When I was reading chapter 8 over developing early number concepts and number sense I was able to learn lots of great information throughout the chapter. I liked how the book gave a clear definition of the term number sense so I was able to become more knowledgeable on the subject. I also learned more about the four different types of relationships that children develop with numbers which are patterned sets, one and two more, one and two less, anchors or benchmarks of 5 and 10 and lastly part-part-whole relationships. I loved how the book went into detail about each of the relationships and also showed us the reader an example and an activity associated with the relationship. When reading through the chapter and the activities associated with the chapter there were 28 different activities that a teacher could use in his or her future classroom. This chapter will be a great resource for me when I begin teaching because I can come back to this chapter and look at all of the different activities associated with number sense. I also enjoy performing the different activities in class so that I get the hands on experience in performing the activities so that I can decide whether or not I would want to use the activity in my future classroom. Overall I learned lots of great information about number sense when reading through this chapter.
Chapter 8, More – less- same, the basic concept that children start with to learn to add and subtract. I know it sounds easy, but with working with children I’ve found it’s not easy. I have even resorted to using candy on one child. She can be a little stubborn and manipulative did not work so I tried M&M’s and they worked great. When you break it down I can’t believe how much goes into simple addition. This chapter is jam packed with activities. I got a thought that I could put these activities along with others from the book on cards and make a file of them. Great for everyday use, easy for a substitute to pull out in a moment’s notice, or fill in when there is extra time. Using (and, is) as a way of using plus and equal. This chapter shows multiple ways of using manipulative. These basics are carried on through multiplication and division; place value, estimation doubles and near doubles. I love the fact this chapter uses graphs, because our children seem to have so much trouble with graphs. The program we use for mathematics at the school I work uses mental math and I think it’s great review for the children.
I agree with Brooke M. There really is so much information and it is broke down very nicely. It's packed with activities. It is great to teach children in many different ways because there is always several children that don't get it the first way we teach it so, different ways help children learn in different ways. It also helps children from getting board with learning. Concentrating on playing a new game may keep that child in the classroom from behaving inappropriately.
In response to Tammy M., I agree with you Tammy that this chapter is packed with different activities for all grade levels in order to help the students in the classroom understand the concept of number sense. I think that it would be a really great idea to put all of the activities in a file so that as a future teacher you will have easy access to the activities and will not have to flip through the book to find the activity. I also agree that the chapter was able to show me as reader lots of different ways that students can use a manipulative in order to help them understand the concept of number sense. Lastly I like that the school you mentioned in your blog uses mental math as a review because I think that is a great way for students to review in order to use their brain and not just a calculator.
Chapter 8 was all about developing early number concepts and number sense. Number sense in understand numbers and their relationships. This chapter discussed concepts that students learn and provided numerous activities to help students understand these concepts with the use of manipulatives. This chapter even showed software and how it can be used to help teach students these concepts. This relates back to chapter 7 and using technology to teach mathematics. One thing that the text discusses in this chapter is that numbers are related to one another in a variety of ways. I think this is a tough concept for students to understand. When they first start seeing numbers, they see them as an individual number. I think it is hard for them to understand that 7 can be 6 and 1, 5 and 2, and many other numbers can be related to 7. Students need help to see this, and some of the activities in this chapter can help. This chapter provides a list of ten research-based recommendations to help teachers develop activities for students. These are wonderful ideas for all teachers to look at when deciding on activities. This chapter will be one of those chapters that I continue to use throughout this semester and throughout my career as a teacher to find good activities.
I like the way you did not give up on your student who wouldn't use a manipulative and found something that worked for them. I agree that this chapter provides numerous good activities that you can have planned on lesson plans or you can pull out quickly when you need a re-teach or enhancement activity.
I have to begin by saying that the term number sense has always been a term I never really understood. How do we assess if a student has a good number sense? One student may be able to read numbers very well others may have a hard time with this skills but the one that can not read the number can add numbers more accurately than the one that can read the numbers. What does this say about each student? I have always wondered if there are identification tools for number sense or do teachers just know by the way the students can identify and manipulate numbers in number sentences? This chapter gave a clear understanding of what is number sense and how we can assess the students knowledge of numbers. I find that the part/part/whole relationship is a concept that many students can understand using this terminology. The literature connections at the end of each chapter have been very useful for me. I am keeping a file of literature resources. Using literature during math discussions can help students grasp math concepts.
Comment for: Elizabeth Sills The use of technology can increase a students number sense. Creating movable numbers on a Smartboard or allowing a student to use a calculator may increase the knowledge of the concept we are teaching. Putting together fun ways to learn through technology may decrease the students anxiety levels of math and give them a positive viewpoint. I would like to add that the teachers attitude toward math is another key component to the success of the students. I always say; positive attitude are contagious.
I believe Chapter 8 was jammed packed with great activities! Developing number sense so our kiddos can understand the real world can be difficult. However, I believe the more we use hands on activities, the more positive interactions our kiddos will have, and then the kids will want to learn math.
In my internship in the first grade, my teacher uses the tens mat in almost all her lessons. Our numbering system is a base ten, and if we can get our students to deeply understand numbers up to ten, aren't all the other numbers just a pattern?
One last thing before I go: I know Dr. Stramel discouraged touch points, but I have personally seen many students do so well with them. It is another strategy to learn basic math facts. And, like the calculator debate, students eventually learn the facts and will rely less on the touch points the more they have opportunities to use them.
In response to Jena, I too love the literature connections at the end of each chapter. I really enjoyed the "Goodnight Moon" activity in the previous chapter. I was tickled to see one of my favorite authors, Eric Carle was highlighted in this chapter. His book, "The Very Hungry Caterpillar" has so many extensions one could do. There are so many patterns in that book!
I love the activities that this chapter offered. I found "find the same amount" very interesting because it gives the teacher something to observe. The teacher will be able to identify level of understanding by how they pick the cards. Another thing I really liked about this chapter was the assessment points and how it indicated what to watch for. I can see to where I could utilize a lot of this chapter in my own classroom. I think as adults we take counting for granted and do not really understand how important the early stages of mathematics is. My experience has been working with older students 1-12 grade. I tell them that learning their basic facts is very important because math is a process. I still believe this after this chapter, but now I believe it even begins in preschool because one concept builds upon another.
To Lacey: I agree a lot of hands on activities is a very good way for students to work. I have never fully understood how touch math works. I think I may know now. Personally, I think touch math (if it is done the way I think) should be a last option for a student.
The activities in this chapter were actually awesome. I do think that teachers can use this in the classroom easily. Some of the ideas I see in my internship 1st grade classroom. Such as counting on and counting back. The students are basically going over things they learned last year, but moving a step forward in them all. I feel that counters are amazing. Counters help students see the problem the are doing. It is interactive and useful to every student. Even if they know the fact, it is important to get them to use the manipulative because their may be a problem that they do not know, and they need to know how to work the problem using manipulatives.
Patterns are something else I never realized were that important. Now that I am older, I do not realize I am using patterns to figure out numbers, but I am. Teaching children patterns will help them learn the numbers faster, without having to count all of the dots on the paper.
To Elizabeth: I agree that this will be a good chapter to refer to. It is hard to understand to pre-k and K students. A concept that may seem easy is actually brand new for these new learners. I think this chapter holds a lot of good activities for a teacher to use with young students.
Number sense is kind of confusing. Children each have strengths and weaknesses and we cannot say they have number sense, when we really cannot tell that well. I also felt that the part part whole concept is very understandable for students. There are so many ways to teach part part whole using different methods. I think that this is a lesson that could be taught over a week using a different method every single time.
@Jena Sims I like how you mentioned that you did not totally understand what number sense was. I think that a lot of people do not understand what exactly number sense is. I was one of those people that did not have a 100% grasp on the concept. I feel like this chapter really helped me understand a student’s number sense.
First of all I love how this chapter started out with the subtitle Big Idea. Most schools are pushing for the “Big Idea” to be displayed in all classrooms so it was very appropriate to have it start our chapter. I loved all the activities offered in this chapter. I like activity 8.5 about the rhythmic counting. I think it is so smart to have children have rhythm while they count. Kind of like when students sing the days of the week song. We are taught about multiple entry points and I think we have to use many different styles to teach our students. I really liked the general definition and background of number sense. Like others above, I was not totally familiar with the origin or the actual accepted definition.
In response to chapter eight I found the list of ten recommendations to half teachers develop high quality learning activities to be wonderful. After being in a fairly typical classroom while they are learning mathematics I have developed a deeper appreciation for the techniques suggested in this book. Our class does not use manipulatives very often, and I can’t help but think that if they did the students would understand on such a deeper level. I especially liked the suggestion about enhancing a child’s natural interest , I also liked that they make a point of reiterating that mathematics should be meaningful to the child. Regarding the concept of more, less and the same; the authors made very good points. As a mom I find myself always asking my two year old if she wants more, never have I asked her if she wanted less. I know she understands the concept of more- and probably doesn’t have an understanding of less. This is something I’m going to try to work on. I also liked the section about part-part- whole relationships. I like the way the authors suggested small things that you can do to alter the thinking pattern and inspire mathematical though in different directions. This chapter was full of amazing activities that I hope I’ll be able to bring into my internship class and hopefully spark a little light into their normal routine of… dare I say it… workbooks.
In response to Jeanette, I too liked the assessment points mentioned in this chapter. I think that the indicators are a very useful thing to include when speaking to an audience of pre-service teachers, and perhaps even a few seasoned teachers could benefit from a review of these. You are so right when you say that mathematical concepts begin in preschool. I like that the book made mention of specific ages and indicators of mathematical knowledge at those ages. Of course, every student is different, but it is nice to have a baseline to judge from. My littlest daughter, nearly two, counts backwards from eight, but she probably doesn’t really know what she is doing. However her four year old sister does it with her fingers and miscellaneous objects, so I think she understands that the numbers represent something. It is interesting to see the awareness develop and it is truly amazing.
I found the ten research-based recommendations for teachers to be really beneficial. Number sense is clearly an important aspect (if not the most important aspect) in math. These recommendations make it clearer when it comes to how I should teach math in my classroom. I think back to the lecture when Dr. Stramel had us pick which two in our opinions were the most important. I honestly could not pick two, because I think all ten have some sort of importance within mathematical instruction, none of which outweigh the others.
I also loved the activity ideas in this chapter. They are simple and most, if not all, can be made rather inexpensively. I think that any lesson that isn’t a lecture can help a student learn and grasp a concept that much easier! I also love that we were able to see a lot of these during the lecture via AdobeConnect.
You brought up a really good point that I didn’t even think about while reading. I’m around kids all the time due to my job as a nanny, and I always ask them or will be asked for more of something, but I can’t recall a time I asked or was asked for less. The concept understanding definitely needs developing. I like that you are going to attempt to make it a point to work on that with your daughter!
I also agree on the activities. I think there is something (if not multiple things) from every class I have taken that I would love to play around with in my internship classes.
I found Chapter 8 very informative. I was able to relate this number concepts and number sense to what the students are learning in my internship. I have been observing them and they are learning how to stand on the number and then hop forward or back. The students have a number line on their desks and it makes it really easy for them to complete the problem. In response to Emily- I also found the recommendations to be very helpful in teaching math in my future classes.
After reading chapter 8, I found out that meaningful counting begins around preschool. I also liked the activities and different way of teaching these materials they had throughout the chapter. That is definitely something that I would use if I were to teach students that young. I also found it interesting to read about, the relationships children should develop with numbers. Those relationships included; pattern sets one and two more, one and two less, anchors, or "benchmarks" of 5 and 10, and part-part-whole relationships. I also thought it was interesting how the chapter mentioned that just measuring and recording results will not be very effective for students unless there is a reason for the children to be interested in, or think about the results. I feel like a gained quite a bit of knowledge and got some very good ideas from this chapter.
Emily M- I also enjoyed reading about number sense. Dr. Stramel really stresses the importance of knowing number sense. Now I think we all have a better grasp of what it actually is. I found the activities to be very helpful as well. Sometimes, I have a hard time trying to think like a student at that young of an age. It's helpful having these resources right in front of us.
Chapter 8 was about developing early number concepts and number sense. I found this chapter particularly helpful since I don’t have much experience working with younger students. I really liked the way this chapter was organized, it started with explaining a concept, then went to an activity, and then also mentioned things that you should “pause and reflect” about. Many of the activities even used manipulatives, which I like because I sometimes struggle with making lessons hands on and this gave me more ideas of how they can be used. I also liked that the text stated what we should be looking for as students complete the activities, and which behaviors indicate a low or high level of understanding. Until reading this chapter I hadn’t realized fully how hard number sense can be for young children to grasp. Numbers are first taught as just individual numbers, but then students must learn the different patterns and relationships that exist between the numbers. I like how the text showed how this can be hard when it talked about the relationship for the numbers 10 through 20. “Initially students do not see a numeric pattern in the numbers between 10 and 20. Rather, these number names are simply ten additional words in the number sequence.” It seems that students would realize that the numbers between 10 and 19 are the same as the numbers before 10, but just with a “1” in front. However, the concept of one 10 and six 1’s for example (16) is hard for students to understand. Overall, this chapter taught me a lot about early number concepts, gave me many activities that could be used, and also helped me know what to look for when teaching these concepts.
I also liked the activities that were listed throughout the chapter. I especially appreciated that they were all great alternatives to pencil and paper assignments. I also feel I learned a lot about early math concepts from reading this chapter. I have mostly worked with older students (3, 4, and 5th) and so I feel I learned a lot about what concepts students must learn.
I felt as though Chapter 8 had a lot of great information. I learned that more, less,and same are concepts a child learned before they even start school. I think that goes to show that it is important for students to be learning when they aren't in school. The book mentioned how number sense can be a vague word, but I felt the definition given in the book was good. It said that number sense is when you have a good intuition about number and their relationships. Now that I have heard the definition and read it, I understand it better now. The book talked about the four different types of relationships that children can and should develop with number; patterned sets, one and two more, one and two less, anchors or benchmarks of 5 and 10, and part-part-whole relationships.I felt as though this chapter had a lot of great activities to go along with every title or subtitle. I enjoyed getting to see them applied in class even though I wasn't in the on-campus class.
In response to Matthew B, I to enjoyed the activities that were in the chapter. I felt like they were great ways the explain how to put what you read into an activity. I liked the statement from the book as well about measurement and recording. I feel it goes with most things students learn and that everything they learn needs to have a purpose in their eyes.
Chapter 8 was very informational about the basic concepts that children learn to add and subtract. This chapter was full of activities for teachers to use in the classroom. I have gained so many activities from this book and we are just in chapter 8. This chapter shows how to use manipulatives. I have been excited to use manipulatives This chapter used graphs and shows different things to do about place value. This chapter was very useful to me to help me work with children that are struggling with math. Students have trouble knowing that there are more ways to get the same answer. They need to understand that there is more than one way. These activities are great and look very interesting. I am definitely bookmarking this chapter along with a few others that have been of major interest to me.
In response to Kayla R--- I agree that chapter 8 was very informational. I enjoyed the activities that it gave in this chapter. I have really learned a lot from this textbook and along with many other textbooks I have had to use in my last few semesters of interning, I am adding this book to my group of books to keep and use often. I even think I may use some of the activities next semester during my student teaching.
Chapter 8 was about developing number concepts and number sense. The activity that stuck out to me the most was the Part-Part-Whole Method on page 134. My mentor teacher uses this method a lot in her classroom to teach about joining sentences and separation sentences. The common core standards resource they have come with weekly flyers for the students to practice this method on. The students use their snap cubes and respond very well to having a physical representation of the stories. One thing I’ve definitely noticed though is how distracting the snap cubes can be if the students are playing with them instead of using them as a math tool. It is important to watch for this and remind them that they are not toys, they are tools.
I also enjoyed the Patterned Set Recognition Plates with the different colored dots on them. This a cheap and very effective way to teach the students patterns and how a number can have several different patterns to it. Very cost-effective!!
I have also been very excited to use the manipulatives and create different lesson plans with them. When I first received my kit in the mail I went through it to see what it included. I was surprised to find so many tools I had used in elementary school but had forgotten some of them since. The activities in this textbook have been helpful and I am excited to try them in my own classroom some day.
Chapter 8 was about early number concepts and number sense. I think this is very important for students to understand how numbers are related to one another. Students so often are just give naked number problem and a procedure to follow that they loss the sense of the numbers and what they are solving for. It’s also important for them to learn these so that they can self check themselves. It drives me nuts when I see a student that is doing a division problem and their answer is bigger than what they are dividing, when I ask them how they got that answer they just tell me they followed the steps. They were unable to see the relationship between the three numbers (they didn’t have a sense of the numbers). This chapter was full of activities that a teacher could do to help student have this sense. Finally I think the use of manipulative or actions is very important a math classroom this is the only way to relate math to other areas of the world.
In chapter 8 the focus was mainly on activities that can be used to help students with number sense. Number sense is not something that comes easily to all students. It is important to find different ways to explain number sense because not all students will understand if you introduce it in a certain manner. I liked that the chapter gave all those activities that can be used to help a student with number sense. I've seen some of those activities used in my internship classroom. They use counters and base tens blocks a lot. They usually use those manipulatives to help them count on and not have to go back and count every single one again. They also used the tens frames. While using these they were learning patterns. The students knew that there were two rows of five. If the whole top row had dots and one dot was on the bottom they knew that it was 5 and they had to count on 1.
I also liked how the text talked about how difficult it can be for the students to see a relationship for the numbers 10-20. This is another time when it is important to teach the students about patterns. I remember earlier in the year I was at my internship and the students were working with money. It was hard for some of the students to see how ten pennies was the same as one dime and how two dimes and nickle was the same as a quarter. My mentor teacher did a great job of visually and physically explaining how that worked by using the base ten blocks.
Chapter 8 was about developing early number concepts and number sense. The first thing I found helpful the ten research based recommendations to help teachers develop high quality learning activities. Since most of math taught today is hands-on, this will be a good guide to go by. There was also a couple of assessment notes/tips for teachers to use, which will come in handy. The rest of the chapter was filled with wonderful activities for Pre-k to early elementary. I don't know that I can pick out a favorite because all of them were fun and educational to play. One that I will be using this week with my small group in first grade is the Ten Frame. We are studying more and less in math and I feel this will tie in very well. In fact, in the coming weeks I will probably use several of these activities with my group because they all tie with the unit they are doing on number sense. This book will be an excellent resource when I have my own classroom.
In response to Carissa K. I can easily see the how the manipulative could be distracting in a classroom. I have seen the teacher not pass them out until she is ready for the students to use them, if you just put them on their desk and tell them not to mess with them yet it always causes problems because it’s too tempting. We have to make sure that students understand that these are tools and I think the longer you use them in the classroom the better it will be. I’m all for cost effective ways, so I also liked the plates. I know there is a website for teachers telling you how to create manipulative for all subjects using very cheap material, I’m just not for sure what it’s called. My mother uses it for her science class.
I agree, number sense is not something that comes easily to all students. In my first grade internship class, the whole year is about number sense. I work with small groups of children and I find it interesting how each one of them use different strategies to get the same answer. They have taught me so much. This chapter of activities will be great to use with my first grade groups.
The chapter gives the ten research-based recommendations to help teachers develop high-quality learning activities for children ages 3 to 6, which we discussed in class. I like all the positive statements about math. Of course, that is to be expected in a Mathematics course. But it helps me to incorporate positive thoughts into my outlook on Mathematics. I am getting rather excited about teaching mathematics to children because of the fact that they have choices today in how they reach the correct answers. I like it that math isn’t just rote memorization anymore, but involves teaching tools that are hands on and give children visuals, from the figure on p. 127 with the less/same/more and the ten frames that we discussed in class as shown on page 133. This chapter was practical and full of hands-on teaching strategies. I am excited about this because I think learning should involve whatever method works, and most of the time visuals and manipulatives enhance learning.
Number sense is something that I have enjoyed learning about recently in class. Making sense of number is a topic that I remember struggling with at times when I was younger. Learning about new ways to approach it has helped me to understand teaching in a whole new way. I never knew how using manipulatives can help student's learning as much as it does. Number sense is one of the first things you learn about in school, and it is the foundation of Math Education. It seems to me that is a huge part of a students learning process- with out it I don't think they will be as successful in school. I also really enjoyed learning about ten frames- they seem like a great way to teach and learn!
In response to Carrie H: I like how you mentioned the hands-on teaching strategies. They were another one of my favorite parts about this week/chapter. I learn so much better through hands on experiences anyways- i think students do too!
To me chapter 8 was very useful. I really enjoyed all of the activities that can be used for number sense. Not only does this chapter teach us the number sense, but it provides us with ways to help students by using these activities. It is so important to do these activities, because for visual learners this helps them!
It’s crazy to me to think back at a time when I didn’t know what a number meant? The text mentions how many kids can count but don’t comprehend the physical amount that number represents. Anytime I have ever seen a toddler count I am have been totally impressed. I didn’t realize that they simply do it from observation and memorizing. Chapter 8 discusses number concepts and number sense which are extremely important for our little ones to grasp. The 10 recommendations given I think are a very structured development path for students. Just from experience, my main concern with math was the time shortage. It seemed like our math hour ran away in 15 minutes and students would still have questions. The chapter gives some really neat activities for early elementary students to do to help with number sense. I like the idea of using computers for practice and repetition. I remember doing math facts and 1 minute timed test every day but there are so many computers games that can help students hold onto the number concept and relate it to things happening in their life.
In response to Carrie H,
I can’t say I am yet excited to teach math but I am more comfortable with the curriculum compared to the beginning of the year. Like you mentioned, math isn’t what it used to be and teachers and students have options today. They have options on presentation, practice and assessment. Students need variety so nothing should ever be repetitive for you as the teacher or for your students. You can show them a couple different ways to comprehend the concept and accommodate each individual student. Hopefully by the end of the year I will have full confidence in my math teaching abilities.
Chapter eight 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. talks about how teachers can help students understand numbers. Numbers can be very difficult for some people to understand and then for other is seems to come naturally. This chapter gives many different methods and activities teachers can use to assist students in the classroom. This chapter of the textbook provided me with new thought and ideas and made me look on my own experiences. Something that I learned in this chapter of the text book was “ten research-based recommendations to help teachers develop high-quality learning activities for children aged 3-6” (Van de Walle et al., 126). I think that all these ideas are important to think when developing lessons but one this I think I view highly of is the first one which states “Enhance children’s natural interest in mathematics and their disposition to use it to make sense of their physical and social works (Van de Walle et al., 126). If students are interesting in a subject they are more likely to be active learning and want to learn about that certain subjects. Also in this chapter I leaned about many different activities that I can use in my classroom to keep math fun and interesting for my students. One game I really thought was interesting was the “Real Counting On” on page 129. This game seems like it would keep the students engaged and interesting in the activity. I always like when students can have a variety of objects to "play" with because they seem to enjoy it more. I also like the idea of the ten frame. I had never seen this before but as I was talking to different students and teachers it seems to be very popular. A piece of information that made think about my experiences was the “How Many Are Hidden Activity”. This is a game I have seen in many different classrooms play. I think this is a fun game because students can play in teams there is not a lot of wait time. There are many different strategies that I used as a child but they seem to be a lot different then what students do now. I remember using stacking cubes and that was really all. I don't think it is good to rely on too many different tools because then it is hard for students to do the math on their own.
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.
Jennifer pen reply to Katie C., I agree with you that it is important for teachers to teach math so that students will understand how to workout a problem and not just have to memorized. For example when remembering the times tables I think that it is a lot better for students to be able to know a strategy for figuring it out then have the whole thing memorized. I want my students to really think about math and think outside the box. I also like the idea of doing time tests every day so students can see their progress if nothing else.
This chapter includes information on how hard it is for children to learn number sense in a number of places and does it best to make that clear. One of the things that educated adults sometimes have a hard time realizing is how hard these things really are. This is one of the reasons why we should never say something like this is simple or this is so easy. Most likely at least one student in the class will not find it so easy and will wonder what is wrong with them, why do they not find it easy. In life there are many things that are easy for adults that are hard for children to learn, starting with walking and talking and then moving to many of the concepts learned in school.
I enjoyed reading this chapter and feel like it did its best to teach me how to teach math to children in at least certain grades. One of the things that this chapter made clear is that children will not learn math without doing math, and a lot of it. While math may be the pursuit of laziness you cannot learn it without doing it. This chapter includes a lot of examples that will help children learn the concepts covered by this chapter. I enjoyed this chapter and feel that it does a good job of covering how you can teach basic number sense to children. As a substitute teacher I have seen a number of children who are still counting fingers, at least part of the time, into second and third grade. Clearly these students still need work on number sense and basic math facts, even if they are things that they should know at their grade level. The activities in this chapter are all things that would be fun for students at the correct grade level. As teachers we need to remember to make sure they are learning the material. Learning some material is better for the children long term then covering twice that much that they did not learn.
Chapter eight discussed one of the most important math concepts students will ever learn of, number sense. I think number sense is a concept that just keeps building. Students will come to school with a good idea of what numbers are and that knowledge will build to counting, adding, relationships, and operations. Students knowledge of number sense will just keep growing and growing throughout the years. I work with students in the field who greatly struggle with math and I feel like part of the reason is because their number sense knowledge is that of a much lower grade level student. It’s not that they haven’t been taught about key concepts but it’s more they haven’t been taught it in a way that catered to their understanding. I really enjoyed all of the fun activities listed through this chapter. Especially the ones that tied in to number sense in their world. I think learning is made easier when it can be looked at though a real life situation. When a student can use their classroom as an example of being 15 feet wide rather than just seeing it in written form it makes things easier. Visualization makes things easier. This is one thing I try to do with the students in my internship classroom. I try to relate their math problems to real life scenarios. This always seems to help but I’m working on getting them do relate the problems to real life without my help. I encourage them to tell me bout any experiences or memories they have that relate to the current problem in some way. I suppose with repetition it will just become habit for them to do.
Cassandra, I also felt chapter eight was extremely useful with all of the fun activities we can utilize as future educators. I enjoy textbooks that have actual activities and games I will be able to use in the future. I was a visual learner and I feel like many students are. I also feel like if there is a fun activity or game that can be used for a concept then I would rather use it than some worksheet. I think these activities give opportunity for fun and change in the same old routine. This chapter and this book all together will definitely be an asset for us in the future!
There are so many wonderful activities in this chapter and I am anxious to try them all out, but one in particular caught my eye. "Ten Frames" (pg 133) I have been working with a student who has a very difficult time with adding, subtracting, and grouping for purposes of adding and subtracting. Right now we count on our fingers or we count items such as crayons or tongue depressors. I will ask her how much 8 + 3 is and she will count out 8 tongue depressors and put them into a pile and then count out 3 tongue depressors and put them in a separate pile and then finally count the 8 (1,2,3,4,5,6,7,8.... -pause and think-...9...10...11)
She is also totally thrown by groups of 10. I will ask her how many tens are in 32 and she might say anything from 6 to 106. I am thinking that if we work with the 10 frames she might be able to grasp hold of the idea. Any thoughts?
Chapter 8 talked about number sense, which is understanding numbers and their relationships. It is hard for students to understand that different numbers are related. I know in my internship I have a student who just doesn't understand much about math. I try as hard as I can when I am there to try and get him to understand more. It is hard for me because I have never had someone who doesn't understand like this. But, it is a very good thing for me to learn how to deal with. I think that one thing he has trouble with is understanding the relationships that numbers have. Like how 7 times 6 is 42. If he knows that, he has a hard time understanding that 7+6 is 13. It is hard for him to grasps the different signs and how the numbers fit together in a equation. But, he is getting better as the year goes on! Now I know how hard it can be to teach math!
You said math is the pursuit of laziness, but you can't learn math without doing math. I agree with you 100%. Sometimes doing math problems over and over is boring, but you have to do that to learn how to solve it. I don't think that students should be doing 50 question assignments, but I do think that 10-12 problems is a great homework assignment to have them do, just so they can do a few problems and keep it fresh in their minds. Great saying!
To Tammy I have a reward system going with one student using stones that she will count out on a grid that is 5 by 10. Each day she works well, she will receive 3 stones of which she adds to her others. She lines them up in the grid and counts them out. Her rewards come with specific amounts. This has kept her on task and especially when she see's that she only gets the stones for working hard. It is unfortunate that this is what is takes, in my grade school days, there was no such thing as a reward except for your grades. But then that was before dirt. :)
From Jennifer Pence: Chapter eight 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. talks about how teachers can help students understand numbers. Numbers can be very difficult for some people to understand and then for other is seems to come naturally. This chapter gives many different methods and activities teachers can use to assist students in the classroom. This chapter of the textbook provided me with new thought and ideas and made me look on my own experiences. Something that I learned in this chapter of the text book was “ten research-based recommendations to help teachers develop high-quality learning activities for children aged 3-6” (Van de Walle et al., 126). I think that all these ideas are important to think when developing lessons but one this I think I view highly of is the first one which states “Enhance children’s natural interest in mathematics and their disposition to use it to make sense of their physical and social works (Van de Walle et al., 126). If students are interesting in a subject they are more likely to be active learning and want to learn about that certain subjects. Also in this chapter I leaned about many different activities that I can use in my classroom to keep math fun and interesting for my students. One game I really thought was interesting was the “Real Counting On” on page 129. This game seems like it would keep the students engaged and interesting in the activity. A piece of information that made think about my experiences was the “How Many Are Hidden Activity”. This is a game I have seen many different classrooms play. I think this is a fun game because students can play in teams there is not a lot of wait time. 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.
This chapter includes information on how hard it is for children to learn number sense in a number of places and does it best to make that clear. One of the things that educated adults sometimes have a hard time realizing is how hard these things really are. This is one of the reasons why we should never say something like this is simple or this is so easy. Most likely at least one student in the class will not find it so easy and will wonder what is wrong with them, why do they not find it easy. In life there are many things that are easy for adults that are hard for children to learn, starting with walking and talking and then moving to many of the concepts learned in school.
Chapter 8
I enjoyed reading this chapter and feel like it did its best to teach me how to teach math to children in at least certain grades. One of the things that this chapter made clear is that children will not learn math without doing math, and a lot of it. While math may be the pursuit of laziness you cannot learn it without doing it. This chapter includes a lot of examples that will help children learn the concepts covered by this chapter. I enjoyed this chapter and feel that it does a good job of covering how you can teach basic number sense to children. As a substitute teacher I have seen a number of children who are still counting fingers, at least part of the time, into second and third grade. Clearly these students still need work on number sense and basic math facts, even if they are things that they should know at their grade level. The activities in this chapter are all things that would be fun for students at the correct grade level. As teachers we need to remember to make sure they are learning the material. Learning some material is better for the children long term then covering twice that much that they did not learn.
My children all had trouble counting items, they could count up to 100 or beyond great but when they had to count items they would usually all count items twice . I like the idea of having 5 children stand at the front of the room with 5 chairs and when the children start counting the 1st child sits down on 1 and so on. This gives the students a visual of what they are counting and will help them to remember that a number is not just an idea but it represents something x number of times. This chapter is just full of ideas to get your students actively involved in counting and learning what numbers represent and what happens when you take something away from a group and so on. I enjoyed it greatly. At the end of the chapter the literature connection will be a wonderful asset to us when we are teaching. We can look at that and get wonderful ideas on how to incorporate literature into our math.
I agree that when a student can see something than they can relate to it better. I have a hard to estimating what 15 feet would look like unless I saw it for myself so I imagine children probably struggle with that quite a bit. I like how you said you are trying to get the students to relate to the problems on a personal level. That will get them thinking deeper about the problem and will be something that they learn instead of memorize.
One of the things that I learned and that stuck out to me was teaching math in other ways than teaching math. I have often thought back to my days as a student in elementary school and wondered how I learned best. One of the ways I learned best was when I was learning with realizing it. I was so engaged in what was going on that I was soaking up what was being said. As I go into the classrooms and observe, I can see that this is still the case. They learn without realizing it. Integrating subjects has been a huge part of how my teacher teaches. There is always at least two subjects that she integrates and the students learn more about the subjects integrated than the subject that is actually being taught. Obviously this is not always the case but it is true in the situations that I have observed.
I enjoyed reading your post. It is important to find those areas of interests in your classroom and capitalize on those interests by working them into the classrooms. If students are engaged in the lesson, they learn much more than when they are not.
Chapter 8 talks about number sense. It had great information in it, but I still had to re-read sections to make sure I was understanding it correctly! It is crazy to think that when kids learn it is through observation and memorization. My Math internship is so difficult at times because as an adult it just comes easy to me! It is hard to teach a kids basic concepts when we just automatically know the answer. I work with a student that is very low and he does not grasp anything. I am usually pretty good at finding new ways to present information and show different ways, but sometimes i struggle with this. The book did give many great examples in how to apply a variety of activities.
I agree with you about liking the researched based recommendations when developing quality activities. It will be an excellent guide to go by. I also liked how the book gave a variety of activities to help. This can be a difficult thing to not only teach but also make sure that the children are understand the information. I think this chapter was very informative!
I thought that what Betsy brought up in class today, regarding what she had learned at the conference on Monday, about "Number Sense" was really interesting. Betsy said that there was one person who talked about not just giving the students the problem and telling them to solve it but also give them the answer and basically say, "Here's the problem and the answer now show me why it's right." I had never thought of that strategy but it makes a lot of sense to me. To me, doing that basically gives you the goal and you are trying to figure out how to get that goal. I think I would have learned some areas of math a lot quicker had that strategy been used. If you don't know the answer and you don't know how to get the answer then you are in quite a "pickle." But if you already know the problem and you know the answer then it's basically a cheap way to check your work and know if you are solving the problem correctly.
Katie C. I honestly can’t remember when I started realizing how much a number represented or what it meant. In my internship we have been going over place values a lot since I have been there and covered it in more ways than I can think of at the moment but there are some students who are still struggling to grasp that concept ones, tens, hundreds, thousands, etc. I can’t even remember covering that material in grade school because it just seems so basic to me. The students in my internship have all gotten a lot better at it but still struggle at times. I think they are all finally starting realize just what a number represents which is great.
Chapter 8 on developing early number concepts and sense seemed basic to me as a reader. However as an everyday substitute I see students struggling with this clear up to fourth grade. The chapter stated that children learn at home and in preschool to count using their fingers or manipulatives. I just subbed in preschool for eight days the last two weeks, and we counted everything!!! During calendar time, we counted the days of the month, so for September we counted to 30. Then on Monday we started in October and only had to count to then that week. We also counted how many days we had been in school and how many students chose chocolate, white or strawberry milk. In preschool, meaningful counting is very important. I feel that they have a definite meaning attached to counting in preschool. While all of the avenues discussed in chapter 8 are started in preschool, many students struggle with more and less up to fourth grade. Currently, in second grade we are working on more and less and the students are really struggling with it. I appreciate all of the activities are text offers and I am certain they will help me in the future to help my students succeed!
I really enjoyed the activities in this chapter. I feel like children take better to math when it becomes fun for them. When students are stuck doing worksheets all the time, it is much easier for them to lose interest. I wish that my math internship used more activities such as these because most of what occurs in my math internship is worksheets. I would love to see some of these activities in action. Does anyone have a story of observing any of these activities?
In response to Michelle A., I find it interesting that your second grade internship class is struggling with more and less. I taught pre-k and I recall working on more and less with those students. Most of them understood it, so I would have assumed that by the time they reached 2nd grade, that they would have completely grasped the concept. That is very interesting to me. I wonder why that is. Thank you for sharing with us!
Having worked specifically in a Kindergarten classroom room in the past many of the concepts explained in chapter 8 were familiar to me. I have had experience with students who numbers come easily too and they are able to identify the patterns of numbers immediately, then I have also worked with students who struggle greatly with understanding any concept of numbers. I enjoyed reading about the concept of one and two more, one and two less. I often catch myself focusing on only one way in which to comprehend a number but in using this concept one realizes the ways in which numbers are related to one another. The section on estimation and measurement reminds me of the 4th grade and above Accelerated Math work the students complete. There are numerous questions in regards to estimation and measurements in relation to real-world ideas and concepts such as “Which is the most likely length of the top of a desk?” A. 2 centimeters B. 2 feet C. 2 inches D. 2 miles. The student is being asked to think about the problem using real-world examples. I think concept is great for understanding measurement and estimation. In the Kindergarten classroom graphs are used all of the time. They graph everything from favorite colors to favorite foods. The students enjoy seeing the results of the entire class put all on one chart and there are many activities that teachers can have students do before and after creating the charts.
In Response to Jen- I agree that visual interpretation of math concepts is a wonderful way for students to grasp the concept of numbers and counting. I believe using visual experiences and real-world concepts is the best way to teach math to students. Instead of just seeing numbers that students are able to relate the information to things they already know. I also like the idea of incorporating literature into math lessons, but as I have been researching literature to use with my lesson plans, the higher the grade level you work with the harder it is to find goo literature to go with specific lessons.
I thought the information about number sense was interesting! After reading this chapter, I feel kind of like I'm missing out because in my internship class, there is usually about 5-10 minutes of instruction time before the students work on worksheets for the remainder of the class. There have only been a couple of times where there was an activity done during the entire class time. I feel like I am missing out on observing children and trying to assess, although difficult, how their number sense is. Over all I enjoyed the chapter, it simply made me realize what I may be missing out on.
I have found in my practicums/internships that patterns are key for primary students. Whether it's with reading or mathematics, the routine of almost memorizing helps them and encourages them to go on further and learn more. However, on the negative side, some students I have observed get familiar with the patterns and can't seem to get beyond them. It's as if they are "stuck". For me, I have noticed that it takes a while, but again, every student learns and develops differently.
I too realize now more and more how much or how little past teachers integrated lessons into mathematics. I personally enjoy when reading is integrated, which can be with ay subject.
When I was reading chapter 8 over developing early number concepts and number sense I was able to learn lots of great information throughout the chapter. I liked how the book gave a clear definition of the term number sense so I was able to become more knowledgeable on the subject. I also learned more about the four different types of relationships that children develop with numbers which are patterned sets, one and two more, one and two less, anchors or benchmarks of 5 and 10 and lastly part-part-whole relationships. I loved how the book went into detail about each of the relationships and also showed us the reader an example and an activity associated with the relationship.
ReplyDeleteWhen reading through the chapter and the activities associated with the chapter there were 28 different activities that a teacher could use in his or her future classroom. This chapter will be a great resource for me when I begin teaching because I can come back to this chapter and look at all of the different activities associated with number sense. I also enjoy performing the different activities in class so that I get the hands on experience in performing the activities so that I can decide whether or not I would want to use the activity in my future classroom. Overall I learned lots of great information about number sense when reading through this chapter.
Chapter 8, More – less- same, the basic concept that children start with to learn to add and subtract. I know it sounds easy, but with working with children I’ve found it’s not easy. I have even resorted to using candy on one child. She can be a little stubborn and manipulative did not work so I tried M&M’s and they worked great. When you break it down I can’t believe how much goes into simple addition. This chapter is jam packed with activities. I got a thought that I could put these activities along with others from the book on cards and make a file of them. Great for everyday use, easy for a substitute to pull out in a moment’s notice, or fill in when there is extra time. Using (and, is) as a way of using plus and equal. This chapter shows multiple ways of using manipulative. These basics are carried on through multiplication and division; place value, estimation doubles and near doubles. I love the fact this chapter uses graphs, because our children seem to have so much trouble with graphs. The program we use for mathematics at the school I work uses mental math and I think it’s great review for the children.
ReplyDeleteI agree with Brooke M. There really is so much information and it is broke down very nicely. It's packed with activities. It is great to teach children in many different ways because there is always several children that don't get it the first way we teach it so, different ways help children learn in different ways. It also helps children from getting board with learning. Concentrating on playing a new game may keep that child in the classroom from behaving inappropriately.
ReplyDeleteIn response to Tammy M.,
ReplyDeleteI agree with you Tammy that this chapter is packed with different activities for all grade levels in order to help the students in the classroom understand the concept of number sense. I think that it would be a really great idea to put all of the activities in a file so that as a future teacher you will have easy access to the activities and will not have to flip through the book to find the activity. I also agree that the chapter was able to show me as reader lots of different ways that students can use a manipulative in order to help them understand the concept of number sense. Lastly I like that the school you mentioned in your blog uses mental math as a review because I think that is a great way for students to review in order to use their brain and not just a calculator.
Chapter 8 was all about developing early number concepts and number sense. Number sense in understand numbers and their relationships. This chapter discussed concepts that students learn and provided numerous activities to help students understand these concepts with the use of manipulatives. This chapter even showed software and how it can be used to help teach students these concepts. This relates back to chapter 7 and using technology to teach mathematics. One thing that the text discusses in this chapter is that numbers are related to one another in a variety of ways. I think this is a tough concept for students to understand. When they first start seeing numbers, they see them as an individual number. I think it is hard for them to understand that 7 can be 6 and 1, 5 and 2, and many other numbers can be related to 7. Students need help to see this, and some of the activities in this chapter can help. This chapter provides a list of ten research-based recommendations to help teachers develop activities for students. These are wonderful ideas for all teachers to look at when deciding on activities. This chapter will be one of those chapters that I continue to use throughout this semester and throughout my career as a teacher to find good activities.
ReplyDeleteIn response to Tammy,
ReplyDeleteI like the way you did not give up on your student who wouldn't use a manipulative and found something that worked for them. I agree that this chapter provides numerous good activities that you can have planned on lesson plans or you can pull out quickly when you need a re-teach or enhancement activity.
I have to begin by saying that the term number sense has always been a term I never really understood. How do we assess if a student has a good number sense? One student may be able to read numbers very well others may have a hard time with this skills but the one that can not read the number can add numbers more accurately than the one that can read the numbers. What does this say about each student? I have always wondered if there are identification tools for number sense or do teachers just know by the way the students can identify and manipulate numbers in number sentences? This chapter gave a clear understanding of what is number sense and how we can assess the students knowledge of numbers. I find that the part/part/whole relationship is a concept that many students can understand using this terminology. The literature connections at the end of each chapter have been very useful for me. I am keeping a file of literature resources. Using literature during math discussions can help students grasp math concepts.
ReplyDeleteComment for: Elizabeth Sills
ReplyDeleteThe use of technology can increase a students number sense. Creating movable numbers on a Smartboard or allowing a student to use a calculator may increase the knowledge of the concept we are teaching. Putting together fun ways to learn through technology may decrease the students anxiety levels of math and give them a positive viewpoint. I would like to add that the teachers attitude toward math is another key component to the success of the students. I always say; positive attitude are contagious.
Lacey Keller
ReplyDeleteI believe Chapter 8 was jammed packed with great activities! Developing number sense so our kiddos can understand the real world can be difficult. However, I believe the more we use hands on activities, the more positive interactions our kiddos will have, and then the kids will want to learn math.
In my internship in the first grade, my teacher uses the tens mat in almost all her lessons. Our numbering system is a base ten, and if we can get our students to deeply understand numbers up to ten, aren't all the other numbers just a pattern?
One last thing before I go: I know Dr. Stramel discouraged touch points, but I have personally seen many students do so well with them. It is another strategy to learn basic math facts. And, like the calculator debate, students eventually learn the facts and will rely less on the touch points the more they have opportunities to use them.
Lacey Keller
ReplyDeleteIn response to Jena,
I too love the literature connections at the end of each chapter. I really enjoyed the "Goodnight Moon" activity in the previous chapter. I was tickled to see one of my favorite authors, Eric Carle was highlighted in this chapter. His book, "The Very Hungry Caterpillar" has so many extensions one could do. There are so many patterns in that book!
I love the activities that this chapter offered. I found "find the same amount" very interesting because it gives the teacher something to observe. The teacher will be able to identify level of understanding by how they pick the cards.
ReplyDeleteAnother thing I really liked about this chapter was the assessment points and how it indicated what to watch for. I can see to where I could utilize a lot of this chapter in my own classroom. I think as adults we take counting for granted and do not really understand how important the early stages of mathematics is. My experience has been working with older students 1-12 grade. I tell them that learning their basic facts is very important because math is a process. I still believe this after this chapter, but now I believe it even begins in preschool because one concept builds upon another.
To Lacey: I agree a lot of hands on activities is a very good way for students to work. I have never fully understood how touch math works. I think I may know now. Personally, I think touch math (if it is done the way I think) should be a last option for a student.
ReplyDeleteThe activities in this chapter were actually awesome. I do think that teachers can use this in the classroom easily. Some of the ideas I see in my internship 1st grade classroom. Such as counting on and counting back. The students are basically going over things they learned last year, but moving a step forward in them all. I feel that counters are amazing. Counters help students see the problem the are doing. It is interactive and useful to every student. Even if they know the fact, it is important to get them to use the manipulative because their may be a problem that they do not know, and they need to know how to work the problem using manipulatives.
ReplyDeletePatterns are something else I never realized were that important. Now that I am older, I do not realize I am using patterns to figure out numbers, but I am. Teaching children patterns will help them learn the numbers faster, without having to count all of the dots on the paper.
To Elizabeth: I agree that this will be a good chapter to refer to. It is hard to understand to pre-k and K students. A concept that may seem easy is actually brand new for these new learners. I think this chapter holds a lot of good activities for a teacher to use with young students.
ReplyDeleteJena Simms
ReplyDeleteNumber sense is kind of confusing. Children each have strengths and weaknesses and we cannot say they have number sense, when we really cannot tell that well. I also felt that the part part whole concept is very understandable for students. There are so many ways to teach part part whole using different methods. I think that this is a lesson that could be taught over a week using a different method every single time.
@Jena Sims
ReplyDeleteI like how you mentioned that you did not totally understand what number sense was. I think that a lot of people do not understand what exactly number sense is. I was one of those people that did not have a 100% grasp on the concept. I feel like this chapter really helped me understand a student’s number sense.
First of all I love how this chapter started out with the subtitle Big Idea. Most schools are pushing for the “Big Idea” to be displayed in all classrooms so it was very appropriate to have it start our chapter. I loved all the activities offered in this chapter. I like activity 8.5 about the rhythmic counting. I think it is so smart to have children have rhythm while they count. Kind of like when students sing the days of the week song. We are taught about multiple entry points and I think we have to use many different styles to teach our students. I really liked the general definition and background of number sense. Like others above, I was not totally familiar with the origin or the actual accepted definition.
In response to chapter eight I found the list of ten recommendations to half teachers develop high quality learning activities to be wonderful. After being in a fairly typical classroom while they are learning mathematics I have developed a deeper appreciation for the techniques suggested in this book. Our class does not use manipulatives very often, and I can’t help but think that if they did the students would understand on such a deeper level. I especially liked the suggestion about enhancing a child’s natural interest , I also liked that they make a point of reiterating that mathematics should be meaningful to the child.
ReplyDeleteRegarding the concept of more, less and the same; the authors made very good points. As a mom I find myself always asking my two year old if she wants more, never have I asked her if she wanted less. I know she understands the concept of more- and probably doesn’t have an understanding of less. This is something I’m going to try to work on.
I also liked the section about part-part- whole relationships. I like the way the authors suggested small things that you can do to alter the thinking pattern and inspire mathematical though in different directions.
This chapter was full of amazing activities that I hope I’ll be able to bring into my internship class and hopefully spark a little light into their normal routine of… dare I say it… workbooks.
In response to Jeanette, I too liked the assessment points mentioned in this chapter. I think that the indicators are a very useful thing to include when speaking to an audience of pre-service teachers, and perhaps even a few seasoned teachers could benefit from a review of these.
ReplyDeleteYou are so right when you say that mathematical concepts begin in preschool. I like that the book made mention of specific ages and indicators of mathematical knowledge at those ages. Of course, every student is different, but it is nice to have a baseline to judge from. My littlest daughter, nearly two, counts backwards from eight, but she probably doesn’t really know what she is doing. However her four year old sister does it with her fingers and miscellaneous objects, so I think she understands that the numbers represent something. It is interesting to see the awareness develop and it is truly amazing.
I found the ten research-based recommendations for teachers to be really beneficial. Number sense is clearly an important aspect (if not the most important aspect) in math. These recommendations make it clearer when it comes to how I should teach math in my classroom. I think back to the lecture when Dr. Stramel had us pick which two in our opinions were the most important. I honestly could not pick two, because I think all ten have some sort of importance within mathematical instruction, none of which outweigh the others.
ReplyDeleteI also loved the activity ideas in this chapter. They are simple and most, if not all, can be made rather inexpensively. I think that any lesson that isn’t a lecture can help a student learn and grasp a concept that much easier! I also love that we were able to see a lot of these during the lecture via AdobeConnect.
@ Adrianne Hoefler
ReplyDeleteYou brought up a really good point that I didn’t even think about while reading. I’m around kids all the time due to my job as a nanny, and I always ask them or will be asked for more of something, but I can’t recall a time I asked or was asked for less. The concept understanding definitely needs developing. I like that you are going to attempt to make it a point to work on that with your daughter!
I also agree on the activities. I think there is something (if not multiple things) from every class I have taken that I would love to play around with in my internship classes.
I found Chapter 8 very informative. I was able to relate this number concepts and number sense to what the students are learning in my internship. I have been observing them and they are learning how to stand on the number and then hop forward or back. The students have a number line on their desks and it makes it really easy for them to complete the problem.
ReplyDeleteIn response to Emily-
I also found the recommendations to be very helpful in teaching math in my future classes.
After reading chapter 8, I found out that meaningful counting begins around preschool. I also liked the activities and different way of teaching these materials they had throughout the chapter. That is definitely something that I would use if I were to teach students that young. I also found it interesting to read about, the relationships children should develop with numbers. Those relationships included; pattern sets one and two more, one and two less, anchors, or "benchmarks" of 5 and 10, and part-part-whole relationships. I also thought it was interesting how the chapter mentioned that just measuring and recording results will not be very effective for students unless there is a reason for the children to be interested in, or think about the results. I feel like a gained quite a bit of knowledge and got some very good ideas from this chapter.
ReplyDeleteEmily M-
ReplyDeleteI also enjoyed reading about number sense. Dr. Stramel really stresses the importance of knowing number sense. Now I think we all have a better grasp of what it actually is. I found the activities to be very helpful as well. Sometimes, I have a hard time trying to think like a student at that young of an age. It's helpful having these resources right in front of us.
Chapter 8 was about developing early number concepts and number sense. I found this chapter particularly helpful since I don’t have much experience working with younger students. I really liked the way this chapter was organized, it started with explaining a concept, then went to an activity, and then also mentioned things that you should “pause and reflect” about. Many of the activities even used manipulatives, which I like because I sometimes struggle with making lessons hands on and this gave me more ideas of how they can be used. I also liked that the text stated what we should be looking for as students complete the activities, and which behaviors indicate a low or high level of understanding. Until reading this chapter I hadn’t realized fully how hard number sense can be for young children to grasp. Numbers are first taught as just individual numbers, but then students must learn the different patterns and relationships that exist between the numbers. I like how the text showed how this can be hard when it talked about the relationship for the numbers 10 through 20. “Initially students do not see a numeric pattern in the numbers between 10 and 20. Rather, these number names are simply ten additional words in the number sequence.” It seems that students would realize that the numbers between 10 and 19 are the same as the numbers before 10, but just with a “1” in front. However, the concept of one 10 and six 1’s for example (16) is hard for students to understand. Overall, this chapter taught me a lot about early number concepts, gave me many activities that could be used, and also helped me know what to look for when teaching these concepts.
ReplyDelete@ Matthew B
ReplyDeleteI also liked the activities that were listed throughout the chapter. I especially appreciated that they were all great alternatives to pencil and paper assignments. I also feel I learned a lot about early math concepts from reading this chapter. I have mostly worked with older students (3, 4, and 5th) and so I feel I learned a lot about what concepts students must learn.
I felt as though Chapter 8 had a lot of great information. I learned that more, less,and same are concepts a child learned before they even start school. I think that goes to show that it is important for students to be learning when they aren't in school. The book mentioned how number sense can be a vague word, but I felt the definition given in the book was good. It said that number sense is when you have a good intuition about number and their relationships. Now that I have heard the definition and read it, I understand it better now. The book talked about the four different types of relationships that children can and should develop with number; patterned sets, one and two more, one and two less, anchors or benchmarks of 5 and 10, and part-part-whole relationships.I felt as though this chapter had a lot of great activities to go along with every title or subtitle. I enjoyed getting to see them applied in class even though I wasn't in the on-campus class.
ReplyDeleteIn response to Matthew B,
ReplyDeleteI to enjoyed the activities that were in the chapter. I felt like they were great ways the explain how to put what you read into an activity. I liked the statement from the book as well about measurement and recording. I feel it goes with most things students learn and that everything they learn needs to have a purpose in their eyes.
Chapter 8 was very informational about the basic concepts that children learn to add and subtract. This chapter was full of activities for teachers to use in the classroom. I have gained so many activities from this book and we are just in chapter 8. This chapter shows how to use manipulatives. I have been excited to use manipulatives This chapter used graphs and shows different things to do about place value. This chapter was very useful to me to help me work with children that are struggling with math. Students have trouble knowing that there are more ways to get the same answer. They need to understand that there is more than one way. These activities are great and look very interesting. I am definitely bookmarking this chapter along with a few others that have been of major interest to me.
ReplyDeleteIn response to Kayla R---
ReplyDeleteI agree that chapter 8 was very informational. I enjoyed the activities that it gave in this chapter. I have really learned a lot from this textbook and along with many other textbooks I have had to use in my last few semesters of interning, I am adding this book to my group of books to keep and use often. I even think I may use some of the activities next semester during my student teaching.
Carissa Kruse
ReplyDeleteChapter 8-BLOG-
Chapter 8 was about developing number concepts and number sense. The activity that stuck out to me the most was the Part-Part-Whole Method on page 134. My mentor teacher uses this method a lot in her classroom to teach about joining sentences and separation sentences. The common core standards resource they have come with weekly flyers for the students to practice this method on. The students use their snap cubes and respond very well to having a physical representation of the stories. One thing I’ve definitely noticed though is how distracting the snap cubes can be if the students are playing with them instead of using them as a math tool. It is important to watch for this and remind them that they are not toys, they are tools.
I also enjoyed the Patterned Set Recognition Plates with the different colored dots on them. This a cheap and very effective way to teach the students patterns and how a number can have several different patterns to it. Very cost-effective!!
In response to April B...
ReplyDeleteI have also been very excited to use the manipulatives and create different lesson plans with them. When I first received my kit in the mail I went through it to see what it included. I was surprised to find so many tools I had used in elementary school but had forgotten some of them since.
The activities in this textbook have been helpful and I am excited to try them in my own classroom some day.
Chapter 8 was about early number concepts and number sense. I think this is very important for students to understand how numbers are related to one another. Students so often are just give naked number problem and a procedure to follow that they loss the sense of the numbers and what they are solving for. It’s also important for them to learn these so that they can self check themselves. It drives me nuts when I see a student that is doing a division problem and their answer is bigger than what they are dividing, when I ask them how they got that answer they just tell me they followed the steps. They were unable to see the relationship between the three numbers (they didn’t have a sense of the numbers). This chapter was full of activities that a teacher could do to help student have this sense. Finally I think the use of manipulative or actions is very important a math classroom this is the only way to relate math to other areas of the world.
ReplyDeleteIn chapter 8 the focus was mainly on activities that can be used to help students with number sense. Number sense is not something that comes easily to all students. It is important to find different ways to explain number sense because not all students will understand if you introduce it in a certain manner. I liked that the chapter gave all those activities that can be used to help a student with number sense. I've seen some of those activities used in my internship classroom. They use counters and base tens blocks a lot. They usually use those manipulatives to help them count on and not have to go back and count every single one again. They also used the tens frames. While using these they were learning patterns. The students knew that there were two rows of five. If the whole top row had dots and one dot was on the bottom they knew that it was 5 and they had to count on 1.
ReplyDeleteIn response to Lindsay Sabala:
ReplyDeleteI also liked how the text talked about how difficult it can be for the students to see a relationship for the numbers 10-20. This is another time when it is important to teach the students about patterns. I remember earlier in the year I was at my internship and the students were working with money. It was hard for some of the students to see how ten pennies was the same as one dime and how two dimes and nickle was the same as a quarter. My mentor teacher did a great job of visually and physically explaining how that worked by using the base ten blocks.
Chapter 8 was about developing early number concepts and number sense. The first thing I found helpful the ten research based recommendations to help teachers develop high quality learning activities. Since most of math taught today is hands-on, this will be a good guide to go by. There was also a couple of assessment notes/tips for teachers to use, which will come in handy. The rest of the chapter was filled with wonderful activities for Pre-k to early elementary. I don't know that I can pick out a favorite because all of them were fun and educational to play. One that I will be using this week with my small group in first grade is the Ten Frame. We are studying more and less in math and I feel this will tie in very well. In fact, in the coming weeks I will probably use several of these activities with my group because they all tie with the unit they are doing on number sense. This book will be an excellent resource when I have my own classroom.
ReplyDeleteIn response to Carissa K.
ReplyDeleteI can easily see the how the manipulative could be distracting in a classroom. I have seen the teacher not pass them out until she is ready for the students to use them, if you just put them on their desk and tell them not to mess with them yet it always causes problems because it’s too tempting. We have to make sure that students understand that these are tools and I think the longer you use them in the classroom the better it will be. I’m all for cost effective ways, so I also liked the plates. I know there is a website for teachers telling you how to create manipulative for all subjects using very cheap material, I’m just not for sure what it’s called. My mother uses it for her science class.
In response to Monse R.,
ReplyDeleteI agree, number sense is not something that comes easily to all students. In my first grade internship class, the whole year is about number sense. I work with small groups of children and I find it interesting how each one of them use different strategies to get the same answer. They have taught me so much. This chapter of activities will be great to use with my first grade groups.
The chapter gives the ten research-based recommendations to help teachers develop high-quality learning activities for children ages 3 to 6, which we discussed in class. I like all the positive statements about math. Of course, that is to be expected in a Mathematics course. But it helps me to incorporate positive thoughts into my outlook on Mathematics. I am getting rather excited about teaching mathematics to children because of the fact that they have choices today in how they reach the correct answers. I like it that math isn’t just rote memorization anymore, but involves teaching tools that are hands on and give children visuals, from the figure on p. 127 with the less/same/more and the ten frames that we discussed in class as shown on page 133. This chapter was practical and full of hands-on teaching strategies. I am excited about this because I think learning should involve whatever method works, and most of the time visuals and manipulatives enhance learning.
ReplyDeleteEmily M.~ I agree that these are great activities and are mostly inexpensive to create! I will take all the help with learning tools that I can get!
ReplyDeleteNumber sense is something that I have enjoyed learning about recently in class. Making sense of number is a topic that I remember struggling with at times when I was younger. Learning about new ways to approach it has helped me to understand teaching in a whole new way. I never knew how using manipulatives can help student's learning as much as it does. Number sense is one of the first things you learn about in school, and it is the foundation of Math Education. It seems to me that is a huge part of a students learning process- with out it I don't think they will be as successful in school. I also really enjoyed learning about ten frames- they seem like a great way to teach and learn!
ReplyDeleteIn response to Carrie H:
I like how you mentioned the hands-on teaching strategies. They were another one of my favorite parts about this week/chapter. I learn so much better through hands on experiences anyways- i think students do too!
@ Carrie H.
ReplyDeleteI agree that this chapter was full of hands-on teaching strategies. It is so useful to see all of these things so we can use!
To me chapter 8 was very useful. I really enjoyed all of the activities that can be used for number sense. Not only does this chapter teach us the number sense, but it provides us with ways to help students by using these activities. It is so important to do these activities, because for visual learners this helps them!
ReplyDeleteKatie Coulter
ReplyDeleteChapter 8
It’s crazy to me to think back at a time when I didn’t know what a number meant? The text mentions how many kids can count but don’t comprehend the physical amount that number represents. Anytime I have ever seen a toddler count I am have been totally impressed. I didn’t realize that they simply do it from observation and memorizing. Chapter 8 discusses number concepts and number sense which are extremely important for our little ones to grasp. The 10 recommendations given I think are a very structured development path for students. Just from experience, my main concern with math was the time shortage. It seemed like our math hour ran away in 15 minutes and students would still have questions. The chapter gives some really neat activities for early elementary students to do to help with number sense. I like the idea of using computers for practice and repetition. I remember doing math facts and 1 minute timed test every day but there are so many computers games that can help students hold onto the number concept and relate it to things happening in their life.
In response to Carrie H,
I can’t say I am yet excited to teach math but I am more comfortable with the curriculum compared to the beginning of the year. Like you mentioned, math isn’t what it used to be and teachers and students have options today. They have options on presentation, practice and assessment. Students need variety so nothing should ever be repetitive for you as the teacher or for your students. You can show them a couple different ways to comprehend the concept and accommodate each individual student. Hopefully by the end of the year I will have full confidence in my math teaching abilities.
Chapter eight 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. talks about how teachers can help students understand numbers. Numbers can be very difficult for some people to understand and then for other is seems to come naturally. This chapter gives many different methods and activities teachers can use to assist students in the classroom. This chapter of the textbook provided me with new thought and ideas and made me look on my own experiences.
ReplyDeleteSomething that I learned in this chapter of the text book was “ten research-based recommendations to help teachers develop high-quality learning activities for children aged 3-6” (Van de Walle et al., 126). I think that all these ideas are important to think when developing lessons but one this I think I view highly of is the first one which states “Enhance children’s natural interest in mathematics and their disposition to use it to make sense of their physical and social works (Van de Walle et al., 126). If students are interesting in a subject they are more likely to be active learning and want to learn about that certain subjects.
Also in this chapter I leaned about many different activities that I can use in my classroom to keep math fun and interesting for my students. One game I really thought was interesting was the “Real Counting On” on page 129. This game seems like it would keep the students engaged and interesting in the activity. I always like when students can have a variety of objects to "play" with because they seem to enjoy it more. I also like the idea of the ten frame. I had never seen this before but as I was talking to different students and teachers it seems to be very popular.
A piece of information that made think about my experiences was the “How Many Are Hidden Activity”. This is a game I have seen in many different classrooms play. I think this is a fun game because students can play in teams there is not a lot of wait time.
There are many different strategies that I used as a child but they seem to be a lot different then what students do now. I remember using stacking cubes and that was really all. I don't think it is good to rely on too many different tools because then it is hard for students to do the math on their own.
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.
Jennifer pen reply to
ReplyDeleteKatie C.,
I agree with you that it is important for teachers to teach math so that students will understand how to workout a problem and not just have to memorized. For example when remembering the times tables I think that it is a lot better for students to be able to know a strategy for figuring it out then have the whole thing memorized. I want my students to really think about math and think outside the box.
I also like the idea of doing time tests every day so students can see their progress if nothing else.
Response to Lindsay Sabala
ReplyDeleteThis chapter includes information on how hard it is for children to learn number sense in a number of places and does it best to make that clear. One of the things that educated adults sometimes have a hard time realizing is how hard these things really are. This is one of the reasons why we should never say something like this is simple or this is so easy. Most likely at least one student in the class will not find it so easy and will wonder what is wrong with them, why do they not find it easy. In life there are many things that are easy for adults that are hard for children to learn, starting with walking and talking and then moving to many of the concepts learned in school.
Chapter 8
ReplyDeleteI enjoyed reading this chapter and feel like it did its best to teach me how to teach math to children in at least certain grades. One of the things that this chapter made clear is that children will not learn math without doing math, and a lot of it. While math may be the pursuit of laziness you cannot learn it without doing it. This chapter includes a lot of examples that will help children learn the concepts covered by this chapter. I enjoyed this chapter and feel that it does a good job of covering how you can teach basic number sense to children. As a substitute teacher I have seen a number of children who are still counting fingers, at least part of the time, into second and third grade. Clearly these students still need work on number sense and basic math facts, even if they are things that they should know at their grade level. The activities in this chapter are all things that would be fun for students at the correct grade level. As teachers we need to remember to make sure they are learning the material. Learning some material is better for the children long term then covering twice that much that they did not learn.
Chapter eight discussed one of the most important math concepts students will ever learn of, number sense. I think number sense is a concept that just keeps building. Students will come to school with a good idea of what numbers are and that knowledge will build to counting, adding, relationships, and operations. Students knowledge of number sense will just keep growing and growing throughout the years. I work with students in the field who greatly struggle with math and I feel like part of the reason is because their number sense knowledge is that of a much lower grade level student. It’s not that they haven’t been taught about key concepts but it’s more they haven’t been taught it in a way that catered to their understanding.
ReplyDeleteI really enjoyed all of the fun activities listed through this chapter. Especially the ones that tied in to number sense in their world. I think learning is made easier when it can be looked at though a real life situation. When a student can use their classroom as an example of being 15 feet wide rather than just seeing it in written form it makes things easier. Visualization makes things easier. This is one thing I try to do with the students in my internship classroom. I try to relate their math problems to real life scenarios. This always seems to help but I’m working on getting them do relate the problems to real life without my help. I encourage them to tell me bout any experiences or memories they have that relate to the current problem in some way. I suppose with repetition it will just become habit for them to do.
Cassandra,
ReplyDeleteI also felt chapter eight was extremely useful with all of the fun activities we can utilize as future educators. I enjoy textbooks that have actual activities and games I will be able to use in the future. I was a visual learner and I feel like many students are. I also feel like if there is a fun activity or game that can be used for a concept then I would rather use it than some worksheet. I think these activities give opportunity for fun and change in the same old routine. This chapter and this book all together will definitely be an asset for us in the future!
There are so many wonderful activities in this chapter and I am anxious to try them all out, but one in particular caught my eye. "Ten Frames" (pg 133)
ReplyDeleteI have been working with a student who has a very difficult time with adding, subtracting, and grouping for purposes of adding and subtracting. Right now we count on our fingers or we count items such as crayons or tongue depressors. I will ask her how much 8 + 3 is and she will count out 8 tongue depressors and put them into a pile and then count out 3 tongue depressors and put them in a separate pile and then finally count the 8 (1,2,3,4,5,6,7,8.... -pause and think-...9...10...11)
She is also totally thrown by groups of 10. I will ask her how many tens are in 32 and she might say anything from 6 to 106. I am thinking that if we work with the 10 frames she might be able to grasp hold of the idea. Any thoughts?
Chapter 8 talked about number sense, which is understanding numbers and their relationships. It is hard for students to understand that different numbers are related. I know in my internship I have a student who just doesn't understand much about math. I try as hard as I can when I am there to try and get him to understand more. It is hard for me because I have never had someone who doesn't understand like this. But, it is a very good thing for me to learn how to deal with. I think that one thing he has trouble with is understanding the relationships that numbers have. Like how 7 times 6 is 42. If he knows that, he has a hard time understanding that 7+6 is 13. It is hard for him to grasps the different signs and how the numbers fit together in a equation. But, he is getting better as the year goes on! Now I know how hard it can be to teach math!
ReplyDeleteJeremiah Gramkow,
ReplyDeleteYou said math is the pursuit of laziness, but you can't learn math without doing math. I agree with you 100%. Sometimes doing math problems over and over is boring, but you have to do that to learn how to solve it. I don't think that students should be doing 50 question assignments, but I do think that 10-12 problems is a great homework assignment to have them do, just so they can do a few problems and keep it fresh in their minds. Great saying!
To Tammy
ReplyDeleteI have a reward system going with one student using stones that she will count out on a grid that is 5 by 10. Each day she works well, she will receive 3 stones of which she adds to her others. She lines them up in the grid and counts them out. Her rewards come with specific amounts. This has kept her on task and especially when she see's that she only gets the stones for working hard.
It is unfortunate that this is what is takes, in my grade school days, there was no such thing as a reward except for your grades. But then that was before dirt. :)
From Jennifer Pence:
ReplyDeleteChapter eight 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. talks about how teachers can help students understand
numbers. Numbers can be very difficult for some people to understand and
then for other is seems to come naturally. This chapter gives many
different methods and activities teachers can use to assist students in
the classroom. This chapter of the textbook provided me with new thought
and ideas and made me look on my own experiences.
Something that I learned in this chapter of the text book was “ten
research-based recommendations to help teachers develop high-quality
learning activities for children aged 3-6” (Van de Walle et al., 126). I
think that all these ideas are important to think when developing lessons
but one this I think I view highly of is the first one which states
“Enhance children’s natural interest in mathematics and their disposition
to use it to make sense of their physical and social works (Van de Walle
et al., 126). If students are interesting in a subject they are more
likely to be active learning and want to learn about that certain
subjects.
Also in this chapter I leaned about many different activities that I can
use in my classroom to keep math fun and interesting for my students. One
game I really thought was interesting was the “Real Counting On” on page
129. This game seems like it would keep the students engaged and
interesting in the activity.
A piece of information that made think about my experiences was the “How
Many Are Hidden Activity”. This is a game I have seen many different
classrooms play. I think this is a fun game because students can play in
teams there is not a lot of wait time.
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.
From Jeremiah Gramkow:
ReplyDeleteResponse to Lindsay Sabala
This chapter includes information on how hard it is for children to learn number sense in a number of places and does it best to make that clear. One of the things that educated adults sometimes have a hard time realizing is how hard these things really are. This is one of the reasons why we should never say something like this is simple or this is so easy. Most likely at least one student in the class will not find it so easy and will wonder what is wrong with them, why do they not find it easy. In life there are many things that are easy for adults that are hard for children to learn, starting with walking and talking and then moving to many of the concepts learned in school.
Chapter 8
I enjoyed reading this chapter and feel like it did its best to teach me how to teach math to children in at least certain grades. One of the things that this chapter made clear is that children will not learn math without doing math, and a lot of it. While math may be the pursuit of laziness you cannot learn it without doing it. This chapter includes a lot of examples that will help children learn the concepts covered by this chapter. I enjoyed this chapter and feel that it does a good job of covering how you can teach basic number sense to children. As a substitute teacher I have seen a number of children who are still counting fingers, at least part of the time, into second and third grade. Clearly these students still need work on number sense and basic math facts, even if they are things that they should know at their grade level. The activities in this chapter are all things that would be fun for students at the correct grade level. As teachers we need to remember to make sure they are learning the material. Learning some material is better for the children long term then covering twice that much that they did not learn.
My children all had trouble counting items, they could count up to 100 or beyond great but when they had to count items they would usually all count items twice . I like the idea of having 5 children stand at the front of the room with 5 chairs and when the children start counting the 1st child sits down on 1 and so on. This gives the students a visual of what they are counting and will help them to remember that a number is not just an idea but it represents something x number of times. This chapter is just full of ideas to get your students actively involved in counting and learning what numbers represent and what happens when you take something away from a group and so on. I enjoyed it greatly. At the end of the chapter the literature connection will be a wonderful asset to us when we are teaching. We can look at that and get wonderful ideas on how to incorporate literature into our math.
ReplyDeleteShannon H,
ReplyDeleteI agree that when a student can see something than they can relate to it better. I have a hard to estimating what 15 feet would look like unless I saw it for myself so I imagine children probably struggle with that quite a bit. I like how you said you are trying to get the students to relate to the problems on a personal level. That will get them thinking deeper about the problem and will be something that they learn instead of memorize.
One of the things that I learned and that stuck out to me was teaching math in other ways than teaching math. I have often thought back to my days as a student in elementary school and wondered how I learned best. One of the ways I learned best was when I was learning with realizing it. I was so engaged in what was going on that I was soaking up what was being said. As I go into the classrooms and observe, I can see that this is still the case. They learn without realizing it. Integrating subjects has been a huge part of how my teacher teaches. There is always at least two subjects that she integrates and the students learn more about the subjects integrated than the subject that is actually being taught. Obviously this is not always the case but it is true in the situations that I have observed.
ReplyDeleteJennifer,
ReplyDeleteI enjoyed reading your post. It is important to find those areas of interests in your classroom and capitalize on those interests by working them into the classrooms. If students are engaged in the lesson, they learn much more than when they are not.
Chapter 8 talks about number sense. It had great information in it, but I still had to re-read sections to make sure I was understanding it correctly! It is crazy to think that when kids learn it is through observation and memorization. My Math internship is so difficult at times because as an adult it just comes easy to me! It is hard to teach a kids basic concepts when we just automatically know the answer. I work with a student that is very low and he does not grasp anything. I am usually pretty good at finding new ways to present information and show different ways, but sometimes i struggle with this. The book did give many great examples in how to apply a variety of activities.
ReplyDeletein response to Angela S,
ReplyDeleteI agree with you about liking the researched based recommendations when developing quality activities. It will be an excellent guide to go by. I also liked how the book gave a variety of activities to help. This can be a difficult thing to not only teach but also make sure that the children are understand the information. I think this chapter was very informative!
I thought that what Betsy brought up in class today, regarding what she had learned at the conference on Monday, about "Number Sense" was really interesting. Betsy said that there was one person who talked about not just giving the students the problem and telling them to solve it but also give them the answer and basically say, "Here's the problem and the answer now show me why it's right." I had never thought of that strategy but it makes a lot of sense to me. To me, doing that basically gives you the goal and you are trying to figure out how to get that goal. I think I would have learned some areas of math a lot quicker had that strategy been used. If you don't know the answer and you don't know how to get the answer then you are in quite a "pickle." But if you already know the problem and you know the answer then it's basically a cheap way to check your work and know if you are solving the problem correctly.
ReplyDeleteKatie C.
ReplyDeleteI honestly can’t remember when I started realizing how much a number represented or what it meant. In my internship we have been going over place values a lot since I have been there and covered it in more ways than I can think of at the moment but there are some students who are still struggling to grasp that concept ones, tens, hundreds, thousands, etc. I can’t even remember covering that material in grade school because it just seems so basic to me. The students in my internship have all gotten a lot better at it but still struggle at times. I think they are all finally starting realize just what a number represents which is great.
Chapter 8 on developing early number concepts and sense seemed basic to me as a reader. However as an everyday substitute I see students struggling with this clear up to fourth grade. The chapter stated that children learn at home and in preschool to count using their fingers or manipulatives. I just subbed in preschool for eight days the last two weeks, and we counted everything!!! During calendar time, we counted the days of the month, so for September we counted to 30. Then on Monday we started in October and only had to count to then that week. We also counted how many days we had been in school and how many students chose chocolate, white or strawberry milk. In preschool, meaningful counting is very important. I feel that they have a definite meaning attached to counting in preschool. While all of the avenues discussed in chapter 8 are started in preschool, many students struggle with more and less up to fourth grade. Currently, in second grade we are working on more and less and the students are really struggling with it. I appreciate all of the activities are text offers and I am certain they will help me in the future to help my students succeed!
ReplyDelete@ Dina,
ReplyDeleteBless you for working with the low end student. Sometimes it is very difficult and brings out your creativity!!
I really enjoyed the activities in this chapter. I feel like children take better to math when it becomes fun for them. When students are stuck doing worksheets all the time, it is much easier for them to lose interest. I wish that my math internship used more activities such as these because most of what occurs in my math internship is worksheets. I would love to see some of these activities in action. Does anyone have a story of observing any of these activities?
ReplyDeleteIn response to Michelle A.,
ReplyDeleteI find it interesting that your second grade internship class is struggling with more and less. I taught pre-k and I recall working on more and less with those students. Most of them understood it, so I would have assumed that by the time they reached 2nd grade, that they would have completely grasped the concept. That is very interesting to me. I wonder why that is. Thank you for sharing with us!
Having worked specifically in a Kindergarten classroom room in the past many of the concepts explained in chapter 8 were familiar to me. I have had experience with students who numbers come easily too and they are able to identify the patterns of numbers immediately, then I have also worked with students who struggle greatly with understanding any concept of numbers. I enjoyed reading about the concept of one and two more, one and two less. I often catch myself focusing on only one way in which to comprehend a number but in using this concept one realizes the ways in which numbers are related to one another. The section on estimation and measurement reminds me of the 4th grade and above Accelerated Math work the students complete. There are numerous questions in regards to estimation and measurements in relation to real-world ideas and concepts such as “Which is the most likely length of the top of a desk?” A. 2 centimeters B. 2 feet C. 2 inches D. 2 miles. The student is being asked to think about the problem using real-world examples. I think concept is great for understanding measurement and estimation. In the Kindergarten classroom graphs are used all of the time. They graph everything from favorite colors to favorite foods. The students enjoy seeing the results of the entire class put all on one chart and there are many activities that teachers can have students do before and after creating the charts.
ReplyDeleteIn Response to Jen-
ReplyDeleteI agree that visual interpretation of math concepts is a wonderful way for students to grasp the concept of numbers and counting. I believe using visual experiences and real-world concepts is the best way to teach math to students. Instead of just seeing numbers that students are able to relate the information to things they already know. I also like the idea of incorporating literature into math lessons, but as I have been researching literature to use with my lesson plans, the higher the grade level you work with the harder it is to find goo literature to go with specific lessons.
I thought the information about number sense was interesting! After reading this chapter, I feel kind of like I'm missing out because in my internship class, there is usually about 5-10 minutes of instruction time before the students work on worksheets for the remainder of the class. There have only been a couple of times where there was an activity done during the entire class time. I feel like I am missing out on observing children and trying to assess, although difficult, how their number sense is. Over all I enjoyed the chapter, it simply made me realize what I may be missing out on.
ReplyDeleteI have found in my practicums/internships that patterns are key for primary students. Whether it's with reading or mathematics, the routine of almost memorizing helps them and encourages them to go on further and learn more. However, on the negative side, some students I have observed get familiar with the patterns and can't seem to get beyond them. It's as if they are "stuck". For me, I have noticed that it takes a while, but again, every student learns and develops differently.
ReplyDeleteIn response to Joel,
ReplyDeleteI too realize now more and more how much or how little past teachers integrated lessons into mathematics. I personally enjoy when reading is integrated, which can be with ay subject.
I meant, integrated other subjects into mathematics...
ReplyDelete