concept for a lot of children to master. The wording of problems is sometimes confusing to a child and there are also the questions of why we would need to estimate. This chapter did a good job of explaining reasons for estimation and put it very plainly so the future instructor can use many of the suggestions in this chapter with very little adaptation. The suggested activities in this section were brilliant and I can envision myself using many of these suggestions within my own classroom eventually.
In response to Jena S: I agree with you that students are being introduced to concepts are earlier ages, and I also agree that it is a good thing that teachers are using the same terms in different grades. I also feel that it builds continuity from each grade and it probably helps the student develop the sense that most things in mathematics are related. I agree that invented strategies should be encouraged. I like you had a little trouble with estimation and think that there were a number of suggestions within this chapter that would have been useful for us. I believe that we will probably taking a lot of the same things from this text for our future classrooms.
Chapter 11 Developing whole number place Value Concepts is very familiar to me because I have had the opportunity to watch my mentor teacher teach this concept to classroom of 27 students. She has used the based ten blocks and emphasized each place. For instance, in the number 734 the students understand their are 4 ones, 3 ten and 7 hundred. She demonstrated this with the manipulative and than had the students who the base ten blocks to demonstrate it back to here. I felt like this chapter had a lot of good activities that a teacher can use in the classroom. Chapter 12 Developing Strategies for Whole number computation. Wow things have changed a lot since I have been in school. I have noticed the vocabulary has changed from borrowing to regrouping and the many different strategies that have been introduced. I am not against new strategies as long as the students understand material. In my internship class my mentor teacher is very open to the students coming up with different ways to reach the same conclusion. For instance a student may be adding 50+29. It may be easier to add 50+30 and subtract one. One day in my internship class she gave the students different problems to solve. One problem had to be done with pencil and paper, another mental math and another using a calculator. The students were able to see where each of these methods had their place. I think as teachers we need to keep in mind that students are individuals and different methods are going to work for different students. Chapter 13 Using Computational Estimation with Whole Numbers I think estimation is a tough concept for students because they want to be correct. Estimation sometimes gets confused with rounding. In my internship class the 3rd graders have just finished with this section and they seemed to struggle with the concept somewhat. My mentor told them to look for key vocabulary to decide if they were to estimate. The key word for them was about. The problems they had to work involved deciding if it was to be an exact answer or estimate. They seemed to do better when they cued in on the correct vocabulary.
To Adrianne: I agree with much of what you said. I am a very visual learner. Usually if I can see it and do it with my hands I have got the concept down. However, way back when I was in school we sat in our chairs and listened to the teacher go on and on and on about something. I remember my mind would wonder. I think kids are very curious and like to do hands on materials. As teachers we need to move from the idea that our job is to lecture and allow the kids to learn from doing as well.
To Kristie: I am so glad that you recognize that learning these concepts starts as early as PreK. I believe it is so important for students to understand that mathematics is a process and each skill carries onto another. I worry about students who don't master a certain math skill and it causes them to fall further behind. Mathematics is so important and as we move into a more technical society math is becoming more important.
Chapter 11 talked about developing whole number place value concepts. It mentions that children learn to count to 100 as early as kindergarten, but only by ones. it also talked about the role of counting: counting by ones, counting by groups and singles, counting by tens and ones. It is important to incorporate the grouping by tens concept with what they know about number from counting by ones. The chapter gives lots of activities for teaching students about grouping numbers.
Chapter 12 is about developing whole number computation. Direct modeling was mentioned within the chapter and that is the use of manipulatives or drawings along with counting to represent directly the meaning of an operation or story problem. The chapter talks about student invented strategies and talked about how students come up with strategies to solve certain problems and they have not been taught those strategies. In class we talked about how if a students understands and can explain their answer they should be able to use the strategy. What works for one student may not work for another so I feel if students find a strategy that works for them and they understand it and can explain then they can use it.
Chapter 13 is using computational estimation with whole numbers. It talked about the three types of estimation: measurement estimation, quantity estimation, and computational estimation. It gives suggestions for teaching computation estimation: use real examples, use language estimation, use context to help with estimates, use context to help wiht estimates, accept a range of estimates, focus on flexible methods not answers, and ask for information but no answer.
In response to Jeanette, I agree that the way things in math are done have changed. I feel like I'm learning to be a teacher, but also learning the way students are taught these days. My mentor teacher encourages different ways in which to solve problems. She often asks if anyone else got a different answer or solved it a different way. When I was in elementary school I found estimation to be difficult because I wanted an exact number.
Chapter 11 is about developing whole-number place-value concepts. This is what the students in my internship have been working on lately, and I can see when it clicks and I can also see why it is confusing. There are students that just can't understand with decimals how the tenth spot is bigger than the hundredth spot. My mentor teacher uses base 10 blocks, and they seem to help, but they will finally understand one question then be lost on the next. I can see how important this is, and it needs to start early. My last internship was in first grade, and they counted the days of school with straws and bundled into tens when they could. This is a good way to begin students understanding of place-value. Chapter 12 is about developing strategies for whole-number computation. In this chapter I got the most useful information out of student-invented strategies. I had never really thought of this, I guess once you get older and set in your ways you have certain ways of doing things. Not young students though, they come up with strategies that work for them, and as long as it gets them to understand the concept then we need to be supportive of it. Students need to be able to use strategies that work for them. This chapter discusses all the benefit of student-invented strategies. I found it very interesting when we did this in class. It was great to hear other students ideas of how to solve problems. Chapter 13 is about using computational estimation with whole numbers. This is another concept that students have worked on in my internship class. They use the term ball park estimate, which was something I don't remember hearing when I was in school. One thing I found important is to not use the word guess. Students are not guessing they are using some form of reasoning to estimate the number. One idea from the text that I think is a good one is to ask for information not the answer. Especially for students that have trouble with estimating this will put them at ease not to get the answer correct. You can give them a problem then ask them if the number is over or under 100. I didn't really know that there was so much involved in estimating, but this chapter brought some very good information to the table.
I agree that it is frustrating to have teachers tell you what something is, then never show you why. By doing this students will never get the why. My mentor teacher uses a lot of manipulatives and I really like that about her. I have seen how they help the students understand the process, not just the answer. That is so important for their future.
Chapter 11 was about how teachers can teach whole-number place-value concepts. One interesting concept in this chapter was the different ways that students can count sets. Some students may count one at a time, or some might group them. I think that as a student develops, they will begin to us more logical and efficient ways of counting. I like using the cubes, rods, and flats to illustrate the concept. Chapter 12 was on developing strategies for whole-number computations. I liked reading this chapter because we have been talking about it in our classes. What I have caught on to is that each child may approach a problem in their own way. They will use the procedure that they understand best. It’s not the teachers’ job to tell the student that there is only one correct way to do something; they are there to support the child in their learning. Chapter 13 was on computational estimation with whole numbers. This was my favorite chapter out of the three because my internship class just taught this a couple weeks ago. Needless-to-say, it took them a while to understand the concept. The book identified what might have been their problem; estimation is not guessing. When I would ask them what they thought the answer might be on an estimation problem, they would guess thinking that was what I expected. It wasn’t until I wrote how I would tackle the problem that they began to understand the concept.
In response to Jena- I think that you bring up a good point that I’m sure the students would ask you. Why do we estimate? I think that estimating is a great skill to have because it does truly save time. For example, which is quicker in Walmart? Estimating how much you have in your cart or adding the exact price up? Students and children always like to ask “why” and I think that it is a valid question. Students need to know the reason behind the work we give them. They will have more buy in if they know.
In chapter 11 it was about whole-number place-value concepts. The very first thing that the chapter talks about is base-ten-concepts. In my current internship at Roosevelt My teacher makes a big deal about 10s with Zero-The-Hero. Every time that we are in school for a tenth day, Zero-The-Hero comes to visit us. He/She groups the ten ones of straws into a bundle of ten. With this students start becoming familiar with place value. I think that we do need to make a big deal out of tens because there are lots of short-cuts that students can use if they have a good concept of 10s. Chapter 12 is about developing strategies for whole-number computation. I really liked the Student-Invented Strategies for addition and subtraction “one goal should be to extend students’ knowledge of basic facts and the ten-structure of the number system so that counting is not required.” One thing that I loving that Dr. Stramel continues to say is that we need to let our students try new ways to get answers, but we need to make sure the students know and understand and can explain if the students would do their problem a different way. Chapter 13 talking about estimation with whole numbers. One thing that I think of that I do on an everyday basis, is when I go to the grocery store I estimate how much it will be when I check out. One of the ways that my group at my table do when we are supposed to do the math problem with different ways, is we estimate and round up or down numbers to get close to our answer. My students in my internship haven't started learning about estimation but I think that its never to early to start to learn.
To Jena: I agree with what Andrew says. I think that we need to teach our students how to estimate because like I said in my post that I do this on a almost everyday basis, when every I go to the grocery store I estimate how much it will be so I know how much money to have ready. So when a student would ask me I would say because you will use it when you get older and we need to start practicing it now.
Jena- I agree with you on how whole number place value is being taught earlier and earlier. I subbed in a pre-k classroom not long ago and they were placing straws in a pocket for each day they were in school and rubber banding them together in groups of ten. Its funny to think how the teachers work to use the terminology and the students don't really even think anything of it! Hopefully teaching it early will help it come naturally later!
As usual I found the examples throughout these three chapters to be incredibly insightful. Hopefully one day I will take advantage of having this textbook as a resource.
In Chapter 11 I enjoyed reading about the Base Ten manipulatives, and how these manipulatives can be used. In my internship classroom I was able to see how Base Ten blocks can be used. It is nice to be able to relate textbook information to real life use and experience.
I never would have thought that cultural differences were in algorithms. Chapter 12 provided me with some very useful information on this. Students come from different backgrounds, and some students even come from different cultures. Because I am from America, and have lived here my entire life, does not mean that every student understand algorithms in the way I. I need to be sure to take into account all of my students’ backgrounds. I also thought that it was great to be able to see some student-invented problem solving techniques. Certainly there are some ways to solve problems that are quicker, but if a student can reach the correct answer and explain it properly, there is no need to tell that student he or she is incorrect.
I had no idea that there were three types of estimation. There is measurement estimation, quantity estimation, and computational estimation. I have used every type of estimation but I was never told that a specific example is an example of one specific type of estimation. I also like that the book stressed using real examples of estimation on page 242. Using real life situations in anything is one way to guarantee students will learn and retain information.
I also saw the Base Ten manipulatives being used in my internship. My teacher refers to them as bits (ones), rods (tens), and flats (hundreds). I know there is a name that is used for the thousands, but I can’t recall it at the moment.
I also thought it was incredibly insightful to have the chance to look into student-invented problem solving techniques. I think it is important to let a student do as he or she chooses as long as they reach the correct answer and are able to explain how they reached the answer and how it’s correct.
One thing I loved about today's class was when we did problems using estimation and then discussed how we estimated. For example, on one problem one person rounded the numbers to the nearest hundred, another rounded to the nearest 10, and the other rounded to the nearest 25. It was quite intriguing to see all the different ways. What was most interesting was that all of the estimations came out to equal the same number which was something that I had never seen before. But with all of the other problems we got different answers but were all within the range of about 10. Estimation is a key tool that students should be able to learn how to use to help get a general idea of what the actual answer is because sometimes in life there may not be any choice but to estimate.
Emily M. I completely agree that using real life situations, no matter what the type of problem is, will help to guarantee that students learn the material. When students see that there is a way that they may use it somewhere other than school there is more motivation to learn the material. It will also stay with them better because they might use it on a somewhat regular basis which will be that much more practice for the student.
When reading through Chapter 11 dealing with the areas of developing whole number place value concepts I was able to learn lots of helpful information for my future career. I especially liked the figure 11.1 on page 189 that showed three different but equivalent groupings of 53 objects. A tip that I found helpful in chapter 11 is when it talks about how a good base ten model for ones, tens, and hundreds needs to be proportional which I feel is so important. This means that the ten model is physically ten times larger than the one and the hundred model is ten times larger than the ten model. I also loved the idea of using place value mats in the classroom in order to help with the concept of place value. Overall I loved all of the activities presented throughout this chapter. When reading through Chapter 12 over developing strategies for whole number computation I was able to learn some interesting facts and tips for my future classroom. I found the figures 12.5 and 12.6 on page 221 to be helpful to me to show me different inverted strategies that students have created for addition with 2 digit numbers and strategies for subtraction by counting up. I liked how the book thoroughly explained the idea of cluster problems to me as the reader. Before reading this chapter I was unable of how exactly a cluster problem was and now I am able to understand it. Overall I loved how this chapter explained different student invented strategies for multiplication as well as division. When reading through Chapter 13 over using computational estimation with whole numbers I was able to learn lots of helpful information in this subject area for my future teaching as well as my future classroom. I liked how the book talked about the three different types of estimation which are measurement estimation, quantity estimation, and computational estimation. I also found the rounding methods to be very helpful to me in understanding how to teach estimation in my classroom someday as well as the importance in teaching estimation. Lastly I found the calculator activities to be good to use in a classroom someday. Overall estimation is such an important skill to know in daily life so that you know how to use it properly in the world.
In response to Kayla R., I agree with you Kayla that in chapter 11 it talked about how children in kindergarten learn to count up to the number 100 but only by ones. I am constantly seeing this practice put into effect in my kindergarten internship classroom. The teacher has a 100’s chart and is always reviewing the numbers to 100 with the kindergarten students. I also feel that it is important to incorporate the grouping of tens concept with what they know about the numbers by counting by ones. I also enjoyed the activities mentioned throughout chapter 11. I also noticed that chapter 12 talks a lot about student invented strategies which I feel is good for a teacher to understand and appreciate. I agree with you 100% that if a student can explain how they solved the problem and the student is able to get the correct answer then the student without a doubt should be able to use the strategy. I agree with you that all of the students in the classroom are different and a strategy that may work for one student may not work with another student. I also found it helpful that in chapter 13 the three types of estimation were mentioned and explained in detail. Lastly I also noticed that the chapter gave suggestions for teaching computation estimation. I really enjoyed the activities that were given throughout chapter 13 that were related to the area of estimation. Overall great post Kayla!!!
Chapter 11 talked about whole number place value concepts. I vaguely remember working with base tens blocks as a child. Sometimes I think it is confusing, but other times it helps show the “big picture”. I also wonder how we are suppose to teach a concept we ourselves may not understand. For example, most of us were taught to add the traditional way. How do we show our students there are other ways when we can’t even do it ourselves? I like the examples the book showed and the activities we did in class. It helped me understand the place-value concepts better. Chapter 12 was over whole number computation. One of the things I liked was on page 217 where it talked about traditional algorithms. It said that often younger students pick things up from older siblings or parents. They will come to school and say “my dad taught me a shortcut” and will often refuse to learn a different way. The book said that once the traditional way is understood, then it shall be looked at as one more strategy for the classroom tool box. Which I think is a great idea. We should be accepting of the different strategies children will use, not just stuck on one way. The first graders in my internship have been using the number line to help them add and subtract. I have always hated number lines. I think it was because I never understood the correct way to use them? Or maybe it was because I never needed to use them? The first graders have taught me a lot about how to use them and I can see how they are a useful tool, just not useful for me. Chapter 13 was about estimation with whole numbers. I can say that when I was in elementary school, we hardly ever estimated. That is probably why when we were doing the estimation activities in class I had the hardest time. It took more work and thinking to think of what number to round too and then to remember that number and think of what to round the next number to and remember that number and so on. Its not that I never estimate, because I estimate when shopping all the time, its just that it is easier for me to just do the traditional way of adding, subtracting, dividing, and multiplying.
In reply to Lane: I really enjoyed your post. I also thought it was really neat how everyone estimated differently. What I really liked about your post was your last sentence. I liked how you said if the student has no other choice then they could always estimate. This made me think of state testing. If students know how to estimate, then they have a better chance of selecting the right answer.
These were 3 really informative chapters. Chapter 11 was over place value. This can be a very tricky concept for some students. I work as a paraprofessional and = I have taught this to my students and some pick this up pretty quickly, then again, there are some that really struggle with this concept and it is the same way in a regular education classroom. I enjoyed how the book showed different activities you can do with learning place value. Chapter 12 was over whole number computation. Again, I like how the text provided different methods and activities for this concept. I also think it is key to remember, everyone learns different so what may work for one student, may not work for another student. This is definitely important to remember in mathematics in the classroom. Lastly, chapter 13 was over estimation with whole numbers. I really enjoyed Professor Stramels lecture over this. I am definitely going to use her activity of the over/under. I believe this is a great way to teach estimation and I believe the students would enjoy it as well. I am glad we got a chance to read about estimation and how to teach it because estimation is such an important concept that students will need to know forever.
In response to Emily M-I completely agree with you, using real-life problems are a great way to teach students. It gives them things to relate with and lets them know they really do need to learn what concept you are teaching at the time. I am sure there are many students that brush off different lessons because they think they will never need to know this and will never use this in the future but by using real-life situations will put things into perspective for them! Great post Emily!
Chapter 11 Whole-Number Place-Value Concepts Chapter 11 talks about counting by one, counting by groups, and counting by 10’s. I work with children every day that can’t count by 2’s, 5’s or tens. I think this is such an important skill that makes counting so much easier. This is a skill that they carry with them from Kindergarten all the way through their lives. As adults we use these skills every day. Now I see teachers using it in all sorts of ways, during calendar especially. The think I like most about having children count by numbers is you can use anything to count with craft sticks, coffee stirs, coins, and beans. Coffee sticks and craft sticks are great for combining and grouping together, groups of 10 with a rubber band or ties. This is such a great way for our visual learners to see 50 in the tens place and 4 in the ones. This section is once again packed with activities. Chapter 12 Developing Strategies for Whole-Number Computation The part of this chapter that really stuck out was about creating an environment for inventing strategies. When we are so hurried to get something taught and stay on schedule we forget to let the children use the brain God gave them. Let them use different experiences that they have had that will aid them to find new and different ways to solve problems, because not every problem is going to be introduced the same way. Cluster problems – I’ve learned to teach them to break them down to just a couple of numbers at a time or adding by columns and hundreds then tens and last ones. The division algorithm is great for children that are new to division or have problems with division. Myself I don’t like the new way of dividing it takes me too long. Chapter 13Using Computational Estimation with Whole Numbers Focusing on the flexible methods is important. It is important for them to learn to use strategies to find their answers not think that they have to do it a particular way. It’s more important to see how they get their answer and can they justify their answer. I think it’s important to give everyone time to try to solve the problem and let the children tell each other how they solved it. They can learn from each other. Estimation is such a needed skill yet most of the time we really don’t realize that were using it.
Megan B. I like what you said about real world problems. Kids love things that seem real. If your teaching money from a worksheet they won't want to learn. Bring in some cans of food and other packaged groceries and the children jump at the chance to play store, buy groceries and learn what change to give back. Even as adults we think the same way, if I can't apply it to something I will be doing why learn it.
Chapter 11 is about developing whole number place value concepts. These concepts start at grades as young as preschool. It is very important for students to start learning about whole numbers young. In my first grade internship classroom the students learn about place value by counting the days they are in school every day. When they get to 10 individual straws they make a bundle of 1. This is the basis of place value. This chapter has a lot of information and activities about how to teach children to use base ten blocks when doing math. I think that manipulatives are so important in the classroom and teaching children to use them will only benefit them. I saw one point in chapter 11 that I feel was very difficult for children and that was numbers beyond 1000. It is hard for children to understand what is beyond 1000. Because you cannot actually get 1000 little cubes out its hard to see what you want. The best way I think is to use 10 flats. Chapter 12 states that rather than a single method of subtracting; the most appropriate method can and should change flexibility as the numbers and the context change. I know we have talked in class a lot about student inventing and I think this is a great strategy to use. It is good for your students to come up with ideas of their own. If they cannot think of a strategy then they can ask for help from the instructor though. Using base ten is a good way to teach any problem. Teaching children to trade when adding and subtracting can help them in the long run. Chapter 13 is all about estimation. Estimation is not just a guess. It has to be an educated guess. I know that if you tell the children in my internship to estimate, they will just choose a number without looking at the problem. A lot of the students won’t even look at the problems when you want them to. So making sure that they understand what an educated guess is is a good idea. Estimation is a good way for students to figure out problems. When learning to do math it is good to estimate so children can relate problems.
I think that in class by showing how just us 15 all round and figure out problems differently shows how children are going to do things differently too. There are so many different ways. Some child might just want to round to 2's. Which is different but it might be easier for him to do that.
Somethings that I took away from ch. 11 is that using manipulative's, such as base 10 blocks, is a great tool to use for students to visualize what is being taught. Sometimes as a student I was not always able to understand things unless I was able to visualize it. Once I have had the objects in my hand and used them, usually I can visualize them down the road in my head without have them in my hands. There are so many different ways to teach place value but I think that using manipulative's is probably the best. Chapter 12 is interesting. There are many strategies in this chapter that I have never thought of or seen. These are just other ways to reach those who don't understand concepts. It will be difficult, I think, to teach these other strategies and use them when it has been engrained in our heads of a way that seems right. It is also important to allow the students the freedom to come up with their own techniques if none of the strategies work for them. In chapter 13, computational estimation is something that I have never used before. It is a different way to teach but it can be effective and easy to do in your head. As a teacher, I will not limit students to using one method, as long as they can explain it. For the first few assignments that they are using that technique, I would like for them to show their work. I know this is not Dr. Stramel's first choice but I believe that if a student is learning a new technique, they need to prove that it can work. After the first few assignments of showing their work they will not be required to show their work after the assignments.
Tammy, I agree with you that it takes too long to divide using the new method. I also think that if we are going to introduce strategies into the classroom, they need to be effective strategies. Do not allow students to use them for a long time and then tell them that they are not able to use it. If we are teaching the strategies, maybe we can tell them which one will benefit them more and leave the options of which one they want to use up to the student.
Chapters 11-13 are about whole-number place-values. Chapter 11 is about whole-number place-value concepts. I believe the most valuable manipulative that could be used during this section would be the base ten models. This manipulative allows students to see visually whole numbers. Once students have a complete understanding of whole-numbers they then can be used to help students with decimals. Another section that I found important about this chapter was that it is equally important that students are able to express the whole number verbally; this is a skill that I think is sometimes forgotten. We often assume that if they can write them they understand them, but they must also be able to read them. Chapter 12 is about the computation of whole-numbers. This is what we think of when we think of elementary math, adding 4+3, and subtracting 11-4. These skills are very important in the fundamentals of math, it create the base for all math to come. This chapter was discussed in detail in class, because it is so important to allow students to create their own way to solve these problems. Once students are able to solve addition and multiplication problems, they will move to multiplication and subtracting. I think this is one of the most controversial areas in math, should students be made to memorize their multiplication facts. I believe that a mixer of teacher led, student created, the use of manipulative, and drills is the best way to help students master multiplication facts. I don’t think one single method should be used all the time. The final section is over estimating whole numbers. I think this section is so important because it is the way that most of us to math in our adult lives. This is a skill that is very important concepts to teach students, it allows them to look at math in not just a black and white way. Overall all of these sections are important fundamentals for the first steps in teaching mathematical concepts. I really enjoyed how the section gave examples of different ways to solve math problems that are different than the traditional way.
In response to Joel S. I also think that the base ten blocks are one of the most important manipulative to use when teaching whole number. You pointed out that it was important for you to see the problem visually, this is important when teaching to multiple learners. I totally agree with you, It is very difficult for me to teach math using a different method than the traditional way. But it is very important for them to develop their own ways to solve the problems, by allowing them to do this I think they will have a better understanding of the math concept. Finally in my schooling estimating was not a much discussed area, so it is very difficult for me to do it. It is actually much easier for me to work out the whole problem rather than guess. One last note, I am also a full believer in having students showing their work, I think it helps them refine their skills when learning a new concepts. I don’t care much about what steps they used to solve the problem, just that they used some method to solve it.
Lacey Keller Chapters 11, 12, and 13 presented information regarding whole numbers. I found it interesting how these three chapters showed how students computate the different math problems. For this here math lover, it was sometimes difficult to figure out the rhyme and reasoning of some of the problems. Most times, I think people should just be able to think in terms like me!
I think the best information from these chapters came about estimation. I think this skill is one of the most important skills we can teach our students. It is a skill that will be used everyday. No matter your chosen walk of life, you will always find yourself estimating.
Again, I liked the websites shown in these chapters. I checked out the digital manipulatives...it is cool!
In response to Rebecca B., I agree with you that students should have a strong mixture of mathematical problems should be delivered to our students instead of memorizing facts. This drill and kill stuff is okay, but showing students how to use these skills in real life situations is more practical. Also, when teachers use one-minute timed tests, it only allows the students to practice for a short amount of time!
Chapter 11 on the development of whole number and place value concepts provided good information. While I understand that are students all learn differently and at all different levels, I ponder the thought of losing most of them in all the different ways of teaching one concept. In second grade, we should be reinforcing addition and moving forward into subtraction. It is almost the end of the first semester and we have students that are struggling with addition of basic numbers. Many of these students need one-on-one to go back to the basics of addition and practice. But instead, we have to spend days on teaching other methods to work a problem, such as base-ten groupings. The chapter talks about teaching our students to put things into groups of ten to make it easier to count. I agree that it is easier for most of our students to count by groups of ten, and using it throughout the day with tasks and classroom chores is a great reinforcement. The chapter goes on to discuss integration of groupings with words. In my experience, this is a fairly easy concept to teach and understand using base ten blocks. As the students finally make the transition from addition to subtraction, groupable models are very helpful. This chapter provides many great strategies for teaching using base ten, it is just so important not to move into this until the student is completely ready. I feel that this is where many students are lost, and then every lesson from then on is history. Chapter 12 on developing strategies for whole number computation is a little more complex. I agree with the chapter that direct modeling is a must. Our district is so fortunate to have hovercams and smart boards which makes this so much easier! The student invented strategies paragraph really got me thinking. In many lectures, we have always been taught that kids learn from kids. The chapters points out that the students cannot use or teach their invented strategies unless they have been evaluated for accuracy. I think that it is very important to let our students share their ways of doing the problem with the class using the smart board. As a class, the procedure can be evaluated and if correct used by students that understand it. My concern with this is that there are many teachers that require the students to use the formula they teach, so it is not going to benefit them to use their “created” strategies. I was a bit surprised when the chapter discussed traditional algorithms. With a little thought, I realized that this is something our students develop early on. As the chapter went on to discuss strategies, I was excited to see subtracting by counting up! I use this technique with many of my students and most of them seem to grasp it pretty well! The chapter ended up with discussion on multiplication and division strategies and ideas. Chapter 13 discussed using computational estimation with whole numbers. Estimation has been amazingly hard for our third graders this past couple of weeks. The chapter encourages us to use real life examples in teaching our students to use estimation. Estimation makes sense to me when buying groceries or estimating how much I have spent for the month, but we are teaching our students to estimate thousands’. This is where the frustration comes in. The third graders have a little chant they use with estimation and it is “five or more, raise the score – four or less, let it rest”.
Developing Place Value Concepts in Chapter 11 was a very familiar topic. One of my lessons in my FPA was on the topic. Place values seem to be taught to younger ages now than they were when I was going through school. Chapter 12 was over whole number computation which, of course, if an important topic to cover. It seems that the wording used in this chapter differs somewhat from the wording that was used when I was learning about whole number computation. I found it quite interesting and somewhat frustrating to change the wording. I found it frustrating simply because, now as teachers, we will need to learn the new wording and not confuse it with the older wording. Chapter 13 was over computational estimation. Estimation is such an important skill that some may look over. I feel that students know they need to learn to add, subtract, and other basic skills; but estimation can seem unnecessary while, on the contrary, it is important in our everyday lives. We even use it without noticing many, many times throughout our days. Overall, I enjoyed reading this section and thought it was very informative.
In response to Joel Stucky: You said, "Somethings that I took away from ch. 11 is that using manipulatives, such as base 10 blocks, is a great tool to use for students to visualize what is being taught." I completely agree. Visualization of math is such an important thing to provide for students. There are so many students that simply cannot grasp the math concept when it is taught as just a concept. Students often times need a concrete thing to see, touch, and feel to truly understand just how math works.
@ Jenna ~ On estimation, I am right there with ya! Last week I was working with third graders and man they were struggling with estimation. Later in the day I was visiting with their classroom teacher and he said "estimation is very important, I use it daily". Really I thought to myself. I feel that most of our students are doing good to get the concepts of addition and subtraction down. I want them to be able to balance a checkbook and be able to run their households, I am not so sure that estimation is as important as we make it.
Chapter 11 is about Whole –Number Place-Value concepts. This is something that holds no meaning to children before they start school. However, it is something that can be picked up and understood quickly if they are given proper models. Many teachers use a straw for each day and then group them by tens and then again in one group of 100 once the 100th day of school is reached. There are many other models that can be used throughout the classroom to help them understand the meaning of place value. For example, many math teachers use Base Ten math tools with their students. Also, Tens frames are used in math and can help students understand the importance of Fast 10’s in Math.
Chapter 12 was about strategies for whole-number computation there are multiple strategies to use and help students to learn when teaching different concepts within mathematics. And because every student learns different understands different concepts in different ways, the students must be taught as many concepts as possible. Often times students are looking for the simplest way to get the answer. With this in mind students will often come up with their own strategies for arriving at the correct solution. They must be taught that they may not always come up with the correct solution using the strategies they create on their own.
Chapter 13 was about using computational estimations. The concept of rounding is the most widely used strategy for estimation. It is always easier to estimate and use mental math when using a familiar whole number. I know that I use rounding very often in my daily life when trying to figure different information out. I especially use rounding when I am driving to know how long it will take me to get from place to place and how much gas I will need.
In response to Kymberly R... It seems as though everything seems to be taught at earlier ages now than it was when I was in school. The students are expected to retain so much more information and it surprises me how well they do with all of the information they are given on a daily basis.
Reading 3 chapters for this week, there was a lot of information to take in! After reading everything I have realized how little I truly know about Mathematics and everything it entails. We recently began using an intervention program at our school titled “Camelot Learning- Math Intervention Curriculum.” Numerous of the activities and strategies explained in our text are directly related to the Camelot Math interventions I am now using with my students. I can say one thing… I am learning many of the strategies right along with the students. There are so many ways in which to perform Math problems, as shown in our text! I am grateful to have this text especially when it comes time to teach Math in the classroom. There are so many strategies in this book that my brain cannot even wrap around them! I really like the idea of letting students “invent strategies.” When I am working with my students they often come up with ways in which to complete the problems that I have to really study their method to understand what they are doing! It truly is amazing to see what student’s minds can come up with when they are allowed to address their own learning strategies.
In response to Kymberly- I also enjoyed reading each of these chapters. There was so much great information to help me when I am in the classroom teaching. I have always used the most basic strategies when it comes to completing Math problems. These chapters had me thinking I have no idea what I am doing! There were so many concepts that I had to reread and write out the problems myself to figure out how the book even explained to do them! It is amazing to me that the book stresses the importance of letting students use “student-invented” strategies. When I am working with my students at school, they do this quite often and many times they throw me for a loop! I have to have them explain their strategy to me numerous times just so I can understand what they have done! Most of the time they have done a great job of figuring out how to complete the problem but many times it seems as though they took the longest way around to get there!
The mind of an elementary school student is open to all kinds of things. They will invent things that will work for them, if allowed to. As adults we do not understand they way they do it because our minds have closed themselves off to things different from what they know. As teachers we need to understand that our students will come up with all kinds of different ways to get it done. Our job is to understand it before we say anything about it. To many teachers say don't do it like that without first understanding what they did.
I am a collection of habits, I like to do the same thing in the same way again and again; which may be part of why I leaned math in the traditional way. As I finished reading these chapters I realized that for a person like me; they are best in small doses.
I understand that everyone is not like me, good thing to because one of me is boring enough.
These chapters are useful, they reminded me that I need to carefully make sure that I understand that my students may not learn the way I do, may not get it done the way I do.
My biggest problem with these chapters is when they discuss the traditional method, or at least claim they are going to discuss it. I say claim to because I am not sure they actually did and in fact think that they did not.
If that is the traditional method then in the 18 to 20 years since I finished the sixth grade an entire traditional method has come and is ready to go. I say that because they did not even spend enough time on how I learned it for me to say they covered it in passing.
That is my biggest problem with the book, its total disrespect for the teaching of math in a way that worked for me. This book is quite sure that no student can, ever has, or ever will learn math the way I learned it; and that is a problem for me.
Each week after reading a chapter in our math text, I become more confident in my abilities to teach math. When I first started this class in August, my biggest fear as a teacher was teaching math. Since I have struggled in math all of my life, how in the world was I suppose to teach it! But our text is so hands on and that is exactly what I need. Chapter 11 helped us to learn to teach place value, which is one of the hardest things for students to understand. The activities in the chapter cover a range of ages and abilities which will be very helpful if I teach in an LD classroom. The etools by Pearson Scott Foresman is a website that I would love to use as an enrichment and study tool for my students. Chapter 12 is about developing strategies for whole-number computation. The chapter begins with the lowest level with children using manipulatives and direct modeling and ends with multiple factor division and multiplication. I actually learned new ways to do math in this chapter that I had not learned before. I come from the old math (which means it has been 26 years since I was in 6th grade) and we were not given all of these different options to find solutions. It was the teachers way or it was wrong. I am glad to know that educator finally figured out that every student does not learn the same way and that does not make them wrong. I feel I would have been a much more successful math student in this day and time period. Chapter 13 discusses another part of math that seems to be difficult for many students, estimation. I did not understand the cluster problems for estimation on page 244. I looked at it several times and still do not see what they are doing. I did like the suggestion on page 249 on how to test computational estimation. Doing the Guess boxes on the overhead is a great idea. I have helped students with math benchmarks and when it comes to estimation, if they don't understand it, they just work the problem out. So how do you really know if they understand it or not. As always, I have a bundle of activities to add to my toolbox!
Chapter 11 covered Developing Whole Number Place Value Concepts in the classroom. I found this chapter very interesting because I find it difficult sometimes to teach place value to young students. I just recently observed a lesson over place value and the students had a hard time grasping the concept. I found the examples to be very helpful in preparing lessons in the future. Chapter 12 covered Developing for Whole Number Computation. The section that I found most interesting was on Student Invented Strategies. I enjoyed reading this section because it talked about expanding on methods that have already been introduced. I found a lot of useful information in the text that I can use to help me and my students in the future. Chapter 13 covered Using Computational Estimation with Whole Numbers. I am surprised to say that I had either forgotten about or never knew the different types of estimation. Measurement estimation, quantity estimation and computational estimation. One statement that I found useful is that students often confuse estimation with guessing. I think that it is important to make sure the students know what the difference is. In response to: Jeremiah I am the same way. Once I find a successful way to do something I tend to stick with it. This chapter reminded me that there are ways to solve problems and that sometimes it is helpful to branch out.
I too love our textbook. It will be a very valuable resource for me as I begin my career in teaching. I am also learning how to do math in different ways as my students learn. Our school teaches math through hands-on and investigations. They rarely do any worksheets, so this book comes in handy when needing activities to help teach a concept. Good luck in your career!
Chapter 11~ Developing Whole-Number Place-Value Concepts gave me a lot to think about. Although it went over a lot of basic knowledge, it also pointed out the importance of the terminology of using tens and groups of tens. I am realizing that I need the visuals in the text to help me to overcome my traditional views of problem solving. I am really happy that the way that mathematics is being taught is changing~ I think that is so important. This chapter really showed the use of base-ten blocks and how to use them.
Chapter 12: Even though math was really difficult for me and I would have benefitted from different ways of doing problems, I cling tightly to the methods I have learned. It was a stretch for me to try to solve problems in different ways during the adobe connects when the on campus students were finding as many ways to solve problems as they could. It is evident to me that the use of manipulatives is so instrumental to making math make sense. I even see that in the 6th grade classroom I am doing my internship in. The students have no hesitation in drawing visual aids on white boards, like fraction circles or base-ten blocks to illustrate the problem and provide themselves with a visual. Last week I was in a 2nd/3rd grade classroom in which the students were taught only one way to solve problems. Because of what I am learning here and what I have seen in internship, I was really surprised. The class did a story problem that was an addition problem. When they completed it, I first asked someone to tell me what their answer was and then I asked how they got the answer. The student told me how they got the answer, and so I asked, “did anyone solve this in a different way?” And then I asked, “Is there another way to solve this problem?” and the class unanimously answered “no.” Chapter 13: Estimation. I loved this chapter. This is relatively new to me. Of course, we all estimate. But as a valid way to do math, it is new. I liked the problems in the chapter and how we worked on them “in class” (adobe connect) and that we were not supposed to do the work, but estimate. The text gave a lot of different strategies for estimating. In the class I am in for internship, I was exposed to it as a way to check the answers. It is a test taking strategy for them as well, checking the answer by rounding down and then rounding up to get a low and high estimation. They did this when multiplying a problem such as .28 * 1.3. Round down and 0 * 1 is 0 and round up and 1 * 2 = 2, so the answer has to be between 0 and 2. They had three possible answers: .364, 3.64 and 36.4. So they knew the answer was .364. I would not have thought of this as a test taking strategy or a way to check answers before seeing it in action. I think I am really fortunate this semester because I am truly in a classroom that implements learning through problem solving. This makes what we read and do in class so much more real and applicable when I see it being used and I see students grasp onto it! I also liked the cluster problems in chapter 13. I am not sure why I liked them. I think it is because the estimations make sense to me. I feel like we are learning ways to do math that make more sense to me!
Angela S.~ I know how you feel about fearing teaching math and how all that we are learning is helping you to feel more and more equipped. That is exactly how I feel. I knew I would do my best at teaching math, but now I feel like I am being given solid tools for teaching math. I even find myself getting excited about it which is completely new for me, I have always hated math!
Chapter 11 – Whole numbers and place values are something that my mentor class has been dealing with all semester it seems like. Early in the chapter it mentions that we learn our numbers at a very early age, but we don’t learn the understanding of those number or place values until much later. That is something that my students seem to be struggling with a little bit in 4th grade. They have a hard time understanding that 48 is actually 4 tens (or 40) and 8 ones. They are getting better but early on they really had a hard time. This chapter continued to hit home for him as it discussed the models for place value and grouping. The students in my class use a lot of the snap cubes and have recently started using the base ten blocks. Dr. Stramel used the ten-frame cards in class, which was the first time I had seen that model. When you do understand the idea of place-value and the number sense behind it, it sometimes is hard to think back to the time when you did not know it. I feel that this chapter does a great job of reminding us what that was like and how we can relate to our students who are just learning.
Chapter 12 – This Chapter talks about strategies for Whole-Number computation. Again, I have been in 4th grade math and this topic really struck a chord with me. It has been so interesting to listen to some of the students in my class talk through the way they solve their problems. Not all of the ways are correct but it is neat to see those gears moving. I really like how Dr. Stramel puts it in her class, it really doesn’t matter how a student gets the answer so long as they can explain how they got there. I agree with this, I don’t really believe that there is just one way to solve problems. It is very interesting to see and read about the examples that were shown and discussed in this chapter. Many times I have asked student why or how and every time it seem I am in awe of their thought process – I love it everytime.
Chapter 13 Computational Estimation with Whole numbers is a concept that doesn’t get enough credit in our text books and curriculum but is very important none the less. Estimation is something I think can be a difficult topic to learn if you haven’t learned your place-values well. If you don’t have a firm grasp on the place-values, learning estimation can really be a struggle, at least with my experience. I do like the idea of using the real life word problems. In my mentor 4th grade classroom they really spent a lot of time on the estimation chapters. It was interesting to read on the strategies after observing the lessons in the classroom. Students seem to “get it” or really struggle when it comes to estimation. With front-end it sometimes seems too easy – you look at the leading number and ignore the rest – what’s the catch! I think that the rounding makes more sense to the students, but again, they really do have to know their place-values.
@ Kristie C – I love that your intern classroom seems to make learning the place-values fun and important. I love the idea of grouping the straws. Being able to understand what is going on and gaining that number sense is SO important. I also think that many times we forget about the value or the presence of zero, so that is neat that your teacher is making sure to include that in the lessons as well. The pumpkin seed idea was really great! I think it is good to keep things fun for kids and place values should not be any different. I also think the 9+ shortcut is a great idea to share with everyone. I love that idea of adding 10 and then taking off 1. Sounds like you are in a great situation with your intern class and your subbing! Keep the good ideas coming.
Chapter 11, 12, and 13 were all fantastic and informational chapters. I really liked how chapter 11 started out talking about place value! It is so important for students to know and understand place value. I also love how this chapter mentioned the hundreds chart. In the classroom I am interning in the hundreds chart is used daily. It is interesting to note when students have it memorized. I was not a fan of the hundreds chart at first, mostly because I did not understand how students used it. But seeing it used is awesome and some students really benefit from the use of the hundreds chart. In chapter 12 I loved all the different strategies like mental math. There are so many different strategies that help different students. I love mental math and it is so interesting to see how different people add and subtract mentally. Chapter 13 mentioned the hundreds chart again. I like how this gave me more insight. It is like a pattern and patterns helps students so much! Awesome!
@Megan B Zero the Hero sounds really neat!
@ Kristi P I agree that these chapter were very informative. Estimation is something that is very interesting. It is very interesting watching students do ball park estimating. Some kids really struggle with this process.
Chapter 11 focuses on place value. The 2nd grade class I intern in has place value pockets. The teacher gives them a number and they have to put their number cards in correctly to show the number she is asking for. They also use it for rounding numbers. She has them put the original number and then they talk about what two numbers it is between. They then have to put in the correct number it would be rounded to. They have pretty much only worked on ones and tens so far. They have done a few hundreds, but they are still having a little problem with ones and tens. Chapter 12 talks about whole-number computation. As long as the student is doing the work and coming out with the right answer, they should be able to do the problems their own way. Teachers have a real problem making it their way only. My son is in the 8th grade and his teacher marks answers wrong if it is the correct answer and all his work shows right, but it is not done her way. She has to understand there is more than one way to do some problems. The teacher I am observing has a huge thing for doubles plus one or minus one. The students really seem to understand that concept when they are working with doubles of a number. Chapter 13 is about estimation of whole numbers. There are three ways to do estimation dn this chapter focused on talking about all three. The students I intern with love to do estimation. They have trouble sometimes about whether they estimate up or down. The teacher gave a chart of a mountain climber and he goes down for number 0 through 4 and up for numbers 5 through 9. They really seem to catch on to it this way.
In response to Lindsay H--- The classroom I am in is also a huge 100 chart user. They use it all the time. I have taken so many notes on how to use it and what it can do for students that are struggling with place values and other things. They have done patterns to see the difference in how numbers go up by a certain number. They were able to see when counting by 5s that only two rows of numbers would be used and not to even look at the other rows. It helped a lot of them struggling.
These were great chapters for me this past couple of weeks because my lesson I taught in my observation class was dealing with place value and estimation. In chapter eleven I loved the section about models for place value. Anytime manipulatives can be used I think teachers should take full advantage of that. I like how it took a group of something like pop cubes to make that double-digit number represent just one entity to show that a number in the tens place is both a single and double digit number. I used this representation when I asked my students to break apart a large number like 415. I had them break it apart and show me what each number truly represented in its place value. So the one in 415 was a single stack of 10. This helped then recognize that even though it was a one since it was in the tens place it was a multiple of 10.
Chapter twelve discussed developing strategies for whole-number computation. I didn’t have much time to teach my lesson but in review I had the students work through problems in a group. I would ask one student to show me how they achieved the answer they did and then I would ask if anyone did it differently. This allowed me to see many student-invented strategies. The text stresses the importance of letting students explore their own strategies instead of just making them do it one strict way. It’s so amazing to see what students come up with when they’re solving a problem. It’s even more amazing to listen to them explain their procedures to their piers. One problem I gave the students was 800 X 4. One student showed his piers that he multiplied 8X2 to get 16 then added 16 to 16 to achieve 32 and then just brought down the two zeros because, as he said, the zeros always win. Some of this might have seemed like more work to other students but it was interesting to see how each and everyone thought about each problem so differently.
Chapter thirteen discussed the focus of my lesson, which was estimation. I really liked the cluster problem examples because they related back to invented strategies. With my estimation lesson I did quite a few estimation activities with the students but one of them was having them estimate the amount of skittles in a jar. I gave them a visual aid by showing them what a group of 100 skittles looked like first. When I asked for the students estimations I also had them explain how each one of them came to their conclusions. One student said she recalled what one hundred skittles looked, just one layer on the bottom. She then counted the layers she saw in the full jar and multiplied that by 100 to achieve her estimation. There were many ways to figure out a close estimation and I really enjoyed being able to listen to each student’s method. My favorite part was that they got to learn from one another and they truly did. Students were asking one another “How does that work” and “Why did you do it this way” and then were having “Ah Ha!” moments all over.
These chapters helped me implement my lesson in a way that students could learn from one another. It was a very eye opening experience for me.
Thank you for sharing the place value pockets idea. That sounds like a great way to teach place value to students and to help with rounding also. I know students can greatly struggle with place value so this activity sounds like one that can help them by being practiced all year long. I also completely agree with what you said about allowing students to work through problems in their own way, as long as they achieve the correct answer. I think that fact has been stressed to us all year but it’s important for us to recognize that many teachers like the one in your example, still view math as their way or the highway. I think that’s one strength our generation will bring to the table. We will be able to allot our students more freedom in mathematics and possibly influence our professional community to do the same. Good post!
Chapter 11: Chapter of the text book Elementary and Middle School Mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed “a complete understanding of place value, including the extension to decimal numeration, develops across the elementary and middle grades” (Van de Walle et al., 2010, p. 187). Place value can be difficult for some students to understand but it is critical to understanding mathematics. Van de Walle states in the textbook that “place-value understanding requires an integration of new and difficult-to-construct concepts of grouping by tens with procedural knowledge of groups are recorded in our place-value scheme, how numbers are written, and how they are spoken” (Van de Walle et al., 2010, p. 188). It seems to be difficult for students at first to group by tens but then they start to see how different numbers will group together and the numbers relationship with each other. A piece of information that I learned from this text was how the text book mentions to go beyond 1000 cubes so students can see what the bigger numbers look like as well. This can be fun for students to see because they will start to understand the numbers that they will be experiencing in the future. I also liked how the book mentioned using the word “and” in numbers. I admit I do use the word “and” incorrectly at times A piece of information that made me look at my own experiences was when the textbook discuss the hundreds chart on page 200. I remember when I was younger the hundreds chart was so important to me and I used this tool all the time. I think that this is like a comforting thing for students to use if they need extra help. I know I would use this tool if I for any reason was unsure of the problem. Chapter 12: Chapter twelve of the text book Elementary and middle school mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed different ways that people figure out mathematical whole-number problems. We need to teach students that there are different strategies that will work for different situations and they do not have to stick to a certain way to do something. When students have a range of strategies to solve problem then it becomes less difficult to solve that particular problem. A piece of information that I learned from this text was how it had examples using the number line. I would do a lot of these problems the same way but I never thought of using the number line before. The number line can be important because it relates the numbers to each other. A piece of information that made me look at my own experiences was the section on “direct modeling” (page 214). According to the textbook direct modeling is “the use of manipultives or drawings along with counting to represent directly the meaning of an operation or story problem” (Van de Walle et al., 2010, p. 214). This is a strategy that was so important to me all through school because I am a visual learner. to be continued
continued... Chapter 13: Chapter thirteen of the text book Elementary and middle school mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed that “computational estimation skills round out full development of flexible and fluent thinking with whole numbers” (Van de Walle et al., 2010, p. 240). Estimating can be difficult for some students because there is not exact answer and the answer will variety. Students are usually taught that they have to have an exact answer but now they are asking not to be perfectly correct. A piece of information that I learned from this text was the over and under approach on page 243 of the text book . This something that I never used when I was in school but will be great for students. This way students can see the starting off point of estimating. A piece of information that made me look at my own experiences was when the book mentioned to use a “nice number” on page 246 of the text. This is something my teachers telling me when I was in school. I had to pick a number that I felt comfortable using and that is how I knew my estimation was on track because estimating should be easier that really doing the proble. References: Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Chapters 11, 12, and 13 discuss how to help students develop math concepts and all give many wonderful ideas for activities. Chapter 11 discusses the concept of basic ideas and place value. Throughout the text it was emphasized that groupings needed to have meaning for students. In order for them to develop the concept fully, they need to have a meaning to group and this is accomplished through starting with ones, giving them many opportunities to group, and then moving on to 10’s. I also liked the section that discussed the “strangeness of ones, tens, and hundreds.” It does sound strange, and must sound especially strange to say “ten ones make one ten.” It helped me understand more fully why place value can be difficult for children. I also appreciated all the different activities that the text provided that can be done with a hundreds chart. I haven’t spent much time in the lower grades, so this is good information for me to have if I ever teach in one of the lower grades. Chapter 12 discusses strategies for whole umber computation. This chapter was very interesting to me because it gave many wonderful activities for adding, subtracting, multiplying and dividing that were so different from how I was taught. I also liked the section on invented strategies. Again, it is very different from how I was taught but I think that students can better develop an understanding of computation through the use of invented strategies as long as they are mathematically sound. Chapter 13 discussed estimation. I think in the past I have taken the fact that I know how to estimate for granted, and didn’t fully realize the importance of this skill, but after reading this chapter I feel I better appreciate it as being a key skill students need. I really enjoyed the over/under activity we did in class and can see myself using this in my class someday. Overall, these chapters gave me many great activities as well as a much better understanding of the types of activities that can be used to help students develop math concepts.
I also liked the over/under activity when I say it in the text and also when we played it in class. I think this is a great way to give students practical examples of when they would use estimation as well as further practice in estimating.
Chapter 11 discussed whole-number and place-value concepts and these can sometimes be difficult for students to understand. Teaching students to count by ones, tens, and hundreds is so important and are basic skills that they will continue to use as they progress through the upper grades. I believe that it’s never too early to start teaching students about place value, even if it’s only by using different colored sticks to represent the ones, tens, and hundreds. They do this in my kindergarten internship classroom when they discuss how many days they have been in school. They have a chart that shows the number of days and these are represented by the appropriate sticks. I liked how the text mentioned that the term “seven ones” can be very confusing to students and this is something that we as adults probably take for granted since we already understand the concept of place-value. Using many teaching techniques and allowing the students to use a variety of manipulatives will help make these concepts easier to understand. Using ten frames and having the students draw pictures to represent problems are other ways they can get more comfortable with base ten.
There were tons of ways to compute whole-numbers as well as student-invented strategies discussed in Chapter 12. We were taught how to do most computations the traditional ways and although this is not wrong, I think we definitely missed out on many learning opportunities. Students should be able to solve problems however feels comfortable to them and they shouldn’t be discouraged from this simply because it’s not the method that the teacher uses. Dr. Stramel mentioned that sometimes teacher may be afraid to let students use their own strategies because they weren’t taught like that and therefore, might find it difficult to answer any questions that the student has about this strategy. I think that teachers should embrace this and use it as an opportunity to learn new strategies from the students. Since I was taught using the traditional algorithms, I found some of the strategies presented in the text to be more work or more difficult. Although it’s tough to learn how to do things new ways after you already have the method down, we could all benefit from learning how to do things in other non-traditional ways. I enjoyed trying to come up with alternative ways to solve the problems in class.
In Chapter 13, there were many activities presented to help students practice estimation. I’m glad that Dr. Stramel made sure that we knew that estimating is not the same as guessing. The more we estimate over time the better we will get. The text discussed rounding and clustering as ways to estimate. There are many real world situations where estimation can come in handy such as guessing how much food to cook for a family dinner or estimating how much money your purchase at the grocery store will cost. It’s important for students to have a lot of practice with estimation while using a variety of techniques. Although some groups of students may end up with different answers after estimating the answer to a certain problem, they should explain how they reached the answer. It was cool to see the ways that all of the students in our class estimated the answers to the problems and they used some methods that I didn’t even think of, such as counting by 25.
Chapter 11 talked about whole number place value. It mentioned that students learn as early as kindergarten how to count to 100. Counting is great, but as a teacher you need to be able to teach other ways to count than just by ones. It is good for students to learn concepts like grouping by twos, fives, or tens. Chapter 12 talked about whole number computation. This chapter talked a lot about student invented strategies, we talked a little about this in class too. I think these are great because they are ways that students came up with. As a teacher, we want the students to learn the way we are teaching it, but if it is easier for them another way, why not let that student use the way that is easiest. As long as it works and they can explain why it works they should be able to use it. Chapter 13 talked about estimation. It told us not to focus on an answer but on methods of how to find the estimation. Teach rounding or context to help with estimating. Students sometimes focus to much on finding the answer and really need to focus on the method and way of finding the way to the answer.
In response to Meghan B: Zero the Hero sounds awesome and I bet the students love it. I’m glad to see that your internship teacher is making a big deal about base ten. I like that you mentioned how it should be acceptable to students to solve problems in a way that makes sense to them, as long as they can explain how the process of how they did it. I agree that the grocery store is a great place for estimation.
I like how you talked about nice numbers which are numbers that the student feels comfortable with. I think this is a great way to teach and help students understand. Some students may be ready for three digit numbers and some may not, but at the same time they can do different numbers and still work on their estimating skills. As long as they are doing the work correctly and finding the right answer why not let them use a number they are comfortable with.
I didn’t realize the plethora of ways there are to use base ten manipulatives. I don’t remember ever seeing base ten blocks or using many manipulatives when I was in grade school. I am grateful for the opportunity to learn about different ways to teach children this oh so important skill. The bundling coffee stirrers reminded me of a strategy I have seen our first grade teacher use. Every morning she holds a math meeting in which all the children sit on the floor near the math bulletin board. They count the number of days they have been in school using straws. Every time they get ten straws they bundle them with a rubber band and place that bundle in a tens cup. When they get ten of the ten bundles, they bundle those together and place it in the hundreds cup. I was surprised to read in chapter 12 that you shouldn’t begin teaching traditional algorithms first, but rather invented strategies should be first. For some reason I assumed that you should teach the traditional ways first and let the students go from there. It makes sense though that they might feel there is only one “right” way if you teach traditional first. Lately as we have been discussing invented strategies in class a lot, I have been wondering how to effectively show students what I or other students see so automatically. The diagrams of each strategy provided in the examples in chapter 12 are the answer. I am a little disappointed with myself that I did not think of that on my own. It’s a good thing I have this book! Chapter 13 is all about teaching estimation. I really like the calculator range game activities because they give the students practice estimating, and the use of the calculator makes them self-checking. The students know right away whether or not they made a reasonable estimation.
Jordan O., I completely agree with you that students should be able to use strategies that make sense to them as long as they work and can be explained. Sometimes the traditional ways just don’t make sense to some people. If we required everyone to solve problems the exact same way, we would be leaving many students behind who are fully capable of solving the problems too, just in different ways.
Chapter 11 was about whole number and place value concepts. We covered many different strategies in my internship dealing with place value. I thought it was interesting that this chapter actually had some of the same example of activities that we used in my internship classroom. One of the examples the chapter mentioned was; 7 tens and 3 ones, 73 all together. Chapter 12 was about whole number computation. there were many examples of student invented strategies. I found all of the different strategies very interesting. Very few of them looked familiar to me. I'm not sure if it's because I was never taught these strategies, or I have been doing the traditional strategies for so long that it just became second nature to me. I did find the information very helpful and I will definitely keep these strategies in mind for the future. Chapter 13 was about using computational estimation with whole numbers. I liked the strategies mentioned where they tell students to round the problem to the nearest ten and then estimate the answer from there. I feel this would be greatly beneficial for students to use. I know there are quite a few students in my internship that use this strategy.
I was also unaware of all of the manipulatives that can be used for base ten problems. I don't remember using hardly any of these strategies. I did find them to be very helpful and I will definitely be using them in my classroom.
Chapter 11 was all about developing place value knowledge. As we have talked about in class, place value and base ten are extremely important concepts. Every student needs to understand these ideas in order to understand higher-level concepts. After reading the section, “The Strangeness of Ones, Tens, and Hundreds,” I completely understand why this concept is so hard for children. It seems so simple, but when I read this section and thought about it, it is very confusing. There are a lot of great activity ideas for helping students learn place value and base ten in this chapter. One idea I really liked from the book was to use base-ten language when first introducing oral names of numbers. Doing this will help students understand what the standard number words really represent.
Chapter 12 covered another important topic. It was about strategies used for whole-number computation. This is another topic we have covered a lot in class. When we are given a problem and asked to come up with different ways to arrive at the answer. In class, we always come up with several ways to complete one computation, and often times one group comes up with an idea or two that others did not. This just goes to show that we all think a little differently, and some strategies make more sense than others to different people. This is why it is important to allow time for what the book refers to as student-invented strategies. We need to give students the opportunity to complete some higher-order thinking and come up with methods for completing computations that make sense to them. Once students have been allowed to do this, then we can introduce them to the traditional algorithms.
Chapter 13 covers using estimation to complete computations. This is a strategy that I do not remember using a lot of in school. Therefore, it is not something that I am completely comfortable with. However, I do see why estimation is an important skill to have. In real-life situations we don’t always have time to stop and do exact computations, estimation is much quicker. The 3rd grade class I am currently interning in did a short unit on estimation to solve multi-digit addition and subtraction problems. Many of the students struggled with this concept. I found several great ideas and activities to suggest for my students to use. One activity I thought was really good and the students would enjoy is the Box Math activity.
I like your example of the WalMart scenario to explain why we estimate to children. If we provide students real life examples and scenarios to work through when learning estimation, rather than just numbers, they will understand its use.
Jennifer Pen Reply to Shannon, Great post! I agree with you. Using popcicle sticks is a great way to show students that these numbers can be separated into groups of different numbers. We do this with straws when I go into some classrooms. We will count and group the days they have been in school. I liked also how you mentioned that some students will do extra work to get an answer but it is easier for them to do it that way. I would always do that do. Even if a my way may take longer it is easier for me and I would rather problems take longer and be easier. Having these different strategies help students learn from each other the different way they may do things.
Using Algorithms can be fun to me, but very complex. Again, I think this goes back to the idea that when I/we were in school, we didn't have near as many options-it was just standard problems/traditional problems. Nowadays, students have more and more options, which is great for their variety of successful ways to complete a problem. As long as the student is getting the correct answer, then it's okay. Some algorithms, I feel take longer than in your head, such as the using the counting blocks and taking away for each value. A lot of times, some students may not be able to do this in their head, but I feel for me as a student it would been more difficult and overwhelming. On the other hand, I do feel that array is fun and informative. I think array gives the students a chance to visually see and display the numbers being added together, or multiplied together. Using manipulatives I feel ALWAYS helps. Even for me as an adult, I sometimes have to stop and draw out pictures. I want to use these resources within my future classroom.
I too was unaware of all the manipulatives! It's amazing how far mathematics has come and how far our future students can become because of the resources. They are visually stimulating, as well as hands-on. I feel all subjects are better presented while incorporating hands-on activities.
Using manipulatives to group and count by ones is a great way for children to learn this concept. They can count the best way for them and still arrive at the correct answer. I think that teaching students to count by 10 is be the first objective. The counting in groups activity would be a great exercise for children to learn how to count by 10 as well as the groups of 10 activity. Having the teacher model how to do the problems is a way for the students to see what to do. Once the students get the hang of counting by 10’s then they can invent their own strategy of what works best for them. One of the most important things that I took from chapter 12 is to go beyond teaching traditional algorithms, but they will happen. Lastly, chapter 13 talks about estimating with whole numbers. To teach estimation use real examples, the language of estimation and context. Focus on methods and not the correct answers when dealing with estimating.
Algorithms can be fun, but mixing it up of how you teach them makes it interesting and allows the students to get an idea that there is not a set way of figuring out problems. I agree that when I was in elementary school there were not many options or manipulatives to use. I want to make sure to allow all the resources I can in my classroom when it comes to math so students can see all the possibilities.
Chapter 11 was about place value. I can remember in school somewhat struggling in this area and I like the many examples the book shows to help me get a better understanding. It also helps in class discussing all of the information and using the base ten blocks. I have a much better understanding now. Chapter 12 was over whole number computation. I thought this chapter was very informative and gave excellent examples in the book. There are so many strategies on how you can do things and we have been learning this in class. This has been very educational for me and I can see a growth in myself in this area. Chapter 13 was about estimating and was my favorite. I loved estimating in school and it brought back some memories in class the other day when we were doing different activities. There are so many ways we can estimate and it can even get confusing as it did even when we were discussing in class as a group. I think overall estimating is important because we use it so often in our everyday lives and don't even realize it. We estimate miles we may be traveling, when buying items, telling time, etc...I really liked all of these chapters and thought they were all very informative.
I agree with you that it is good that children nowadays have the variety of options to help them figure out what works for them! I can remember always having to solve problems one way and one way only. By doing that you are only making that child regress, I believe. If they can do something differently that gives them the correct answer and positive learning then by all means let them! Good post!
In chapter 11 it talks about place value and how hard it is for children to understand it. I have seen children be very confused by this. When there is a number like 154 it is hard for them to grasp that 54 is 10 5's even though it is included in a number that is in the hundreds. One thing the book said in this chapter was to make sure that children do not say the word and when they say numbers, this is something that is still hard for me to do as I have always said and when saying numbers.
Chapter 12 discusses the many different ways that students might use to solve math problems. I like the idea of the place value mats and I think this would be a great way to get students acclimated to adding or subtracting and keeping numbers in their place. That is something that I see in my mentor class quite a bit. Students are getting problems wrong because they line up the problem wrong and get lost in trying to keep everything lined up write. If a teacher were to use the place mats to help the students keep everything in line when they move to paper they might understand better the concept of keeping everything lined up might be easier.
Chapter 13 is about estimation & I have to admit this has not always been my strong suit. I like to have a cut and dry answer, either it is or isn't so I liked this chapter because it will help me to better understand how to teach the concept of estimation. I like the over or under idea and think it would be a great game to play with the students.
I am the opposite of you, I do not like estimation at all, and when you say we use it in our everyday lives I agree. I will estimate but then I find myself working the numbers out to find the exact number I am looking for. I will have to work on this estimation skill to be able to teach it well :).
Katie Coulter Chapters 11,12,13 This past week’s assignment was a lot to take in. Not only was there a lot to read but the information was very important. I felt lost and overwhelmed at times. Class videos definitely helped me out as we progress through each chapter. But thinking outside the box is hard. That is why people who can think so outside and creative get paid way more than the rest of us! It was good to read about all the different strategies of presentation the book brought out and even what we did in class, not being able to use a traditional form of simple multiplication. What these chapters talk about are some very frustrating concepts for grade school children to grasp. I remember during an observation of mine trying to help my teacher reach her students with place value. They were totally lost in this and it was hard even using the base ten concept for them to grasp the amount of the blocks but then seeing it on the board in a value was like to polar opposites. Chapter 12 and 13 gets heavy as we move on to really bringing in other strategies to teach basic algorithm and estimating. I think of myself as more of a traditional type in terms of introducing a new term. I might use some newer technologies or manipulatives but other than that I think more basic and general. This could be a challenge for me. The information again in this chapter was great. There were so many unique methods brought to light for me. I am still kind of overwhelmed at the thought of using something that I haven’t mastered yet. I guess that is why they say you learn something new every day. Looks like grade school math is my new learned concept for the year!
In Response to Dina,
I have seen several post that mention how difficult place value was for them or students they have observed. I don’t remember struggling with this but that doesn’t mean I didn’t, I just don’t remember! As an adult we look at this and get a since of frustration I think when a concept like this is not managed by students. You think it’s easy and makes perfect since but for them it’s new and scary looking so many fight you on the ability to understand instead of just listening. Chapter 11 will sure be a nice reflection to have some day when we stand in front of 20 kids trying to explain place value to them!
Tessa W: Chapter 11 & 12: After reading this chapter, I feel like all of the way I understand numbers is a lot different than everyone else. Which really means that in the end, ALL of my students will have a different way to view numbers. I will have to learn to work with each one of the and accept that each of them is correct as long as the right answer is reached. Now the concepts mentioned in this chapter seem easy to me but I know when I was younger I struggled trying to figure out the right way to understand them. Each person will have a different way to learn and understand different concepts. The best way to learn math is to practice the way you best understand it. Chapter 13: I was reading about estimation and was reminded of how little I thought I used it. When working during a math class I don't usually think of estimating directly but then looking at how I relate math to life I use a lot of "approximately or almost" words. I really like the concept of using tens and hundreds to solve problems. I use grouping in these two areas as well as others when doing most kinds of math. This is one way that I understand and that I can relate to so very well. Grouping is a great way to connect numbers together and do math fast. Which at times is very necessary.
In response to Katie C: I agree, there was a lot of information, but I guess it makes since seeing as there was 3 chapters put together. I also understand how you would want to stick to the basics, it is important to know what you are teaching and the basics are a great place to start. I also know that it is sometimes good to try new things and gain new experiences. Hopefully this book will be able to help you a lot through your first years of teaching!
Chapter 11 is especially interesting to me because I am teaching a 5th grader place value. Using the Groupable Models explained on page 191 is something that I am using now. One of the ways I used the stackable cubes is through a story. I told her she was a construction company and that I was a contractor. I told her that I had a certain number of apartments that I wanted joined together in high rise buildings. The problem came when I went to get a building permit. The city told me I could only stack 10 apartments. Well, I told my student that I did not want any partial high rises. If she could not build a ten story building I wanted the remaining apartments left on the ground level. I then went to her and told her I had a bunch of apartments and wanted as many high rise buildings built as possible. If she went over ten, the city came in and tore it down for violating city laws. She was then to tell me how many 10's buildings I had and how many one's apartments I had.
Jena Simms You mentioned that you had a hard time with estimating and learning the concept. I, too, don't remember being taught to estimate until later grades (if ever) but I know that in real life I use estimation quite a bit. My bills for instance, are not always exact, so I will estimate each month. We estimate when creating a budget. we estimate every time we want to know about how much we need or are spending when we do not have a calculator. i.e. cabbage is 25 cents, bread, 1.39 that's about 2.00 with tax. Kids do not know why they need to know this and any time we can tell them why, when, or where they may be more interesting in knowing how. :)
Chapter 11-- I never realized how important the hundreds chart is to the development of place-value concepts until seeing the students in my internship classroom using it to count by 1s, 2s, 5s, and 10s as high as 2,000. I liked the ideas found in the section about the hundreds chart that involved the chart with the clear pockets to create different activities for patterns and recognizing order mistakes. I hope I can make using and learning with the hundreds chart fun and exciting for my students.
Chapter 12-- Students often create their own techniques to solve math problems. Some students may not easily understand the techniques their teacher has demonstrated and sharing the techniques used by their classmates may provide them with a technique to solving equations that works for them. As adults we grow fond of the ways that have always worked for us and we need to be open to alternative strategies to assist in solving equations.
Chapter 13--Estimation can be an invaluable skill to have in different situations. I have recently used estimation to air up a tire with no pressure gauge. There are times when the instruments we need to measure, calculate, or write out a problem and we have to get as close as we can to the answer as possible by mentally estimating the answer. I don't remember doing estimation in grade school.
In response to Lindsy S.
What I really liked about CH 12 is that it discussed and presented different ways to teach different strategies to work out problems. I was taught one way and only that way was allowed. When I showed my own way to work out problems, getting the same answer as the teacher did, I would not receive credit. I like that this chapter encourages students' individuality when it comes to solving strategies. Encourage, don't discourage!
Chapter 11 discusses place value - something that has been very difficult for my internship students to grasp from day one. For some reason, they just can’t seem to remember that ones are in the “ones place”, tens are in the “tens place”, and hundreds are in the “hundreds place”. This all stems from the fact that they are not really grasping the concept of counting. For instance, they can count to twenty, but many of them still struggle with what happens when they come to 29 or 59, etc. Working with manipulatives does seem to help, but once the manipulatives are taken away, many go back to struggling again. Simple activities like 11.2 in the chapter would really help them to count to ten – and then count by tens. It is the two-digit number names that begin to throw them off (e.g. forty-seven as four tens and seven ones). I LOVE the place value mat shown on page 198! The one with the cups and beans is terrific! “Landmark number” is a term I had never heard, and I think that focusing on these landmark numbers may truly help students to have a reference point. I love the activities that this text provides. I have loved trying so many different approaches to one idea or concept in our methods class, and this book will be instrumental in helping us to do that in our classrooms in the future. Chapter 12 discusses, among many things, student-invented strategies for whole-number computation. I had grown up with teachers telling me that there was “one way” to do things. Our math methods class has really helped to teach the idea that there are MANY ways to do things. It only matters that the method produces correct results. If the student can understand it, explain it, come up with a true statement, and show that the method works in all situations, then the method is fine to use. Most importantly, it helps students to develop true number sense and understand why a solution is what it is. I will say that it would have been VERY difficult for me to embrace this idea in my classroom if I had not met Dr. Stramel and been exposed to the idea that “it is okay” to come up with a different approach. The reality is…I think many of us actually did self-invented strategies when we were younger. We just did them in the margins and erased them once we had the answer so that the teacher wouldn’t see them. I am excited that this chapter deals with multiplication! We have just begun multiplication in my internship class, and the information here will really help. We have already begun by using the same method of representation as shown on page 226 in Figure 12.14. Chapter 13 discusses Estimation – something I have NEVER understood why it has been focused on so much with my children in school. Both daughters have brought home a week’s worth of homework assignments involving estimation, and I have always wondered why it isn’t easier to just teach them how to add, subtract, or measure to be accurate. Through this chapter and our methods class, I do now understand just how much we actually estimate in real world situations, so it is important to address the concept with our students. Sometimes an approximate answer is sufficient as opposed to an exact answer. The three types of estimation – measurement, quantity, and computational – are all something that occur frequently in the real world. I have just taken for granted that I am doing it. I actually hadn’t thought about the fact that “rounding” is a form of estimation, too.
In response to Elizabeth A regarding Chapter 11: I LOVE the method of teaching tens that your internship teacher uses! What a great idea! I, too, do not remember using manipulatives when I was in grade school. This text will be wonderful to help us help our students!
In response to Allison G regarding Chapter 12: I agree that it has been a real eye-opener to find that we often think differently in our class about how to come up with the same ending result. I have enjoyed watching the methods that other students have shown, and it has really helped me to understand the importance of allowing time for student-invented strategies in our own classrooms in the future.
In response to Lindsay S regarding Chapter 13: I took estimation for granted, too. I didn’t even realize I was doing it, so I never really thought about the importance of it. Now that I have read this chapter, I really see how much it is used in real world situations, and I am thankful that I understand that now. I am certain that I will give this concept its due attention when I teach in the future. It truly is VERY important!
Chapter 11 discusses the importance of developing whole-number place-value concepts. Students just starting out in school hold absolutely no concept of the placement of number value. Having subbed in pre-K, I have gotten to see first hand that drill and practice on this begins on the very first day that a child enters a classroom! My intern classroom places straws in a ones place until they reach ten, then they rubber band them together and place them in a tens spot and so on. They also make it a point to talk about the value of zero and on every school that ends in zero they get a special visit from "zero-the-hero". Its a fun way to get the kids interested in place value! Recently, I got the privilege of introducing "hundreds" to the class. We estimated how many pumpkin seeds were in our pumpkin and then counted ten separate cups of ten seeds each and dumped them into one hundreds cup. The kids loved it! I really enjoyed the other ideas and resources the text gave.
ReplyDeleteChapter 12 discussed developing strategies for whole-number computation. Being in kindergarten I haven't got to see whole lot of this during my internship yet. However, I subbed whenever I can and get to see it then. I enjoyed the section on student-invented strategies for addition and subtraction. I personally think it is fine for students to explore other ways in which to solve the problem as long as they are doing the math and figuring it out. One day when I was subbing in 2nd grade i got to introduce doing a +9 shortcut in which you add 10 to the number and then subtract one. Apparently many of the students were struggling with adding nine but after teaching this short cut they seemed to do much better with it! I think that all students really need to be successful with whole-number computation is options. They need to know if they don't understand it one way, that its okay to try to work it another way and figure out what works for them!
Chapter 13 talked about using computational estimation with whole numbers. It told us that there are three times of estimation- measurement (determining measurement without making an exact measurement), quantity (approximating the number of items in a collection), and computational (determining a number that is an approximation of a computation that we cannot or do not wish to determine exactly). It is very important for students to learn estimation and rounding in order to do a quick guess in their head and to be able to check their actual answer.
The concept of whole number place value is being taught at younger and younger ages. I do not remember being taught this concept until about 3rd grade (which was many many years ago). Now the students are immersed into this concept the second they walk into the school doors. I see the teachers beginning to use the same terminology more now which I think enables students to make a connection between grade level learning. The use of base ten blocks or cubes is ideal for teaching this concept in the early stages. The literature connection at the end of the chapter gives some wonderful resources for integrating across curriculum line.
ReplyDeleteChapter 12 is about developing whole number computation sense. I think this starts with number sense. Giving students the tools to understand whole numbers is the beginning of understanding computation. When a student invents a strategy and can explain it to the teacher then this is a way of having the student teach the class a new of computing numbers. Teachers should encourage the invention of new strategies. Some may say, "Whatever works for the student." The teacher should of course give the standard means of computing the answers but when a student comes up with a different way then this should be a praise worthy moment. Again, this chapter has some wonderful resources for integrating literature and technology into math lessons.
Chapter 13 is all about using computational estimation with whole numbers. This is a concept I had a hard time fully understanding when I was a student. I always blamed it on my brain. I just thought my brain did not work that way and could not understand this concept. Now I think it was the way the concept was taught to me. The chapter says that "estimation is a suitable approximation for an exact number." I was never given the reason behind estimating. Why do we estimate? How is estimation used in real life? These are questions I would like to answer for the students I teach. Giving students the reason for doing math is the beginning of students grasping the concept. The suggestions for teaching computational estimation in this chapter are easy to understand and will be useful in the classroom.
Comment for Kristle C:
ReplyDeleteZero the hero is so fun to teach. I learned about this strategy in a K classroom and found that the students really looked forward to another visit from Zero.
The plus 10 strategy for the 9's is a great way to learn both 10's and 9's all in one fell swoop. Good suggestion.
Chapter 13 had the most useful information for me because this is a concept that I want to make sure my students understand and fully grasp. I took away many good strategies and learning lessons from this chapter.
Do you have any epiphanies after the reading or discussions? Any questions or concerns as you prepare to become a teacher of mathematics? Be sure to post one comment AND respond to at least one other person.
ReplyDeleteChapter 11 was very informative, as usual. It is hard for me to remember precisely when or why numerical connections were made. I am certain from the time I was in third grade we never used manipulatives, and I can understand now where most of my frustration in mathematics can be attributed to. I think that early on I never really had a firm understanding of why- things were always just taught to me ‘because that the way it is’, and I guess I had a hard time accepting that. Reading in this chapter about the importance of developing whole number and place value concepts has reinforced most of what we have been presented throughout this book. Hands on activities cement knowledge and build more connections within a childs' knowledge base, that knowledge becomes more meaningful and more useful to a child as they encounter more complex mathematics. They are not simply ‘going through the motions’ but rather they are actively aware of the computations they are performing and understand why they are using the methods that they are using.
Chapter 12 focused on whole number computation. I personally found the suggestions within this chapter to be very useful. I liked that they spent a bit of time devoted to student invented strategies for working with whole number computations. As we have been discussing in class, there is no one way to ‘do’ math, and all approaches should be examined for their usefulness. I may not understand and do things in the same manner as you, but as long as I arrive at the same conclusion consistently my answer is still correct. I think I found this chapter to be so helpful because I am currently in a first grade classroom where a number of students are struggling with subtraction; I think that many of the suggestions in this chapter might help them understand.
Chapter 23 was about computational estimation. I think that estimation can be a difficult concept for a lot of children to master. The wording of problems is sometimes confusing to a child and there are also the questions of why we would need to estimate. This chapter did a good job of explaining reasons for estimation and put it very plainly so the future instructor can use many of the suggestions in this chapter with very little adaptation. The suggested activities in this section were brilliant and I can envision myself using many of these suggestions within my own classroom eventually.
In response to Jena S:
ReplyDeleteI agree with you that students are being introduced to concepts are earlier ages, and I also agree that it is a good thing that teachers are using the same terms in different grades. I also feel that it builds continuity from each grade and it probably helps the student develop the sense that most things in mathematics are related. I agree that invented strategies should be encouraged. I like you had a little trouble with estimation and think that there were a number of suggestions within this chapter that would have been useful for us. I believe that we will probably taking a lot of the same things from this text for our future classrooms.
Chapter 11 Developing whole number place Value Concepts is very familiar to me because I have had the opportunity to watch my mentor teacher teach this concept to classroom of 27 students. She has used the based ten blocks and emphasized each place. For instance, in the number 734 the students understand their are 4 ones, 3 ten and 7 hundred. She demonstrated this with the manipulative and than had the students who the base ten blocks to demonstrate it back to here. I felt like this chapter had a lot of good activities that a teacher can use in the classroom.
ReplyDeleteChapter 12 Developing Strategies for Whole number computation. Wow things have changed a lot since I have been in school. I have noticed the vocabulary has changed from borrowing to regrouping and the many different strategies that have been introduced. I am not against new strategies as long as the students understand material. In my internship class my mentor teacher is very open to the students coming up with different ways to reach the same conclusion. For instance a student may be adding 50+29. It may be easier to add 50+30 and subtract one. One day in my internship class she gave the students different problems to solve. One problem had to be done with pencil and paper, another mental math and another using a calculator. The students were able to see where each of these methods had their place. I think as teachers we need to keep in mind that students are individuals and different methods are going to work for different students.
Chapter 13 Using Computational Estimation with Whole Numbers I think estimation is a tough concept for students because they want to be correct. Estimation sometimes gets confused with rounding. In my internship class the 3rd graders have just finished with this section and they seemed to struggle with the concept somewhat. My mentor told them to look for key vocabulary to decide if they were to estimate. The key word for them was about. The problems they had to work involved deciding if it was to be an exact answer or estimate. They seemed to do better when they cued in on the correct vocabulary.
To Adrianne: I agree with much of what you said. I am a very visual learner. Usually if I can see it and do it with my hands I have got the concept down. However, way back when I was in school we sat in our chairs and listened to the teacher go on and on and on about something. I remember my mind would wonder. I think kids are very curious and like to do hands on materials. As teachers we need to move from the idea that our job is to lecture and allow the kids to learn from doing as well.
ReplyDeleteTo Kristie: I am so glad that you recognize that learning these concepts starts as early as PreK. I believe it is so important for students to understand that mathematics is a process and each skill carries onto another. I worry about students who don't master a certain math skill and it causes them to fall further behind. Mathematics is so important and as we move into a more technical society math is becoming more important.
ReplyDeleteChapter 11 talked about developing whole number place value concepts. It mentions that children learn to count to 100 as early as kindergarten, but only by ones. it also talked about the role of counting: counting by ones, counting by groups and singles, counting by tens and ones. It is important to incorporate the grouping by tens concept with what they know about number from counting by ones. The chapter gives lots of activities for teaching students about grouping numbers.
ReplyDeleteChapter 12 is about developing whole number computation. Direct modeling was mentioned within the chapter and that is the use of manipulatives or drawings along with counting to represent directly the meaning of an operation or story problem. The chapter talks about student invented strategies and talked about how students come up with strategies to solve certain problems and they have not been taught those strategies. In class we talked about how if a students understands and can explain their answer they should be able to use the strategy. What works for one student may not work for another so I feel if students find a strategy that works for them and they understand it and can explain then they can use it.
Chapter 13 is using computational estimation with whole numbers. It talked about the three types of estimation: measurement estimation, quantity estimation, and computational estimation. It gives suggestions for teaching computation estimation: use real examples, use language estimation, use context to help with estimates, use context to help wiht estimates, accept a range of estimates, focus on flexible methods not answers, and ask for information but no answer.
In response to Jeanette,
ReplyDeleteI agree that the way things in math are done have changed. I feel like I'm learning to be a teacher, but also learning the way students are taught these days. My mentor teacher encourages different ways in which to solve problems. She often asks if anyone else got a different answer or solved it a different way. When I was in elementary school I found estimation to be difficult because I wanted an exact number.
Chapter 11 is about developing whole-number place-value concepts. This is what the students in my internship have been working on lately, and I can see when it clicks and I can also see why it is confusing. There are students that just can't understand with decimals how the tenth spot is bigger than the hundredth spot. My mentor teacher uses base 10 blocks, and they seem to help, but they will finally understand one question then be lost on the next. I can see how important this is, and it needs to start early. My last internship was in first grade, and they counted the days of school with straws and bundled into tens when they could. This is a good way to begin students understanding of place-value.
ReplyDeleteChapter 12 is about developing strategies for whole-number computation. In this chapter I got the most useful information out of student-invented strategies. I had never really thought of this, I guess once you get older and set in your ways you have certain ways of doing things. Not young students though, they come up with strategies that work for them, and as long as it gets them to understand the concept then we need to be supportive of it. Students need to be able to use strategies that work for them. This chapter discusses all the benefit of student-invented strategies. I found it very interesting when we did this in class. It was great to hear other students ideas of how to solve problems.
Chapter 13 is about using computational estimation with whole numbers. This is another concept that students have worked on in my internship class. They use the term ball park estimate, which was something I don't remember hearing when I was in school. One thing I found important is to not use the word guess. Students are not guessing they are using some form of reasoning to estimate the number. One idea from the text that I think is a good one is to ask for information not the answer. Especially for students that have trouble with estimating this will put them at ease not to get the answer correct. You can give them a problem then ask them if the number is over or under 100. I didn't really know that there was so much involved in estimating, but this chapter brought some very good information to the table.
In response to Adrienne,
ReplyDeleteI agree that it is frustrating to have teachers tell you what something is, then never show you why. By doing this students will never get the why. My mentor teacher uses a lot of manipulatives and I really like that about her. I have seen how they help the students understand the process, not just the answer. That is so important for their future.
Chapter 11 was about how teachers can teach whole-number place-value concepts. One interesting concept in this chapter was the different ways that students can count sets. Some students may count one at a time, or some might group them. I think that as a student develops, they will begin to us more logical and efficient ways of counting. I like using the cubes, rods, and flats to illustrate the concept.
ReplyDeleteChapter 12 was on developing strategies for whole-number computations. I liked reading this chapter because we have been talking about it in our classes. What I have caught on to is that each child may approach a problem in their own way. They will use the procedure that they understand best. It’s not the teachers’ job to tell the student that there is only one correct way to do something; they are there to support the child in their learning.
Chapter 13 was on computational estimation with whole numbers. This was my favorite chapter out of the three because my internship class just taught this a couple weeks ago. Needless-to-say, it took them a while to understand the concept. The book identified what might have been their problem; estimation is not guessing. When I would ask them what they thought the answer might be on an estimation problem, they would guess thinking that was what I expected. It wasn’t until I wrote how I would tackle the problem that they began to understand the concept.
In response to Jena-
ReplyDeleteI think that you bring up a good point that I’m sure the students would ask you. Why do we estimate? I think that estimating is a great skill to have because it does truly save time. For example, which is quicker in Walmart? Estimating how much you have in your cart or adding the exact price up? Students and children always like to ask “why” and I think that it is a valid question. Students need to know the reason behind the work we give them. They will have more buy in if they know.
In chapter 11 it was about whole-number place-value concepts. The very first thing that the chapter talks about is base-ten-concepts. In my current internship at Roosevelt My teacher makes a big deal about 10s with Zero-The-Hero. Every time that we are in school for a tenth day, Zero-The-Hero comes to visit us. He/She groups the ten ones of straws into a bundle of ten. With this students start becoming familiar with place value. I think that we do need to make a big deal out of tens because there are lots of short-cuts that students can use if they have a good concept of 10s.
ReplyDeleteChapter 12 is about developing strategies for whole-number computation. I really liked the Student-Invented Strategies for addition and subtraction “one goal should be to extend students’ knowledge of basic facts and the ten-structure of the number system so that counting is not required.” One thing that I loving that Dr. Stramel continues to say is that we need to let our students try new ways to get answers, but we need to make sure the students know and understand and can explain if the students would do their problem a different way.
Chapter 13 talking about estimation with whole numbers. One thing that I think of that I do on an everyday basis, is when I go to the grocery store I estimate how much it will be when I check out. One of the ways that my group at my table do when we are supposed to do the math problem with different ways, is we estimate and round up or down numbers to get close to our answer. My students in my internship haven't started learning about estimation but I think that its never to early to start to learn.
To Jena:
ReplyDeleteI agree with what Andrew says. I think that we need to teach our students how to estimate because like I said in my post that I do this on a almost everyday basis, when every I go to the grocery store I estimate how much it will be so I know how much money to have ready. So when a student would ask me I would say because you will use it when you get older and we need to start practicing it now.
Jena- I agree with you on how whole number place value is being taught earlier and earlier. I subbed in a pre-k classroom not long ago and they were placing straws in a pocket for each day they were in school and rubber banding them together in groups of ten. Its funny to think how the teachers work to use the terminology and the students don't really even think anything of it! Hopefully teaching it early will help it come naturally later!
ReplyDeleteAs usual I found the examples throughout these three chapters to be incredibly insightful. Hopefully one day I will take advantage of having this textbook as a resource.
ReplyDeleteIn Chapter 11 I enjoyed reading about the Base Ten manipulatives, and how these manipulatives can be used. In my internship classroom I was able to see how Base Ten blocks can be used. It is nice to be able to relate textbook information to real life use and experience.
I never would have thought that cultural differences were in algorithms. Chapter 12 provided me with some very useful information on this. Students come from different backgrounds, and some students even come from different cultures. Because I am from America, and have lived here my entire life, does not mean that every student understand algorithms in the way I. I need to be sure to take into account all of my students’ backgrounds. I also thought that it was great to be able to see some student-invented problem solving techniques. Certainly there are some ways to solve problems that are quicker, but if a student can reach the correct answer and explain it properly, there is no need to tell that student he or she is incorrect.
I had no idea that there were three types of estimation. There is measurement estimation, quantity estimation, and computational estimation. I have used every type of estimation but I was never told that a specific example is an example of one specific type of estimation. I also like that the book stressed using real examples of estimation on page 242. Using real life situations in anything is one way to guarantee students will learn and retain information.
@ Megan B
ReplyDeleteI also saw the Base Ten manipulatives being used in my internship. My teacher refers to them as bits (ones), rods (tens), and flats (hundreds). I know there is a name that is used for the thousands, but I can’t recall it at the moment.
I also thought it was incredibly insightful to have the chance to look into student-invented problem solving techniques. I think it is important to let a student do as he or she chooses as long as they reach the correct answer and are able to explain how they reached the answer and how it’s correct.
One thing I loved about today's class was when we did problems using estimation and then discussed how we estimated. For example, on one problem one person rounded the numbers to the nearest hundred, another rounded to the nearest 10, and the other rounded to the nearest 25. It was quite intriguing to see all the different ways. What was most interesting was that all of the estimations came out to equal the same number which was something that I had never seen before. But with all of the other problems we got different answers but were all within the range of about 10. Estimation is a key tool that students should be able to learn how to use to help get a general idea of what the actual answer is because sometimes in life there may not be any choice but to estimate.
ReplyDeleteEmily M.
ReplyDeleteI completely agree that using real life situations, no matter what the type of problem is, will help to guarantee that students learn the material. When students see that there is a way that they may use it somewhere other than school there is more motivation to learn the material. It will also stay with them better because they might use it on a somewhat regular basis which will be that much more practice for the student.
When reading through Chapter 11 dealing with the areas of developing whole number place value concepts I was able to learn lots of helpful information for my future career. I especially liked the figure 11.1 on page 189 that showed three different but equivalent groupings of 53 objects. A tip that I found helpful in chapter 11 is when it talks about how a good base ten model for ones, tens, and hundreds needs to be proportional which I feel is so important. This means that the ten model is physically ten times larger than the one and the hundred model is ten times larger than the ten model. I also loved the idea of using place value mats in the classroom in order to help with the concept of place value. Overall I loved all of the activities presented throughout this chapter.
ReplyDeleteWhen reading through Chapter 12 over developing strategies for whole number computation I was able to learn some interesting facts and tips for my future classroom. I found the figures 12.5 and 12.6 on page 221 to be helpful to me to show me different inverted strategies that students have created for addition with 2 digit numbers and strategies for subtraction by counting up. I liked how the book thoroughly explained the idea of cluster problems to me as the reader. Before reading this chapter I was unable of how exactly a cluster problem was and now I am able to understand it. Overall I loved how this chapter explained different student invented strategies for multiplication as well as division.
When reading through Chapter 13 over using computational estimation with whole numbers I was able to learn lots of helpful information in this subject area for my future teaching as well as my future classroom. I liked how the book talked about the three different types of estimation which are measurement estimation, quantity estimation, and computational estimation. I also found the rounding methods to be very helpful to me in understanding how to teach estimation in my classroom someday as well as the importance in teaching estimation. Lastly I found the calculator activities to be good to use in a classroom someday. Overall estimation is such an important skill to know in daily life so that you know how to use it properly in the world.
In response to Kayla R.,
ReplyDeleteI agree with you Kayla that in chapter 11 it talked about how children in kindergarten learn to count up to the number 100 but only by ones. I am constantly seeing this practice put into effect in my kindergarten internship classroom. The teacher has a 100’s chart and is always reviewing the numbers to 100 with the kindergarten students. I also feel that it is important to incorporate the grouping of tens concept with what they know about the numbers by counting by ones. I also enjoyed the activities mentioned throughout chapter 11.
I also noticed that chapter 12 talks a lot about student invented strategies which I feel is good for a teacher to understand and appreciate. I agree with you 100% that if a student can explain how they solved the problem and the student is able to get the correct answer then the student without a doubt should be able to use the strategy. I agree with you that all of the students in the classroom are different and a strategy that may work for one student may not work with another student.
I also found it helpful that in chapter 13 the three types of estimation were mentioned and explained in detail. Lastly I also noticed that the chapter gave suggestions for teaching computation estimation. I really enjoyed the activities that were given throughout chapter 13 that were related to the area of estimation. Overall great post Kayla!!!
Chapter 11 talked about whole number place value concepts. I vaguely remember working with base tens blocks as a child. Sometimes I think it is confusing, but other times it helps show the “big picture”. I also wonder how we are suppose to teach a concept we ourselves may not understand. For example, most of us were taught to add the traditional way. How do we show our students there are other ways when we can’t even do it ourselves? I like the examples the book showed and the activities we did in class. It helped me understand the place-value concepts better.
ReplyDeleteChapter 12 was over whole number computation. One of the things I liked was on page 217 where it talked about traditional algorithms. It said that often younger students pick things up from older siblings or parents. They will come to school and say “my dad taught me a shortcut” and will often refuse to learn a different way. The book said that once the traditional way is understood, then it shall be looked at as one more strategy for the classroom tool box. Which I think is a great idea. We should be accepting of the different strategies children will use, not just stuck on one way. The first graders in my internship have been using the number line to help them add and subtract. I have always hated number lines. I think it was because I never understood the correct way to use them? Or maybe it was because I never needed to use them? The first graders have taught me a lot about how to use them and I can see how they are a useful tool, just not useful for me.
Chapter 13 was about estimation with whole numbers. I can say that when I was in elementary school, we hardly ever estimated. That is probably why when we were doing the estimation activities in class I had the hardest time. It took more work and thinking to think of what number to round too and then to remember that number and think of what to round the next number to and remember that number and so on. Its not that I never estimate, because I estimate when shopping all the time, its just that it is easier for me to just do the traditional way of adding, subtracting, dividing, and multiplying.
In reply to Lane: I really enjoyed your post. I also thought it was really neat how everyone estimated differently. What I really liked about your post was your last sentence. I liked how you said if the student has no other choice then they could always estimate. This made me think of state testing. If students know how to estimate, then they have a better chance of selecting the right answer.
ReplyDeleteThese were 3 really informative chapters. Chapter 11 was over place value. This can be a very tricky concept for some students. I work as a paraprofessional and = I have taught this to my students and some pick this up pretty quickly, then again, there are some that really struggle with this concept and it is the same way in a regular education classroom. I enjoyed how the book showed different activities you can do with learning place value. Chapter 12 was over whole number computation. Again, I like how the text provided different methods and activities for this concept. I also think it is key to remember, everyone learns different so what may work for one student, may not work for another student. This is definitely important to remember in mathematics in the classroom. Lastly, chapter 13 was over estimation with whole numbers. I really enjoyed Professor Stramels lecture over this. I am definitely going to use her activity of the over/under. I believe this is a great way to teach estimation and I believe the students would enjoy it as well. I am glad we got a chance to read about estimation and how to teach it because estimation is such an important concept that students will need to know forever.
ReplyDeleteIn response to Emily M-I completely agree with you, using real-life problems are a great way to teach students. It gives them things to relate with and lets them know they really do need to learn what concept you are teaching at the time. I am sure there are many students that brush off different lessons because they think they will never need to know this and will never use this in the future but by using real-life situations will put things into perspective for them! Great post Emily!
ReplyDeleteChapter 11 Whole-Number Place-Value Concepts
ReplyDeleteChapter 11 talks about counting by one, counting by groups, and counting by 10’s. I work with children every day that can’t count by 2’s, 5’s or tens. I think this is such an important skill that makes counting so much easier. This is a skill that they carry with them from Kindergarten all the way through their lives. As adults we use these skills every day. Now I see teachers using it in all sorts of ways, during calendar especially. The think I like most about having children count by numbers is you can use anything to count with craft sticks, coffee stirs, coins, and beans. Coffee sticks and craft sticks are great for combining and grouping together, groups of 10 with a rubber band or ties. This is such a great way for our visual learners to see 50 in the tens place and 4 in the ones. This section is once again packed with activities.
Chapter 12 Developing Strategies for Whole-Number Computation
The part of this chapter that really stuck out was about creating an environment for inventing strategies. When we are so hurried to get something taught and stay on schedule we forget to let the children use the brain God gave them. Let them use different experiences that they have had that will aid them to find new and different ways to solve problems, because not every problem is going to be introduced the same way. Cluster problems – I’ve learned to teach them to break them down to just a couple of numbers at a time or adding by columns and hundreds then tens and last ones. The division algorithm is great for children that are new to division or have problems with division. Myself I don’t like the new way of dividing it takes me too long.
Chapter 13Using Computational Estimation with Whole Numbers
Focusing on the flexible methods is important. It is important for them to learn to use strategies to find their answers not think that they have to do it a particular way. It’s more important to see how they get their answer and can they justify their answer. I think it’s important to give everyone time to try to solve the problem and let the children tell each other how they solved it. They can learn from each other. Estimation is such a needed skill yet most of the time we really don’t realize that were using it.
Megan B. I like what you said about real world problems. Kids love things that seem real. If your teaching money from a worksheet they won't want to learn. Bring in some cans of food and other packaged groceries and the children jump at the chance to play store, buy groceries and learn what change to give back. Even as adults we think the same way, if I can't apply it to something I will be doing why learn it.
ReplyDeleteChapter 11 is about developing whole number place value concepts. These concepts start at grades as young as preschool. It is very important for students to start learning about whole numbers young. In my first grade internship classroom the students learn about place value by counting the days they are in school every day. When they get to 10 individual straws they make a bundle of 1. This is the basis of place value. This chapter has a lot of information and activities about how to teach children to use base ten blocks when doing math. I think that manipulatives are so important in the classroom and teaching children to use them will only benefit them. I saw one point in chapter 11 that I feel was very difficult for children and that was numbers beyond 1000. It is hard for children to understand what is beyond 1000. Because you cannot actually get 1000 little cubes out its hard to see what you want. The best way I think is to use 10 flats.
ReplyDeleteChapter 12 states that rather than a single method of subtracting; the most appropriate method can and should change flexibility as the numbers and the context change. I know we have talked in class a lot about student inventing and I think this is a great strategy to use. It is good for your students to come up with ideas of their own. If they cannot think of a strategy then they can ask for help from the instructor though. Using base ten is a good way to teach any problem. Teaching children to trade when adding and subtracting can help them in the long run.
Chapter 13 is all about estimation. Estimation is not just a guess. It has to be an educated guess. I know that if you tell the children in my internship to estimate, they will just choose a number without looking at the problem. A lot of the students won’t even look at the problems when you want them to. So making sure that they understand what an educated guess is is a good idea. Estimation is a good way for students to figure out problems. When learning to do math it is good to estimate so children can relate problems.
In response to Lane A.
ReplyDeleteI think that in class by showing how just us 15 all round and figure out problems differently shows how children are going to do things differently too. There are so many different ways. Some child might just want to round to 2's. Which is different but it might be easier for him to do that.
Somethings that I took away from ch. 11 is that using manipulative's, such as base 10 blocks, is a great tool to use for students to visualize what is being taught. Sometimes as a student I was not always able to understand things unless I was able to visualize it. Once I have had the objects in my hand and used them, usually I can visualize them down the road in my head without have them in my hands. There are so many different ways to teach place value but I think that using manipulative's is probably the best. Chapter 12 is interesting. There are many strategies in this chapter that I have never thought of or seen. These are just other ways to reach those who don't understand concepts. It will be difficult, I think, to teach these other strategies and use them when it has been engrained in our heads of a way that seems right. It is also important to allow the students the freedom to come up with their own techniques if none of the strategies work for them. In chapter 13, computational estimation is something that I have never used before. It is a different way to teach but it can be effective and easy to do in your head. As a teacher, I will not limit students to using one method, as long as they can explain it. For the first few assignments that they are using that technique, I would like for them to show their work. I know this is not Dr. Stramel's first choice but I believe that if a student is learning a new technique, they need to prove that it can work. After the first few assignments of showing their work they will not be required to show their work after the assignments.
ReplyDeleteTammy,
ReplyDeleteI agree with you that it takes too long to divide using the new method. I also think that if we are going to introduce strategies into the classroom, they need to be effective strategies. Do not allow students to use them for a long time and then tell them that they are not able to use it. If we are teaching the strategies, maybe we can tell them which one will benefit them more and leave the options of which one they want to use up to the student.
Chapters 11-13 are about whole-number place-values. Chapter 11 is about whole-number place-value concepts. I believe the most valuable manipulative that could be used during this section would be the base ten models. This manipulative allows students to see visually whole numbers. Once students have a complete understanding of whole-numbers they then can be used to help students with decimals. Another section that I found important about this chapter was that it is equally important that students are able to express the whole number verbally; this is a skill that I think is sometimes forgotten. We often assume that if they can write them they understand them, but they must also be able to read them. Chapter 12 is about the computation of whole-numbers. This is what we think of when we think of elementary math, adding 4+3, and subtracting 11-4. These skills are very important in the fundamentals of math, it create the base for all math to come. This chapter was discussed in detail in class, because it is so important to allow students to create their own way to solve these problems. Once students are able to solve addition and multiplication problems, they will move to multiplication and subtracting. I think this is one of the most controversial areas in math, should students be made to memorize their multiplication facts. I believe that a mixer of teacher led, student created, the use of manipulative, and drills is the best way to help students master multiplication facts. I don’t think one single method should be used all the time. The final section is over estimating whole numbers. I think this section is so important because it is the way that most of us to math in our adult lives. This is a skill that is very important concepts to teach students, it allows them to look at math in not just a black and white way. Overall all of these sections are important fundamentals for the first steps in teaching mathematical concepts. I really enjoyed how the section gave examples of different ways to solve math problems that are different than the traditional way.
ReplyDeleteIn response to Joel S.
ReplyDeleteI also think that the base ten blocks are one of the most important manipulative to use when teaching whole number. You pointed out that it was important for you to see the problem visually, this is important when teaching to multiple learners. I totally agree with you, It is very difficult for me to teach math using a different method than the traditional way. But it is very important for them to develop their own ways to solve the problems, by allowing them to do this I think they will have a better understanding of the math concept. Finally in my schooling estimating was not a much discussed area, so it is very difficult for me to do it. It is actually much easier for me to work out the whole problem rather than guess. One last note, I am also a full believer in having students showing their work, I think it helps them refine their skills when learning a new concepts. I don’t care much about what steps they used to solve the problem, just that they used some method to solve it.
Lacey Keller
ReplyDeleteChapters 11, 12, and 13 presented information regarding whole numbers. I found it interesting how these three chapters showed how students computate the different math problems. For this here math lover, it was sometimes difficult to figure out the rhyme and reasoning of some of the problems. Most times, I think people should just be able to think in terms like me!
I think the best information from these chapters came about estimation. I think this skill is one of the most important skills we can teach our students. It is a skill that will be used everyday. No matter your chosen walk of life, you will always find yourself estimating.
Again, I liked the websites shown in these chapters. I checked out the digital manipulatives...it is cool!
Lacey Keller
ReplyDeleteIn response to Rebecca B.,
I agree with you that students should have a strong mixture of mathematical problems should be delivered to our students instead of memorizing facts. This drill and kill stuff is okay, but showing students how to use these skills in real life situations is more practical. Also, when teachers use one-minute timed tests, it only allows the students to practice for a short amount of time!
Chapter 11 on the development of whole number and place value concepts provided good information. While I understand that are students all learn differently and at all different levels, I ponder the thought of losing most of them in all the different ways of teaching one concept. In second grade, we should be reinforcing addition and moving forward into subtraction. It is almost the end of the first semester and we have students that are struggling with addition of basic numbers. Many of these students need one-on-one to go back to the basics of addition and practice. But instead, we have to spend days on teaching other methods to work a problem, such as base-ten groupings. The chapter talks about teaching our students to put things into groups of ten to make it easier to count. I agree that it is easier for most of our students to count by groups of ten, and using it throughout the day with tasks and classroom chores is a great reinforcement. The chapter goes on to discuss integration of groupings with words. In my experience, this is a fairly easy concept to teach and understand using base ten blocks. As the students finally make the transition from addition to subtraction, groupable models are very helpful. This chapter provides many great strategies for teaching using base ten, it is just so important not to move into this until the student is completely ready. I feel that this is where many students are lost, and then every lesson from then on is history.
ReplyDeleteChapter 12 on developing strategies for whole number computation is a little more complex. I agree with the chapter that direct modeling is a must. Our district is so fortunate to have hovercams and smart boards which makes this so much easier! The student invented strategies paragraph really got me thinking. In many lectures, we have always been taught that kids learn from kids. The chapters points out that the students cannot use or teach their invented strategies unless they have been evaluated for accuracy. I think that it is very important to let our students share their ways of doing the problem with the class using the smart board. As a class, the procedure can be evaluated and if correct used by students that understand it. My concern with this is that there are many teachers that require the students to use the formula they teach, so it is not going to benefit them to use their “created” strategies. I was a bit surprised when the chapter discussed traditional algorithms. With a little thought, I realized that this is something our students develop early on. As the chapter went on to discuss strategies, I was excited to see subtracting by counting up! I use this technique with many of my students and most of them seem to grasp it pretty well! The chapter ended up with discussion on multiplication and division strategies and ideas.
Chapter 13 discussed using computational estimation with whole numbers. Estimation has been amazingly hard for our third graders this past couple of weeks. The chapter encourages us to use real life examples in teaching our students to use estimation. Estimation makes sense to me when buying groceries or estimating how much I have spent for the month, but we are teaching our students to estimate thousands’. This is where the frustration comes in. The third graders have a little chant they use with estimation and it is “five or more, raise the score – four or less, let it rest”.
Developing Place Value Concepts in Chapter 11 was a very familiar topic. One of my lessons in my FPA was on the topic. Place values seem to be taught to younger ages now than they were when I was going through school. Chapter 12 was over whole number computation which, of course, if an important topic to cover. It seems that the wording used in this chapter differs somewhat from the wording that was used when I was learning about whole number computation. I found it quite interesting and somewhat frustrating to change the wording. I found it frustrating simply because, now as teachers, we will need to learn the new wording and not confuse it with the older wording. Chapter 13 was over computational estimation. Estimation is such an important skill that some may look over. I feel that students know they need to learn to add, subtract, and other basic skills; but estimation can seem unnecessary while, on the contrary, it is important in our everyday lives. We even use it without noticing many, many times throughout our days. Overall, I enjoyed reading this section and thought it was very informative.
ReplyDeleteIn response to Joel Stucky:
ReplyDeleteYou said, "Somethings that I took away from ch. 11 is that using manipulatives, such as base 10 blocks, is a great tool to use for students to visualize what is being taught." I completely agree. Visualization of math is such an important thing to provide for students. There are so many students that simply cannot grasp the math concept when it is taught as just a concept. Students often times need a concrete thing to see, touch, and feel to truly understand just how math works.
@ Jenna ~
ReplyDeleteOn estimation, I am right there with ya! Last week I was working with third graders and man they were struggling with estimation. Later in the day I was visiting with their classroom teacher and he said "estimation is very important, I use it daily". Really I thought to myself. I feel that most of our students are doing good to get the concepts of addition and subtraction down. I want them to be able to balance a checkbook and be able to run their households, I am not so sure that estimation is as important as we make it.
Carissa Kruse
ReplyDeleteChapters 11-13 BLOG
Chapter 11 is about Whole –Number Place-Value concepts. This is something that holds no meaning to children before they start school. However, it is something that can be picked up and understood quickly if they are given proper models. Many teachers use a straw for each day and then group them by tens and then again in one group of 100 once the 100th day of school is reached. There are many other models that can be used throughout the classroom to help them understand the meaning of place value. For example, many math teachers use Base Ten math tools with their students. Also, Tens frames are used in math and can help students understand the importance of Fast 10’s in Math.
Chapter 12 was about strategies for whole-number computation there are multiple strategies to use and help students to learn when teaching different concepts within mathematics. And because every student learns different understands different concepts in different ways, the students must be taught as many concepts as possible. Often times students are looking for the simplest way to get the answer. With this in mind students will often come up with their own strategies for arriving at the correct solution. They must be taught that they may not always come up with the correct solution using the strategies they create on their own.
Chapter 13 was about using computational estimations. The concept of rounding is the most widely used strategy for estimation. It is always easier to estimate and use mental math when using a familiar whole number. I know that I use rounding very often in my daily life when trying to figure different information out. I especially use rounding when I am driving to know how long it will take me to get from place to place and how much gas I will need.
In response to Kymberly R...
ReplyDeleteIt seems as though everything seems to be taught at earlier ages now than it was when I was in school. The students are expected to retain so much more information and it surprises me how well they do with all of the information they are given on a daily basis.
Reading 3 chapters for this week, there was a lot of information to take in! After reading everything I have realized how little I truly know about Mathematics and everything it entails. We recently began using an intervention program at our school titled “Camelot Learning- Math Intervention Curriculum.” Numerous of the activities and strategies explained in our text are directly related to the Camelot Math interventions I am now using with my students. I can say one thing… I am learning many of the strategies right along with the students. There are so many ways in which to perform Math problems, as shown in our text! I am grateful to have this text especially when it comes time to teach Math in the classroom. There are so many strategies in this book that my brain cannot even wrap around them! I really like the idea of letting students “invent strategies.” When I am working with my students they often come up with ways in which to complete the problems that I have to really study their method to understand what they are doing! It truly is amazing to see what student’s minds can come up with when they are allowed to address their own learning strategies.
ReplyDeleteIn response to Kymberly-
ReplyDeleteI also enjoyed reading each of these chapters. There was so much great information to help me when I am in the classroom teaching. I have always used the most basic strategies when it comes to completing Math problems. These chapters had me thinking I have no idea what I am doing! There were so many concepts that I had to reread and write out the problems myself to figure out how the book even explained to do them! It is amazing to me that the book stresses the importance of letting students use “student-invented” strategies. When I am working with my students at school, they do this quite often and many times they throw me for a loop! I have to have them explain their strategy to me numerous times just so I can understand what they have done! Most of the time they have done a great job of figuring out how to complete the problem but many times it seems as though they took the longest way around to get there!
In response to Angela R
ReplyDeleteThe mind of an elementary school student is open to all kinds of things. They will invent things that will work for them, if allowed to. As adults we do not understand they way they do it because our minds have closed themselves off to things different from what they know. As teachers we need to understand that our students will come up with all kinds of different ways to get it done. Our job is to understand it before we say anything about it. To many teachers say don't do it like that without first understanding what they did.
I am a collection of habits, I like to do the same thing in the same way again and again; which may be part of why I leaned math in the traditional way. As I finished reading these chapters I realized that for a person like me; they are best in small doses.
ReplyDeleteI understand that everyone is not like me, good thing to because one of me is boring enough.
These chapters are useful, they reminded me that I need to carefully make sure that I understand that my students may not learn the way I do, may not get it done the way I do.
My biggest problem with these chapters is when they discuss the traditional method, or at least claim they are going to discuss it. I say claim to because I am not sure they actually did and in fact think that they did not.
If that is the traditional method then in the 18 to 20 years since I finished the sixth grade an entire traditional method has come and is ready to go. I say that because they did not even spend enough time on how I learned it for me to say they covered it in passing.
That is my biggest problem with the book, its total disrespect for the teaching of math in a way that worked for me. This book is quite sure that no student can, ever has, or ever will learn math the way I learned it; and that is a problem for me.
Each week after reading a chapter in our math text, I become more confident in my abilities to teach math. When I first started this class in August, my biggest fear as a teacher was teaching math. Since I have struggled in math all of my life, how in the world was I suppose to teach it! But our text is so hands on and that is exactly what I need. Chapter 11 helped us to learn to teach place value, which is one of the hardest things for students to understand. The activities in the chapter cover a range of ages and abilities which will be very helpful if I teach in an LD classroom. The etools by Pearson Scott Foresman is a website that I would love to use as an enrichment and study tool for my students.
ReplyDeleteChapter 12 is about developing strategies for whole-number computation. The chapter begins with the lowest level with children using manipulatives and direct modeling and ends with multiple factor division and multiplication. I actually learned new ways to do math in this chapter that I had not learned before. I come from the old math (which means it has been 26 years since I was in 6th grade) and we were not given all of these different options to find solutions. It was the teachers way or it was wrong. I am glad to know that educator finally figured out that every student does not learn the same way and that does not make them wrong. I feel I would have been a much more successful math student in this day and time period.
Chapter 13 discusses another part of math that seems to be difficult for many students, estimation. I did not understand the cluster problems for estimation on page 244. I looked at it several times and still do not see what they are doing. I did like the suggestion on page 249 on how to test computational estimation. Doing the Guess boxes on the overhead is a great idea. I have helped students with math benchmarks and when it comes to estimation, if they don't understand it, they just work the problem out. So how do you really know if they understand it or not. As always, I have a bundle of activities to add to my toolbox!
Chapter 11 covered Developing Whole Number Place Value Concepts in the classroom. I found this chapter very interesting because I find it difficult sometimes to teach place value to young students. I just recently observed a lesson over place value and the students had a hard time grasping the concept. I found the examples to be very helpful in preparing lessons in the future.
ReplyDeleteChapter 12 covered Developing for Whole Number Computation. The section that I found most interesting was on Student Invented Strategies. I enjoyed reading this section because it talked about expanding on methods that have already been introduced. I found a lot of useful information in the text that I can use to help me and my students in the future.
Chapter 13 covered Using Computational Estimation with Whole Numbers. I am surprised to say that I had either forgotten about or never knew the different types of estimation. Measurement estimation, quantity estimation and computational estimation. One statement that I found useful is that students often confuse estimation with guessing. I think that it is important to make sure the students know what the difference is.
In response to:
Jeremiah
I am the same way. Once I find a successful way to do something I tend to stick with it. This chapter reminded me that there are ways to solve problems and that sometimes it is helpful to branch out.
In response to Angela R.,
ReplyDeleteI too love our textbook. It will be a very valuable resource for me as I begin my career in teaching. I am also learning how to do math in different ways as my students learn. Our school teaches math through hands-on and investigations. They rarely do any worksheets, so this book comes in handy when needing activities to help teach a concept. Good luck in your career!
Chapter 11~ Developing Whole-Number Place-Value Concepts gave me a lot to think about. Although it went over a lot of basic knowledge, it also pointed out the importance of the terminology of using tens and groups of tens. I am realizing that I need the visuals in the text to help me to overcome my traditional views of problem solving. I am really happy that the way that mathematics is being taught is changing~ I think that is so important. This chapter really showed the use of base-ten blocks and how to use them.
ReplyDeleteChapter 12: Even though math was really difficult for me and I would have benefitted from different ways of doing problems, I cling tightly to the methods I have learned. It was a stretch for me to try to solve problems in different ways during the adobe connects when the on campus students were finding as many ways to solve problems as they could. It is evident to me that the use of manipulatives is so instrumental to making math make sense. I even see that in the 6th grade classroom I am doing my internship in. The students have no hesitation in drawing visual aids on white boards, like fraction circles or base-ten blocks to illustrate the problem and provide themselves with a visual. Last week I was in a 2nd/3rd grade classroom in which the students were taught only one way to solve problems. Because of what I am learning here and what I have seen in internship, I was really surprised. The class did a story problem that was an addition problem. When they completed it, I first asked someone to tell me what their answer was and then I asked how they got the answer. The student told me how they got the answer, and so I asked, “did anyone solve this in a different way?” And then I asked, “Is there another way to solve this problem?” and the class unanimously answered “no.”
Chapter 13: Estimation. I loved this chapter. This is relatively new to me. Of course, we all estimate. But as a valid way to do math, it is new. I liked the problems in the chapter and how we worked on them “in class” (adobe connect) and that we were not supposed to do the work, but estimate. The text gave a lot of different strategies for estimating. In the class I am in for internship, I was exposed to it as a way to check the answers. It is a test taking strategy for them as well, checking the answer by rounding down and then rounding up to get a low and high estimation. They did this when multiplying a problem such as .28 * 1.3. Round down and 0 * 1 is 0 and round up and 1 * 2 = 2, so the answer has to be between 0 and 2. They had three possible answers: .364, 3.64 and 36.4. So they knew the answer was .364. I would not have thought of this as a test taking strategy or a way to check answers before seeing it in action. I think I am really fortunate this semester because I am truly in a classroom that implements learning through problem solving. This makes what we read and do in class so much more real and applicable when I see it being used and I see students grasp onto it! I also liked the cluster problems in chapter 13. I am not sure why I liked them. I think it is because the estimations make sense to me. I feel like we are learning ways to do math that make more sense to me!
Angela S.~ I know how you feel about fearing teaching math and how all that we are learning is helping you to feel more and more equipped. That is exactly how I feel. I knew I would do my best at teaching math, but now I feel like I am being given solid tools for teaching math. I even find myself getting excited about it which is completely new for me, I have always hated math!
ReplyDeleteChapter 11 – Whole numbers and place values are something that my mentor class has been dealing with all semester it seems like. Early in the chapter it mentions that we learn our numbers at a very early age, but we don’t learn the understanding of those number or place values until much later. That is something that my students seem to be struggling with a little bit in 4th grade. They have a hard time understanding that 48 is actually 4 tens (or 40) and 8 ones. They are getting better but early on they really had a hard time. This chapter continued to hit home for him as it discussed the models for place value and grouping. The students in my class use a lot of the snap cubes and have recently started using the base ten blocks. Dr. Stramel used the ten-frame cards in class, which was the first time I had seen that model. When you do understand the idea of place-value and the number sense behind it, it sometimes is hard to think back to the time when you did not know it. I feel that this chapter does a great job of reminding us what that was like and how we can relate to our students who are just learning.
ReplyDeleteChapter 12 – This Chapter talks about strategies for Whole-Number computation. Again, I have been in 4th grade math and this topic really struck a chord with me. It has been so interesting to listen to some of the students in my class talk through the way they solve their problems. Not all of the ways are correct but it is neat to see those gears moving. I really like how Dr. Stramel puts it in her class, it really doesn’t matter how a student gets the answer so long as they can explain how they got there. I agree with this, I don’t really believe that there is just one way to solve problems. It is very interesting to see and read about the examples that were shown and discussed in this chapter. Many times I have asked student why or how and every time it seem I am in awe of their thought process – I love it everytime.
Chapter 13 Computational Estimation with Whole numbers is a concept that doesn’t get enough credit in our text books and curriculum but is very important none the less. Estimation is something I think can be a difficult topic to learn if you haven’t learned your place-values well. If you don’t have a firm grasp on the place-values, learning estimation can really be a struggle, at least with my experience. I do like the idea of using the real life word problems. In my mentor 4th grade classroom they really spent a lot of time on the estimation chapters. It was interesting to read on the strategies after observing the lessons in the classroom. Students seem to “get it” or really struggle when it comes to estimation. With front-end it sometimes seems too easy – you look at the leading number and ignore the rest – what’s the catch! I think that the rounding makes more sense to the students, but again, they really do have to know their place-values.
@ Kristie C –
ReplyDeleteI love that your intern classroom seems to make learning the place-values fun and important. I love the idea of grouping the straws. Being able to understand what is going on and gaining that number sense is SO important. I also think that many times we forget about the value or the presence of zero, so that is neat that your teacher is making sure to include that in the lessons as well. The pumpkin seed idea was really great! I think it is good to keep things fun for kids and place values should not be any different. I also think the 9+ shortcut is a great idea to share with everyone. I love that idea of adding 10 and then taking off 1. Sounds like you are in a great situation with your intern class and your subbing! Keep the good ideas coming.
Chapter 11, 12, and 13 were all fantastic and informational chapters. I really liked how chapter 11 started out talking about place value! It is so important for students to know and understand place value. I also love how this chapter mentioned the hundreds chart. In the classroom I am interning in the hundreds chart is used daily. It is interesting to note when students have it memorized. I was not a fan of the hundreds chart at first, mostly because I did not understand how students used it. But seeing it used is awesome and some students really benefit from the use of the hundreds chart. In chapter 12 I loved all the different strategies like mental math. There are so many different strategies that help different students. I love mental math and it is so interesting to see how different people add and subtract mentally. Chapter 13 mentioned the hundreds chart again. I like how this gave me more insight. It is like a pattern and patterns helps students so much! Awesome!
ReplyDelete@Megan B
Zero the Hero sounds really neat!
@ Kristi P
I agree that these chapter were very informative. Estimation is something that is very interesting. It is very interesting watching students do ball park estimating. Some kids really struggle with this process.
Chapter 11 focuses on place value. The 2nd grade class I intern in has place value pockets. The teacher gives them a number and they have to put their number cards in correctly to show the number she is asking for. They also use it for rounding numbers. She has them put the original number and then they talk about what two numbers it is between. They then have to put in the correct number it would be rounded to. They have pretty much only worked on ones and tens so far. They have done a few hundreds, but they are still having a little problem with ones and tens. Chapter 12 talks about whole-number computation. As long as the student is doing the work and coming out with the right answer, they should be able to do the problems their own way. Teachers have a real problem making it their way only. My son is in the 8th grade and his teacher marks answers wrong if it is the correct answer and all his work shows right, but it is not done her way. She has to understand there is more than one way to do some problems. The teacher I am observing has a huge thing for doubles plus one or minus one. The students really seem to understand that concept when they are working with doubles of a number. Chapter 13 is about estimation of whole numbers. There are three ways to do estimation dn this chapter focused on talking about all three. The students I intern with love to do estimation. They have trouble sometimes about whether they estimate up or down. The teacher gave a chart of a mountain climber and he goes down for number 0 through 4 and up for numbers 5 through 9. They really seem to catch on to it this way.
ReplyDeleteIn response to Lindsay H---
ReplyDeleteThe classroom I am in is also a huge 100 chart user. They use it all the time. I have taken so many notes on how to use it and what it can do for students that are struggling with place values and other things. They have done patterns to see the difference in how numbers go up by a certain number. They were able to see when counting by 5s that only two rows of numbers would be used and not to even look at the other rows. It helped a lot of them struggling.
These were great chapters for me this past couple of weeks because my lesson I taught in my observation class was dealing with place value and estimation. In chapter eleven I loved the section about models for place value. Anytime manipulatives can be used I think teachers should take full advantage of that. I like how it took a group of something like pop cubes to make that double-digit number represent just one entity to show that a number in the tens place is both a single and double digit number. I used this representation when I asked my students to break apart a large number like 415. I had them break it apart and show me what each number truly represented in its place value. So the one in 415 was a single stack of 10. This helped then recognize that even though it was a one since it was in the tens place it was a multiple of 10.
ReplyDeleteChapter twelve discussed developing strategies for whole-number computation. I didn’t have much time to teach my lesson but in review I had the students work through problems in a group. I would ask one student to show me how they achieved the answer they did and then I would ask if anyone did it differently. This allowed me to see many student-invented strategies. The text stresses the importance of letting students explore their own strategies instead of just making them do it one strict way. It’s so amazing to see what students come up with when they’re solving a problem. It’s even more amazing to listen to them explain their procedures to their piers. One problem I gave the students was 800 X 4. One student showed his piers that he multiplied 8X2 to get 16 then added 16 to 16 to achieve 32 and then just brought down the two zeros because, as he said, the zeros always win. Some of this might have seemed like more work to other students but it was interesting to see how each and everyone thought about each problem so differently.
Chapter thirteen discussed the focus of my lesson, which was estimation. I really liked the cluster problem examples because they related back to invented strategies. With my estimation lesson I did quite a few estimation activities with the students but one of them was having them estimate the amount of skittles in a jar. I gave them a visual aid by showing them what a group of 100 skittles looked like first. When I asked for the students estimations I also had them explain how each one of them came to their conclusions. One student said she recalled what one hundred skittles looked, just one layer on the bottom. She then counted the layers she saw in the full jar and multiplied that by 100 to achieve her estimation. There were many ways to figure out a close estimation and I really enjoyed being able to listen to each student’s method. My favorite part was that they got to learn from one another and they truly did. Students were asking one another “How does that work” and “Why did you do it this way” and then were having “Ah Ha!” moments all over.
These chapters helped me implement my lesson in a way that students could learn from one another. It was a very eye opening experience for me.
April,
ReplyDeleteThank you for sharing the place value pockets idea. That sounds like a great way to teach place value to students and to help with rounding also. I know students can greatly struggle with place value so this activity sounds like one that can help them by being practiced all year long. I also completely agree with what you said about allowing students to work through problems in their own way, as long as they achieve the correct answer. I think that fact has been stressed to us all year but it’s important for us to recognize that many teachers like the one in your example, still view math as their way or the highway. I think that’s one strength our generation will bring to the table. We will be able to allot our students more freedom in mathematics and possibly influence our professional community to do the same. Good post!
Chapter 11:
ReplyDeleteChapter of the text book Elementary and Middle School Mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed “a complete understanding of place value, including the extension to decimal numeration, develops across the elementary and middle grades” (Van de Walle et al., 2010, p. 187). Place value can be difficult for some students to understand but it is critical to understanding mathematics. Van de Walle states in the textbook that “place-value understanding requires an integration of new and difficult-to-construct concepts of grouping by tens with procedural knowledge of groups are recorded in our place-value scheme, how numbers are written, and how they are spoken” (Van de Walle et al., 2010, p. 188). It seems to be difficult for students at first to group by tens but then they start to see how different numbers will group together and the numbers relationship with each other.
A piece of information that I learned from this text was how the text book mentions to go beyond 1000 cubes so students can see what the bigger numbers look like as well. This can be fun for students to see because they will start to understand the numbers that they will be experiencing in the future. I also liked how the book mentioned using the word “and” in numbers. I admit I do use the word “and” incorrectly at times
A piece of information that made me look at my own experiences was when the textbook discuss the hundreds chart on page 200. I remember when I was younger the hundreds chart was so important to me and I used this tool all the time. I think that this is like a comforting thing for students to use if they need extra help. I know I would use this tool if I for any reason was unsure of the problem.
Chapter 12:
Chapter twelve of the text book Elementary and middle school mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed different ways that people figure out mathematical whole-number problems. We need to teach students that there are different strategies that will work for different situations and they do not have to stick to a certain way to do something. When students have a range of strategies to solve problem then it becomes less difficult to solve that particular problem.
A piece of information that I learned from this text was how it had examples using the number line. I would do a lot of these problems the same way but I never thought of using the number line before. The number line can be important because it relates the numbers to each other.
A piece of information that made me look at my own experiences was the section on “direct modeling” (page 214). According to the textbook direct modeling is “the use of manipultives or drawings along with counting to represent directly the meaning of an operation or story problem” (Van de Walle et al., 2010, p. 214). This is a strategy that was so important to me all through school because I am a visual learner.
to be continued
continued...
ReplyDeleteChapter 13:
Chapter thirteen of the text book Elementary and middle school mathematics: Teaching developmentally (7 th ed.) by Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. discussed that “computational estimation skills round out full development of flexible and fluent thinking with whole numbers” (Van de Walle et al., 2010, p. 240). Estimating can be difficult for some students because there is not exact answer and the answer will variety. Students are usually taught that they have to have an exact answer but now they are asking not to be perfectly correct.
A piece of information that I learned from this text was the over and under approach on page 243 of the text book . This something that I never used when I was in school but will be great for students. This way students can see the starting off point of estimating.
A piece of information that made me look at my own experiences was when the book mentioned to use a “nice number” on page 246 of the text. This is something my teachers telling me when I was in school. I had to pick a number that I felt comfortable using and that is how I knew my estimation was on track because estimating should be easier that really doing the proble.
References:
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics: Teaching developmentally (7 th ed.). Boston: Allyn & Bacon.
Chapters 11, 12, and 13 discuss how to help students develop math concepts and all give many wonderful ideas for activities. Chapter 11 discusses the concept of basic ideas and place value. Throughout the text it was emphasized that groupings needed to have meaning for students. In order for them to develop the concept fully, they need to have a meaning to group and this is accomplished through starting with ones, giving them many opportunities to group, and then moving on to 10’s. I also liked the section that discussed the “strangeness of ones, tens, and hundreds.” It does sound strange, and must sound especially strange to say “ten ones make one ten.” It helped me understand more fully why place value can be difficult for children. I also appreciated all the different activities that the text provided that can be done with a hundreds chart. I haven’t spent much time in the lower grades, so this is good information for me to have if I ever teach in one of the lower grades.
ReplyDeleteChapter 12 discusses strategies for whole umber computation. This chapter was very interesting to me because it gave many wonderful activities for adding, subtracting, multiplying and dividing that were so different from how I was taught. I also liked the section on invented strategies. Again, it is very different from how I was taught but I think that students can better develop an understanding of computation through the use of invented strategies as long as they are mathematically sound.
Chapter 13 discussed estimation. I think in the past I have taken the fact that I know how to estimate for granted, and didn’t fully realize the importance of this skill, but after reading this chapter I feel I better appreciate it as being a key skill students need. I really enjoyed the over/under activity we did in class and can see myself using this in my class someday. Overall, these chapters gave me many great activities as well as a much better understanding of the types of activities that can be used to help students develop math concepts.
@ Jennifer p
ReplyDeleteI also liked the over/under activity when I say it in the text and also when we played it in class. I think this is a great way to give students practical examples of when they would use estimation as well as further practice in estimating.
Chapter 11 discussed whole-number and place-value concepts and these can sometimes be difficult for students to understand. Teaching students to count by ones, tens, and hundreds is so important and are basic skills that they will continue to use as they progress through the upper grades. I believe that it’s never too early to start teaching students about place value, even if it’s only by using different colored sticks to represent the ones, tens, and hundreds. They do this in my kindergarten internship classroom when they discuss how many days they have been in school. They have a chart that shows the number of days and these are represented by the appropriate sticks. I liked how the text mentioned that the term “seven ones” can be very confusing to students and this is something that we as adults probably take for granted since we already understand the concept of place-value. Using many teaching techniques and allowing the students to use a variety of manipulatives will help make these concepts easier to understand. Using ten frames and having the students draw pictures to represent problems are other ways they can get more comfortable with base ten.
ReplyDeleteThere were tons of ways to compute whole-numbers as well as student-invented strategies discussed in Chapter 12. We were taught how to do most computations the traditional ways and although this is not wrong, I think we definitely missed out on many learning opportunities. Students should be able to solve problems however feels comfortable to them and they shouldn’t be discouraged from this simply because it’s not the method that the teacher uses. Dr. Stramel mentioned that sometimes teacher may be afraid to let students use their own strategies because they weren’t taught like that and therefore, might find it difficult to answer any questions that the student has about this strategy. I think that teachers should embrace this and use it as an opportunity to learn new strategies from the students. Since I was taught using the traditional algorithms, I found some of the strategies presented in the text to be more work or more difficult. Although it’s tough to learn how to do things new ways after you already have the method down, we could all benefit from learning how to do things in other non-traditional ways. I enjoyed trying to come up with alternative ways to solve the problems in class.
In Chapter 13, there were many activities presented to help students practice estimation. I’m glad that Dr. Stramel made sure that we knew that estimating is not the same as guessing. The more we estimate over time the better we will get. The text discussed rounding and clustering as ways to estimate. There are many real world situations where estimation can come in handy such as guessing how much food to cook for a family dinner or estimating how much money your purchase at the grocery store will cost. It’s important for students to have a lot of practice with estimation while using a variety of techniques. Although some groups of students may end up with different answers after estimating the answer to a certain problem, they should explain how they reached the answer. It was cool to see the ways that all of the students in our class estimated the answers to the problems and they used some methods that I didn’t even think of, such as counting by 25.
Chapter 11 talked about whole number place value. It mentioned that students learn as early as kindergarten how to count to 100. Counting is great, but as a teacher you need to be able to teach other ways to count than just by ones. It is good for students to learn concepts like grouping by twos, fives, or tens.
ReplyDeleteChapter 12 talked about whole number computation. This chapter talked a lot about student invented strategies, we talked a little about this in class too. I think these are great because they are ways that students came up with. As a teacher, we want the students to learn the way we are teaching it, but if it is easier for them another way, why not let that student use the way that is easiest. As long as it works and they can explain why it works they should be able to use it.
Chapter 13 talked about estimation. It told us not to focus on an answer but on methods of how to find the estimation. Teach rounding or context to help with estimating. Students sometimes focus to much on finding the answer and really need to focus on the method and way of finding the way to the answer.
In response to Meghan B:
ReplyDeleteZero the Hero sounds awesome and I bet the students love it. I’m glad to see that your internship teacher is making a big deal about base ten. I like that you mentioned how it should be acceptable to students to solve problems in a way that makes sense to them, as long as they can explain how the process of how they did it. I agree that the grocery store is a great place for estimation.
Jennifer P,
ReplyDeleteI like how you talked about nice numbers which are numbers that the student feels comfortable with. I think this is a great way to teach and help students understand. Some students may be ready for three digit numbers and some may not, but at the same time they can do different numbers and still work on their estimating skills. As long as they are doing the work correctly and finding the right answer why not let them use a number they are comfortable with.
I didn’t realize the plethora of ways there are to use base ten manipulatives. I don’t remember ever seeing base ten blocks or using many manipulatives when I was in grade school. I am grateful for the opportunity to learn about different ways to teach children this oh so important skill. The bundling coffee stirrers reminded me of a strategy I have seen our first grade teacher use. Every morning she holds a math meeting in which all the children sit on the floor near the math bulletin board. They count the number of days they have been in school using straws. Every time they get ten straws they bundle them with a rubber band and place that bundle in a tens cup. When they get ten of the ten bundles, they bundle those together and place it in the hundreds cup. I was surprised to read in chapter 12 that you shouldn’t begin teaching traditional algorithms first, but rather invented strategies should be first. For some reason I assumed that you should teach the traditional ways first and let the students go from there. It makes sense though that they might feel there is only one “right” way if you teach traditional first. Lately as we have been discussing invented strategies in class a lot, I have been wondering how to effectively show students what I or other students see so automatically. The diagrams of each strategy provided in the examples in chapter 12 are the answer. I am a little disappointed with myself that I did not think of that on my own. It’s a good thing I have this book! Chapter 13 is all about teaching estimation. I really like the calculator range game activities because they give the students practice estimating, and the use of the calculator makes them self-checking. The students know right away whether or not they made a reasonable estimation.
ReplyDeleteJordan O., I completely agree with you that students should be able to use strategies that make sense to them as long as they work and can be explained. Sometimes the traditional ways just don’t make sense to some people. If we required everyone to solve problems the exact same way, we would be leaving many students behind who are fully capable of solving the problems too, just in different ways.
ReplyDeleteChapter 11 was about whole number and place value concepts. We covered many different strategies in my internship dealing with place value. I thought it was interesting that this chapter actually had some of the same example of activities that we used in my internship classroom. One of the examples the chapter mentioned was; 7 tens and 3 ones, 73 all together.
ReplyDeleteChapter 12 was about whole number computation. there were many examples of student invented strategies. I found all of the different strategies very interesting. Very few of them looked familiar to me. I'm not sure if it's because I was never taught these strategies, or I have been doing the traditional strategies for so long that it just became second nature to me. I did find the information very helpful and I will definitely keep these strategies in mind for the future.
Chapter 13 was about using computational estimation with whole numbers. I liked the strategies mentioned where they tell students to round the problem to the nearest ten and then estimate the answer from there. I feel this would be greatly beneficial for students to use. I know there are quite a few students in my internship that use this strategy.
Elizabeth Adams,
ReplyDeleteI was also unaware of all of the manipulatives that can be used for base ten problems. I don't remember using hardly any of these strategies. I did find them to be very helpful and I will definitely be using them in my classroom.
Chapter 11 was all about developing place value knowledge. As we have talked about in class, place value and base ten are extremely important concepts. Every student needs to understand these ideas in order to understand higher-level concepts. After reading the section, “The Strangeness of Ones, Tens, and Hundreds,” I completely understand why this concept is so hard for children. It seems so simple, but when I read this section and thought about it, it is very confusing. There are a lot of great activity ideas for helping students learn place value and base ten in this chapter. One idea I really liked from the book was to use base-ten language when first introducing oral names of numbers. Doing this will help students understand what the standard number words really represent.
ReplyDeleteChapter 12 covered another important topic. It was about strategies used for whole-number computation. This is another topic we have covered a lot in class. When we are given a problem and asked to come up with different ways to arrive at the answer. In class, we always come up with several ways to complete one computation, and often times one group comes up with an idea or two that others did not. This just goes to show that we all think a little differently, and some strategies make more sense than others to different people. This is why it is important to allow time for what the book refers to as student-invented strategies. We need to give students the opportunity to complete some higher-order thinking and come up with methods for completing computations that make sense to them. Once students have been allowed to do this, then we can introduce them to the traditional algorithms.
Chapter 13 covers using estimation to complete computations. This is a strategy that I do not remember using a lot of in school. Therefore, it is not something that I am completely comfortable with. However, I do see why estimation is an important skill to have. In real-life situations we don’t always have time to stop and do exact computations, estimation is much quicker. The 3rd grade class I am currently interning in did a short unit on estimation to solve multi-digit addition and subtraction problems. Many of the students struggled with this concept. I found several great ideas and activities to suggest for my students to use. One activity I thought was really good and the students would enjoy is the Box Math activity.
Andrew D --
ReplyDeleteI like your example of the WalMart scenario to explain why we estimate to children. If we provide students real life examples and scenarios to work through when learning estimation, rather than just numbers, they will understand its use.
Jennifer Pen Reply to Shannon,
ReplyDeleteGreat post! I agree with you. Using popcicle sticks is a great way to show students that these numbers can be separated into groups of different numbers. We do this with straws when I go into some classrooms. We will count and group the days they have been in school.
I liked also how you mentioned that some students will do extra work to get an answer but it is easier for them to do it that way. I would always do that do. Even if a my way may take longer it is easier for me and I would rather problems take longer and be easier.
Having these different strategies help students learn from each other the different way they may do things.
Chapters 11-13
ReplyDeleteUsing Algorithms can be fun to me, but very complex. Again, I think this goes back to the idea that when I/we were in school, we didn't have near as many options-it was just standard problems/traditional problems. Nowadays, students have more and more options, which is great for their variety of successful ways to complete a problem. As long as the student is getting the correct answer, then it's okay. Some algorithms, I feel take longer than in your head, such as the using the counting blocks and taking away for each value. A lot of times, some students may not be able to do this in their head, but I feel for me as a student it would been more difficult and overwhelming. On the other hand, I do feel that array is fun and informative. I think array gives the students a chance to visually see and display the numbers being added together, or multiplied together. Using manipulatives I feel ALWAYS helps. Even for me as an adult, I sometimes have to stop and draw out pictures. I want to use these resources within my future classroom.
Elizabeth-
ReplyDeleteI too was unaware of all the manipulatives! It's amazing how far mathematics has come and how far our future students can become because of the resources. They are visually stimulating, as well as hands-on. I feel all subjects are better presented while incorporating hands-on activities.
Using manipulatives to group and count by ones is a great way for children to learn this concept. They can count the best way for them and still arrive at the correct answer. I think that teaching students to count by 10 is be the first objective. The counting in groups activity would be a great exercise for children to learn how to count by 10 as well as the groups of 10 activity. Having the teacher model how to do the problems is a way for the students to see what to do. Once the students get the hang of counting by 10’s then they can invent their own strategy of what works best for them. One of the most important things that I took from chapter 12 is to go beyond teaching traditional algorithms, but they will happen. Lastly, chapter 13 talks about estimating with whole numbers. To teach estimation use real examples, the language of estimation and context. Focus on methods and not the correct answers when dealing with estimating.
ReplyDeleteIn response to Rachel C –
ReplyDeleteAlgorithms can be fun, but mixing it up of how you teach them makes it interesting and allows the students to get an idea that there is not a set way of figuring out problems. I agree that when I was in elementary school there were not many options or manipulatives to use. I want to make sure to allow all the resources I can in my classroom when it comes to math so students can see all the possibilities.
Chapter 11 was about place value. I can remember in school somewhat struggling in this area and I like the many examples the book shows to help me get a better understanding. It also helps in class discussing all of the information and using the base ten blocks. I have a much better understanding now. Chapter 12 was over whole number computation. I thought this chapter was very informative and gave excellent examples in the book. There are so many strategies on how you can do things and we have been learning this in class. This has been very educational for me and I can see a growth in myself in this area. Chapter 13 was about estimating and was my favorite. I loved estimating in school and it brought back some memories in class the other day when we were doing different activities. There are so many ways we can estimate and it can even get confusing as it did even when we were discussing in class as a group. I think overall estimating is important because we use it so often in our everyday lives and don't even realize it. We estimate miles we may be traveling, when buying items, telling time, etc...I really liked all of these chapters and thought they were all very informative.
ReplyDeleteIn response to Rachel,
ReplyDeleteI agree with you that it is good that children nowadays have the variety of options to help them figure out what works for them! I can remember always having to solve problems one way and one way only. By doing that you are only making that child regress, I believe. If they can do something differently that gives them the correct answer and positive learning then by all means let them! Good post!
In chapter 11 it talks about place value and how hard it is for children to understand it. I have seen children be very confused by this. When there is a number like 154 it is hard for them to grasp that 54 is 10 5's even though it is included in a number that is in the hundreds. One thing the book said in this chapter was to make sure that children do not say the word and when they say numbers, this is something that is still hard for me to do as I have always said and when saying numbers.
ReplyDeleteChapter 12 discusses the many different ways that students might use to solve math problems. I like the idea of the place value mats and I think this would be a great way to get students acclimated to adding or subtracting and keeping numbers in their place. That is something that I see in my mentor class quite a bit. Students are getting problems wrong because they line up the problem wrong and get lost in trying to keep everything lined up write. If a teacher were to use the place mats to help the students keep everything in line when they move to paper they might understand better the concept of keeping everything lined up might be easier.
Chapter 13 is about estimation & I have to admit this has not always been my strong suit. I like to have a cut and dry answer, either it is or isn't so I liked this chapter because it will help me to better understand how to teach the concept of estimation. I like the over or under idea and think it would be a great game to play with the students.
Dina,
ReplyDeleteI am the opposite of you, I do not like estimation at all, and when you say we use it in our everyday lives I agree. I will estimate but then I find myself working the numbers out to find the exact number I am looking for. I will have to work on this estimation skill to be able to teach it well :).
Katie Coulter
ReplyDeleteChapters 11,12,13
This past week’s assignment was a lot to take in. Not only was there a lot to read but the information was very important. I felt lost and overwhelmed at times. Class videos definitely helped me out as we progress through each chapter. But thinking outside the box is hard. That is why people who can think so outside and creative get paid way more than the rest of us! It was good to read about all the different strategies of presentation the book brought out and even what we did in class, not being able to use a traditional form of simple multiplication. What these chapters talk about are some very frustrating concepts for grade school children to grasp. I remember during an observation of mine trying to help my teacher reach her students with place value. They were totally lost in this and it was hard even using the base ten concept for them to grasp the amount of the blocks but then seeing it on the board in a value was like to polar opposites. Chapter 12 and 13 gets heavy as we move on to really bringing in other strategies to teach basic algorithm and estimating. I think of myself as more of a traditional type in terms of introducing a new term. I might use some newer technologies or manipulatives but other than that I think more basic and general. This could be a challenge for me. The information again in this chapter was great. There were so many unique methods brought to light for me. I am still kind of overwhelmed at the thought of using something that I haven’t mastered yet. I guess that is why they say you learn something new every day. Looks like grade school math is my new learned concept for the year!
In Response to Dina,
I have seen several post that mention how difficult place value was for them or students they have observed. I don’t remember struggling with this but that doesn’t mean I didn’t, I just don’t remember! As an adult we look at this and get a since of frustration I think when a concept like this is not managed by students. You think it’s easy and makes perfect since but for them it’s new and scary looking so many fight you on the ability to understand instead of just listening. Chapter 11 will sure be a nice reflection to have some day when we stand in front of 20 kids trying to explain place value to them!
Tessa W:
ReplyDeleteChapter 11 & 12: After reading this chapter, I feel like all of the way I understand numbers is a lot different than everyone else. Which really means that in the end, ALL of my students will have a different way to view numbers. I will have to learn to work with each one of the and accept that each of them is correct as long as the right answer is reached. Now the concepts mentioned in this chapter seem easy to me but I know when I was younger I struggled trying to figure out the right way to understand them. Each person will have a different way to learn and understand different concepts. The best way to learn math is to practice the way you best understand it.
Chapter 13:
I was reading about estimation and was reminded of how little I thought I used it. When working during a math class I don't usually think of estimating directly but then looking at how I relate math to life I use a lot of "approximately or almost" words. I really like the concept of using tens and hundreds to solve problems. I use grouping in these two areas as well as others when doing most kinds of math. This is one way that I understand and that I can relate to so very well. Grouping is a great way to connect numbers together and do math fast. Which at times is very necessary.
In response to Katie C:
I agree, there was a lot of information, but I guess it makes since seeing as there was 3 chapters put together. I also understand how you would want to stick to the basics, it is important to know what you are teaching and the basics are a great place to start. I also know that it is sometimes good to try new things and gain new experiences. Hopefully this book will be able to help you a lot through your first years of teaching!
Chapter 11 is especially interesting to me because I am teaching a 5th grader place value. Using the Groupable Models explained on page 191 is something that I am using now.
ReplyDeleteOne of the ways I used the stackable cubes is through a story. I told her she was a construction company and that I was a contractor. I told her that I had a certain number of apartments that I wanted joined together in high rise buildings. The problem came when I went to get a building permit. The city told me I could only stack 10 apartments. Well, I told my student that I did not want any partial high rises. If she could not build a ten story building I wanted the remaining apartments left on the ground level.
I then went to her and told her I had a bunch of apartments and wanted as many high rise buildings built as possible.
If she went over ten, the city came in and tore it down for violating city laws.
She was then to tell me how many 10's buildings I had and how many one's apartments I had.
We both had fun.
Jena Simms
ReplyDeleteYou mentioned that you had a hard time with estimating and learning the concept. I, too, don't remember being taught to estimate until later grades (if ever) but I know that in real life I use estimation quite a bit.
My bills for instance, are not always exact, so I will estimate each month. We estimate when creating a budget. we estimate every time we want to know about how much we need or are spending when we do not have a calculator.
i.e. cabbage is 25 cents, bread, 1.39 that's about 2.00 with tax.
Kids do not know why they need to know this and any time we can tell them why, when, or where they may be more interesting in knowing how. :)
Chapter 11-- I never realized how important the hundreds chart is to the development of place-value concepts until seeing the students in my internship classroom using it to count by 1s, 2s, 5s, and 10s as high as 2,000. I liked the ideas found in the section about the hundreds chart that involved the chart with the clear pockets to create different activities for patterns and recognizing order mistakes. I hope I can make using and learning with the hundreds chart fun and exciting for my students.
ReplyDeleteChapter 12-- Students often create their own techniques to solve math problems. Some students may not easily understand the techniques their teacher has demonstrated and sharing the techniques used by their classmates may provide them with a technique to solving equations that works for them. As adults we grow fond of the ways that have always worked for us and we need to be open to alternative strategies to assist in solving equations.
Chapter 13--Estimation can be an invaluable skill to have in different situations. I have recently used estimation to air up a tire with no pressure gauge. There are times when the instruments we need to measure, calculate, or write out a problem and we have to get as close as we can to the answer as possible by mentally estimating the answer. I don't remember doing estimation in grade school.
In response to Lindsy S.
What I really liked about CH 12 is that it discussed and presented different ways to teach different strategies to work out problems. I was taught one way and only that way was allowed. When I showed my own way to work out problems, getting the same answer as the teacher did, I would not receive credit. I like that this chapter encourages students' individuality when it comes to solving strategies. Encourage, don't discourage!
Chapter 11 discusses place value - something that has been very difficult for my internship students to grasp from day one. For some reason, they just can’t seem to remember that ones are in the “ones place”, tens are in the “tens place”, and hundreds are in the “hundreds place”. This all stems from the fact that they are not really grasping the concept of counting. For instance, they can count to twenty, but many of them still struggle with what happens when they come to 29 or 59, etc. Working with manipulatives does seem to help, but once the manipulatives are taken away, many go back to struggling again. Simple activities like 11.2 in the chapter would really help them to count to ten – and then count by tens. It is the two-digit number names that begin to throw them off (e.g. forty-seven as four tens and seven ones). I LOVE the place value mat shown on page 198! The one with the cups and beans is terrific! “Landmark number” is a term I had never heard, and I think that focusing on these landmark numbers may truly help students to have a reference point. I love the activities that this text provides. I have loved trying so many different approaches to one idea or concept in our methods class, and this book will be instrumental in helping us to do that in our classrooms in the future.
ReplyDeleteChapter 12 discusses, among many things, student-invented strategies for whole-number computation. I had grown up with teachers telling me that there was “one way” to do things. Our math methods class has really helped to teach the idea that there are MANY ways to do things. It only matters that the method produces correct results. If the student can understand it, explain it, come up with a true statement, and show that the method works in all situations, then the method is fine to use. Most importantly, it helps students to develop true number sense and understand why a solution is what it is. I will say that it would have been VERY difficult for me to embrace this idea in my classroom if I had not met Dr. Stramel and been exposed to the idea that “it is okay” to come up with a different approach. The reality is…I think many of us actually did self-invented strategies when we were younger. We just did them in the margins and erased them once we had the answer so that the teacher wouldn’t see them. I am excited that this chapter deals with multiplication! We have just begun multiplication in my internship class, and the information here will really help. We have already begun by using the same method of representation as shown on page 226 in Figure 12.14.
Chapter 13 discusses Estimation – something I have NEVER understood why it has been focused on so much with my children in school. Both daughters have brought home a week’s worth of homework assignments involving estimation, and I have always wondered why it isn’t easier to just teach them how to add, subtract, or measure to be accurate. Through this chapter and our methods class, I do now understand just how much we actually estimate in real world situations, so it is important to address the concept with our students. Sometimes an approximate answer is sufficient as opposed to an exact answer. The three types of estimation – measurement, quantity, and computational – are all something that occur frequently in the real world. I have just taken for granted that I am doing it. I actually hadn’t thought about the fact that “rounding” is a form of estimation, too.
In response to Elizabeth A regarding Chapter 11: I LOVE the method of teaching tens that your internship teacher uses! What a great idea! I, too, do not remember using manipulatives when I was in grade school. This text will be wonderful to help us help our students!
ReplyDeleteIn response to Allison G regarding Chapter 12: I agree that it has been a real eye-opener to find that we often think differently in our class about how to come up with the same ending result. I have enjoyed watching the methods that other students have shown, and it has really helped me to understand the importance of allowing time for student-invented strategies in our own classrooms in the future.
In response to Lindsay S regarding Chapter 13: I took estimation for granted, too. I didn’t even realize I was doing it, so I never really thought about the importance of it. Now that I have read this chapter, I really see how much it is used in real world situations, and I am thankful that I understand that now. I am certain that I will give this concept its due attention when I teach in the future. It truly is VERY important!