Chapter 15 introduces us to developing fraction concepts. This has ALWAYS been an area I personally struggle with! In fact when taking my PPST test I actually feared having to do them! That was the only area I was truly nervous about! I think that having these issues will make me a better teacher because I will go above and beyond to make sure that my students know fractions and are comfortable with them! If they don't get a good understanding of them from the get-go they are going to struggle with them for a lifetime! I agree with the text on the importance of using manipulatives to introduce fractions (or pieces) to students. Having students make a shape out of smaller shapes and count how many pieces there are and how many pieces there are if you take away one or two. This gets their brains thinking! Possibly my favorite section in the chapter was on assessing understanding as this is SO important!
Chapter 16 is about developing strategies for fraction computation. The text stresses the importance of giving students ample opportunity to develop fraction number sense prior to and during instruction about common denominators and other procedures for computation. If students don't have a good sense of fractions, they are going to have a terrible time trying to solve them. I think that it is great when educators find ways to help students solve them. "Dividing fractions is as easy as pie, flip the second and multiple" I can still hear my 7th grade math teacher saying this!
In response to chapters 15 and 16 there were several times when I thought to myself, “If only my teachers had approached fractions and decimals in this way.” When I was in elementary school, many years ago; I had a very difficult time developing these concepts, I believe that if my instructors had spent more time working on developing the concept- and less time forcing the computations- my understanding of these concepts would be more established and complete. In fact, in chapter 16 the book says, “it makes sense to delay computation and work on concepts if students are not conceptually ready.” I think that is one of the most brilliant ideas ever- however; I find it hard to institute in this age of standards and assessments. We automatically expect that just because a child is in a certain grade that they have the conceptual understanding required to understand fractions and decimals and it is not always the case. As teachers I feel this puts us in a bind- do we do what is right for our students and focus on developing the concepts- or do we focus on the computations in order to prepare them for the assessments we know they will encounter? It is a tough question. I think in previous chapters in this book they offer several ideas for implementation in earlier grades- that if fully developed and built upon, will leave the student more capable of understanding these larger more complex ideas. I think the primary thing we as mathematics educators must focus on in fostering a numeric sense in students, giving them a firm foundation in reasoning and understanding why at an early age. Then later down the road- when confronted with more complex ideas- the students will not shut down, but rather embrace the challenge of more complex ideas because they feel confident in their mathematical abilities. I realize I didn’t say much in regard to content within these chapters, while reading them I just kept coming back to this ‘big idea’. I feel very strongly that mathematics education in our country is struggling, and the ideas presented within this text, if implemented correctly along with the NCTM guidelines, could really help our students perform better in mathematics.
In response to Kristle C. I too was fearful of fractions on my PPST test, I have always struggled with them as well; probably because I did not have a firm conceptual knowledge of them prior to being forced to compute them using the traditional algorithms. I understand what you were saying about this inspiring you to do a better job in educating your students when it comes to these ideas because I feel much the same way. It is embarrassing to be an adult and still struggle with things you should have learned well as a child- and I don’t want children in my class to go through their life with that sense of embarrassment. It makes me want to give each student more than what I had and I think you are right on target, along with the text, when you suggest the use of manipulatives to achieve this understanding. I also liked the suggestion in the text about always working with manipulatives in more than one way (this might have been covered in lecture) but I believe the premise is sound. I may not understand it one way- but if shown an alternate way I may have a light bulb moment. That is part of the reason why this text is so enlightening to me and I think each one of us, it provides multiple ways to access each student- increasing the chances of creating an ‘I get it’ moment. Thanks for sharing the remarks of your teacher, I wrote that one down for future use- I think it is great!
Adrianne- I just re-read what I wrote and meant to write "multiply" but you probably caught on to that! Lol. I agree with you on the embarrassment of not being comfortable with things like fractions as an adult! I hope that having issues like this will indeed help us better educate and prepare our students!
After reading the topic for chapter 15, developing fraction concepts, I wanted to close my book and fun away. I usually do ok with fractions, but the thought of them scare me! I think the main thing for me and for all students is that if fractions are put into a real world situation it will be so much easier to understand. I also think the use of manipulatives is so important to help students understand fractions. I know they help me. The topic that I found the most interesting in this chapter was using number sense to compare. This section discussed how only 21 percent of fourth graders could explain why one fraction was larger or smaller than another. This is because the actual size of a fraction is hard for students to imagine. It said that they must have a strong mind-set about numbers to be able to do this. It said to help students notice that the larger bottom numbers mean smaller fractions, but this idea must be revisited so students have this information reinforced. Chapter 16 is equally as terrifying to me because it is about developing strategies for fraction computation. I found it interesting that having students draw circles is considered to be the best model for students to develop mental images of fractions. I feel like this is the most common used model, and easiest for students to understand by telling them it's a pizza or a pie. The book also suggested using a number line to model adding and subtracting fractions. I have never seen students use this for this purpose. Mixed numbers and improper fractions is what I feel like I would have the most trouble with. But, the book provides strategies for solving these problems. There were tons of wonderful activities throughout both chapters to help students with fractions. This chapter will be revisited when I am a teacher.
In response to Kristle, like you, fractions scare me. I think this might be because I never really understood the ins and outs of them. I also think this will make me a better teacher. I want all students to really get it, that way they will be ready for the next step, and won't shy away from fractions their whole life.
Chapter 15 Developing Fraction Concepts Fractions are such an everyday use just like money. I think it’s very important that children understand how many ways in real life we use fractions. I think saying three over four is a common thing to say and it will probably be hard to break when using fractions. I say that there are (denominator) pieces and we are using (numerator) pieces. I just have a thought, when teaching measurement with a ruler; we divide it up into fourths and eighths, could we use a printed ruler that has marks that are different colors? Color the ¼, 2/4, ¾ and 4/4 all the same color, that way they can visualize the marks better. I say this because many times they seem as though they can’t see the difference in the marks. I also love the Elmo’s because they really let you enlarge them for teaching. I really liked all the manipulative we have in our kits to help us teach fractions. Chapter 16 Developing Strategies for Fraction Computation This chapter started me off thinking that some of our teachers have a tool kit for each student’s, such as a zippered pencil bag. They contain certain things they will need for math; some coins, templates. I thought of making number lines, hundreds charts, and other templates laminated. I really used the pause and reflect and I think they are very effective teaching tool in this chapter. Fraction computations not only require you to add and subtract them but you have to understand them to begin with, if they don’t get fractions then adding or subtracting them only makes it more difficult.
In response to Adrianna, your right it can be very uncomfortable as an adult and not knowing fractions well. It is very important for them to understand them because we just continue to build onto the basics as we go along. They need to feel comfortable learning. I think teaching has changed so much. It used to be drilled into us, forced on us. We didn't have ways to teach children that were not only fun but, where we could apply to everyday use and visually see.
Chapter 15 talked about the different strategies that can be used for computation with fractions. When it came to adding and subtracting the one strategy that I really liked was the number line. The reason that I liked it so much was because it could be related to using a ruler and measuring things that I build is where I use fractions the most. A number line, such as a ruler, can help students get a better grasp of adding and subtracting fractions because they can visually see what it is they are adding. An example would be 3/4+1/2. If the student knows that there is two 1/4’s in a 1/2 then the student can count the two 1/4 on the number line to find the answer. It personally helped me out the most when I could use the number line and actually see it when I was learning how to add and subtract problems.
Tammy M I completely agree that children need to understand how they will be using fractions in everyday life. Whether it’s with money, using a ruler, etc. The more ways that information can be related to everyday life the more willing students will be to learn the material. I know that is what worked the best with me. Knowing that I was going to be using the information someday helped me to focus more on the material.
I have to begin by saying, "Why didn't I have a teacher who taught me this information?" I feel better now. Again my favorite part of this chapter was the literature connection at the end of the chapter. Maybe this section continues to be my favorite because I love literature. When I can make a connection between literature and math in my classroom I will have a smile on my face. I believe that using the appropriate language when teaching fractions can cut down on much of the confusion that I felt when I learned about fractions. Many teachers use different terminology and this is a point of concern for me. In my classroom I will make sure to call a fraction bar what it is: a division sign. Increasing the number sense when teaching fractions is also another key objectives for me. Continuing to expand the number sense even with fractions is critical to connecting the dots for students. Chapter 16 is another chapter I found to be exceptionally well written and focused on developing strategies for fraction computation. I find that 6th grade students that I test have a hard time with this concept. Changing a fraction to decimal and mixed numbers is a skill that needs to be practiced and practiced. Showing students how one fact relates to another fact is key to making the connection between decimals and fractions. I especially like figure 16.8 and how the author shows the starting amounts, shows the fraction of the starting point, and shows the solution. Woo Hoo for the literature connection at the end of the chapter.
In response to Adrianne Hoefler: I feel the same way about learning fractions. At no point did I feel confident in my computation abilities pertaining to fractions. I did not fully understand fractions until I was an adult. The strategies in these chapters were always visual. I think this was a big difference in the way I learned and they way I will teach fractions.
I related this chapter back to the discussion that we had in class a week or so ago. I’m glad to see that there are many different ways to teach fractions to students. As we said in class, we were taught using a pie or a circle but how often do we actually divide up a circle in real life? When we were presented with fraction problems in class, quite a few of us jumped to solving and illustrating the problem with a circle. I think that the fraction snap cubes are great! They can help visually illustrate a concept that can be tricky for some kids. This chapter helped me realize that we do need to incorporate critical thinking skills more into the classroom. But, we need to do it in a logical way. I liked the activity on page 292 where the student was asked to write out how they came up with the solution. This is a great way for the students to think critically, and explain their answer.
In response to Lane- I also liked using the number line. I don’t think I was shown the number line when I learned how to solve fraction problems. (At least I don’t remember). Your reason and my reason for liking the number line are the same. When you build something, you are either going to have to use a ruler or a tape measure. (You can’t eye ball it!) This would help connect a real world problem to the content.
I think that math is something that every person uses on a day to day basis. It is also something that continues to be built upon as the individual gets older. It can be difficult when a student gets behind but it can be avoided by going the extra mile with the student, which isn't always the easiest or most fun thing to do sometimes. Fractions is one of those areas that can be a little tricky. Using multiple hands-on methods of teaching fractions, I believe, can help those students understand fractions much better. Walking them through each step can be a huge asset as well. Adding and subtracting, multiplying and dividing fractions can be even more of a challenge. I think that adding and subtracting fractions can be even more difficult to teach than multiplying and dividing but the book gives great references and examples. It is fun to teach to students who do not understand a concept. Once the student understands the concept, there is nothing more rewarding than being a part of that.
I do not know if this is what you were trying to say or not but how elementary teachers teach a concept to students such as adding, subtracting, multiplying, and dividing, they will forever use that strategy once they have found one that works for them. You used the example of pies and circles that we all used in elementary school. That visual is forever in our minds and is the first thing I think of when thinking about fractions.
This week we read chapters 15, developing fraction concepts and chapter 16, developing strategies for fraction computation. These two chapters are very closely related, you must first understand the concept of fractions before you can solve problems with them in it. We spent a lot of time on fractions in class because they are such broad area to cover; and for students to fully understand them students need to see that fractions across many constructs. Students need to see that fractions are more than just parts of a whole; they are also ratios, a part of measuring, division, and operations. The main focus of the first chapter is the variety of ways fractions can and should be taught. Teachers need to go beyond the pie pieces because there are not practical life experiences. How often do we really think about the fraction of pie we ate? I also agree with Dr. Stramel about teaching realistic equations rather than ones that are not practical and just naked number problems. In order for students to want to learn fraction they have to be able to relate them to the real life and 17/8 is not a realistic fraction. Finally I love figure 16.9, it shows how to solve multiplication of fraction problems. I was always taught to just multiply the top numbers, then the bottom numbers, and then simplify, but I never knew why the answer always comes out. This figure shows how to demonstrate it to the students so they can actually see why it comes out this way. I did not have any questions about these chapters; I love the new ways to look at math problems that I have always only done one way.
In response to Joel Stucky, You are correct that math is constantly being built on, and fractions are one of those concepts that if you don’t understand at the beginning you definitely won’t understand at the end. It is so important that students have a good foundation and understanding of the concepts of fractions before they are asked to use them or add, subtract, multiply and divide. I also thought that multiplying and dividing are much easier to do than adding and subtracting, but the book gives a lot of great ideas for teaching everything.
Katie Coulter Chapters 15 & 16 This past week while watching a video for my educational psychology class, I saw a teacher demonstrate fractions in a fun way for a class. He used something they can relate to and had a good time playing with, apples. This teacher used a great manipulative that caught the student’s attention. He actually cut an apple in half and explained how there were two pieces, then wrote it on the board then let students get their pre-cut apples out and show him the two halves. Then he got another apple and cut that into fourths. Explaining how there are 4 pieces, wrote it on the board for them and walked through each amount,1/4-2/4-3/4-4/4. It was a very comprehensive concept and he took his time and allowed the children to also experience holding those amounts. In chapter 15 it mentioned several times about explaining to students that items must be the same size to hold the same amount but the shape doesn’t necessarily matter. I don’t know why I was surprised, I should be used to being corrected for my math grammar but I was taken back when they explain how we should properly say a fraction “three fourths”. The whole chapter was a lot to take in. I felt extremely confused at moments on how they were trying to present each concept. I guess when you have taught one way, doing it another way just doesn’t make sense.
Chapter 16 also confused me. I had a hard time really through the steps of the problem based approach and just felt exhausted after reading the words spelt out instead of the numbers just written when used in the paragraphs. This chapter included estimation which I thought was a little much but soon realized the purpose to allowing students to estimate. It gives students a better physical grasp on the fraction it they can estimate it out to a whole or bigger fraction, especially in length. I guess I don’t remember that day we covered length on our rulers because I still don’t know fractions on a tape measure or whatever. I can do fourths and I only remember that because of the dollar! When they got in to the multiplication and division, I thought it was ironic because this morning in observation students were learning how to compute the Greatest Common Factor in a whole number. Students need to be aware of factors as they begin to work with fractions.
Chapter fifteen discussed fraction concepts and I think the first sentence in the chapter really hit the nail on the head saying that many students find fraction concepts to be a challenge. I subbed one day and taught a math lesson about fractions. It was dealing with parts of a whole and the students were just struggling with it. Finally I used tape to have them make their own number lines on their desk. I had them number it 1-10. The students also drew three tic marks in between each number. This helped them see that when they plotted ¾ the dot would go on the third notch right before the whole number, which would be the fourth notch. It wasn’t the easiest way for me but it was for them so I went with it! I would have preferred a model such as popcubes but the students seemed to do fine with the number line so it goes to show the many different methods that can get through to them.
Chapter sixteen continued the discussion of fractions only it went in a little deeper to discuss fraction computation. Fractions can be terribly confusing on their own so when computation is involved it just seems like a mess. I liked the section in the chapter that discussed problem-based number sense approach. It discussed the need to go slow with algorithmic procedures so students really have a chance to develop fraction number sense before doing any computing with them. This will give students a change to discover what they can do with fractions before any strict methods are put in their heads. Fractions are a hard concept so when students can come up with self-invented methods that make perfect sense to them then that’s a major aid.
I like your example of how when teachers use manipulatives that students are familiar with, or that they can relate to, it sort of helps it click by keeping their attention. I’m a big fan of visual hands on aids in teaching so this apple example sounds great. Chapter sixteen was also a bit confusing for me. It was a lot to take in and I too didn’t really think estimation would be an aid in fraction computation at first. Like you said though, estimation helps students get a better grasp on the fractions. It can give them a better knowledge base on fraction number sense by allowing them to see what fractions are close to what whole numbers. Fractions were hard when we were younger and I think they just continue to be a bit frustrating! Good post!
When reading Chapter 15 over developing fraction concepts I was able to learn lots of useful information to use in my own classroom some day and I was also able to learn information about fractions that I didn’t know beforehand. Before reading this chapter I was unaware that the part-whole model is the most commonly used in textbooks today and now that I stop to think about it makes sense to me. I liked how the book also talked about how it is important to say three fourths instead of saying three over four. I liked the section of the chapter that talked about estimating with fractions which is important in any elementary school classroom. The book gave great examples of what to say to students such as what fraction of our class are wearing sweaters or what fraction of our pick picked spaghetti. These were great ways to estimate in the classroom using fractions. Lastly I liked how on page 306 at the end of the chapter it gave different tips that were found throughout the entire chapter with a total of 10 tips which will be great for me to refer back to when I begin teaching. When reading Chapter 16 over developing strategies for fraction computation I was able to learn lots of new information that I will be able to use in my own classroom someday. I liked how the book gave a problem based number sense approach which gave me as the reader four guidelines to follow in order to develop computational strategies. I also liked how the book gave the different ways to develop algorithms which was very helpful. I like how the book pointed out that in order to add or subtract the students don’t have to find common denominators unless they want to or are doing the problem the standard algorithm way. Overall I liked the activity sheet that we did in class which was from figure 16.15 which was dividing the cookies into servings of ½ cookies. I loved the different activities presented throughout this chapter and are planning on using these activities when I begin teaching.
In response to Kristle C., I agree with you Kristle on the area of being nervous about fractions in relation to chapter 15. I agree with you that you as a teacher will go above and beyond in order to help your students understand the concept of fractions so that they are not as worried and nervous about fractions as you were. The fact that if the student doesn’t understand fractions from the beginning of the time teaching them then they will struggle in it that area of fractions the rest of the time is exactly correct. I believe that if students are struggling in an area that the teacher needs to stop and rethink about what they are teaching and how they are teaching it and adapt their instruction to the needs of the students. This will help the students to possibly understand the idea of fractions in a way that is better fitting to them. I also feel that it is so important to use manipulatives in order to help the students understand the concept of fractions. I have some of the same views of the topics in chapter 16 that you had. I feel also that students need to have a strong sense of fractions in order to help them to solve the problem. If the students don’t understand fractions at all or not in the right way then the student will not be able to solve problems dealing with fractions. I also agree with you that it is great when educators find ways to help students to solve the problems dealing with fractions and to slowly but surely help the students to develop a stronger fraction sense.
We have been talking a lot about fractions in class the last few class periods and I realized they are very difficult. They are difficult for me. So I know they must be challenging for children. There are so many different ways you can teach fractions and I think that a teacher should try all the ways until they find what works for their class. It doesn’t really mean that one strategy is going to work for all the students in your classroom. This is why learning all of these different strategies for the classroom.
I think I can honestly say I hope I never have to teach fractions. I just don’t enjoy them at all and I would much rather teach addition and subtraction. Maybe it is because fractions are still very confusing to me and I wouldn’t feel comfortable teaching it to other students.
Your insight on teaching fractions is great. I think you are so right in saying that what is easiest for us may not be the easiest way for the children. I think this is why I do not like fractions very much. I do not understand the deeper computations in fractions and it does get very frustrating. Students learn best with a teacher that knows exactly what is going on.
FRACTIONS! What a scary word! Chapter 15's concepts are useful and helpful, however. This whole book gives great tools and examples. It seems that working with elementary students, and from my own experience, that students are usually scared of fractions... I think that they are just misunderstood. I believe with the correct resources, students can and do fall in love with fractions. I know I have mentioned this book before, but FYI (just as Dr.Stramel described) the Hershey's Bar book and the M & M's are great literature for young students to comprehend fractions.
I know we have been discussing fractions with our class lately, and they can be overwhelming. I think just with any topic within mathematics, fractions are a system that that domino affect each other. In order to understand what 2 + 3 is, you must understand what "2" is, what "3" is, and what "+" is... and how to put the equation all together. The same for fractions. I think that as long as teachers/students make sure and "break down" the steps within fractions and make them as fun as possible, students won't get so frustrated or discouraged with fractions. With that being said, I also feel that we should not just refer to pizza and pies for fractions. I know that within our HOT kit there are several examples of lesson and tools, such as the fraction towers and fraction circles, that can be used for future reference. I look forward to making fractions fun by incorporating choice of what students will compare and contrast fractions to. I also think that in the beginning of learning fractions, group work will be encouraging versus individually (also to help one another).
I too agree, I think that different concepts are meant for different students. Even as an adult, I feel this way with many things. Especially with fractions and their complexities, I think all students should feel comfortable with how THEY comprehend fractions. Whether it's by visually seeing a pizza split into even pieces OR being handed pieces of a chocolate bar OR working it on on paper. There are many ways, and any way is A-Okay. It's finding the concepts that work best that may take time. But I also think along with this idea, it's important to incorporate group work so that students may be able to see how other students comprehend fractions, in turn hoping that they will be able to better attain fractions, too.
Chapter 15 and 16 Chapter fifteen and sixteen 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. discusses how to teach fractions as well as how students learn about fractions. Fractions are a starting off point for many other concepts in math and if students do not understand fractions it may be hard for them to grasp these other concepts. Van de Walle et al. backs up this statement in chapter fifteen of the textbook by saying in the textbook that “This lack of understanding is then translated into difficulties with fraction computation, decimal and percent concepts, and the use of fractions in other content areas, particularly algebra (Van de Walle et al., 2010, p. 286). Van de Walle also states in chapter 16 that “We can use their prior understanding of the whole-number operations to give meaning to fraction computation. This, combined with firm understanding of fractions, provides the foundation for fraction computation” (Van de Walle et al., 2010, p. 309). These two chapters really explain how so many different concepts come together forming new concepts. A piece of information that I learned from chapter fifteen of this text was different strategies that I could use to assist students with estimating fractions. This was always difficult for me in school so it is nice to fine different ways that I did not know about before. I liked the different examples that the textbook uses in figure 15.14 on page 299. A piece of information that I learned from chapter sixteen of Van Walle et al. textbook was a strategy to teach students how to #/# of #/#. This can be a difficult concept for students to understand and I have never done it the way it is described in the textbook on page 319. Figure 19.9 said to start with a fractions and then to divide the other by that fraction. I can think of different manipultives students can use to understand this concept as well. Something interesting mentioned in chapter 15 of Van de Walle et al. textbook was when to teach students different fraction rules. According to the textbook “if students are taught these rules before they have had the opportunity to think about the relative sizes of various fractions, there is little chance they will develop any familiarity with or number sense about fraction size (Van de Walle et al., 2010, p. 300). Another interesting piece of information mentioned in chapter 16 of Van de Walle et al. textbook that made me think about how I will conduct my classroom is “it is important to give students ample opportunity to develop fraction number sense prior to and during instruction about common denominators and other procedures for computation” (Van de Walle et al., 2010, p. 310). Knowing this will assist me in the long run to know what I need to focus on with me students.
Chapter fifteen and sixteen of Van de Walle et al. made me think about when I was learning about was how I always related to fractions. I would always no matter what would think of fractions as a pie. If I was comparing fractions I would ask me self which piece of the pie would I want and that would usually help me. The bad thing about always using this strategy was that it started to get difficult to do larger numbers. I would often times not divide my pie up correctly and then would get the wrong answer. Something from chapter fifteen and sixteen Van de Walle et al. that I would like to use in my classroom is having the students use a variety of manipulatives in the classroom. This chapter of the textbook had many different ideas for how to show the concept for fractions to students and they are a great way to find different ways for students to relate to the material. I also really liked all the different activities that were featured in the lesson. These are ones that I would like to use in my classroom. 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.
I agree with you that fractions are difficult for some students but they don't have to be as long as the teacher explains everything. Fractions always seemed backwards to me and that is why I think it may be difficult for some students. It is just a different way of thinking.
I agree that the variety of approaches given in these two chapters is certainly interesting. When it got to dividing fractions and talked about the common denominator method I really had to slow down because I had not worked with that method, just the invert and multiply method
If we make our students only do something in one way we are not doing the m a favor, no matter what way we make them use.
Math is a subject a lot of people do not like, fractions is then the least favorite part of many people's least favorite subject.
These two chapters fit with the rest of the book in that they approach fractions using the same basic approaches the book uses for the other topics discussed. As before it does not spend a lot of time discussing the so called traditional methods, likely assuming that we know them well. I have never really appreciated that assumption, assumptions are dangerous things.
As teachers we should try not to assume our students do or do not know things, that is why we are supposed to use pretests.
These two chapters do a great job of breaking down the topics covered in a way that is easy to understand and will help us to explain the topics to our students in easy to understand ways.
These two chapters are worth all of the time I have given them and more.
I would agree with how chapter 15 starts! I do think that fractions pose a considerable challenge to students. Overall most students show weakness in fractions. I think it is important in order for students to fully understand fractions that they see the fractions in many different ways. Oddly enough I never realized that pattern blocks could be used for fractions. I had never seen them used for this purpose so I think they would be fantastic! I also like the idea of giving emphasis on seeing fractions as division. Personally I love fractions and always have! I think that chapter 16 is super important. Our students have to be able develop the important strategies to figure out how to figure fractions. I really liked model 16.8. It was neat to see the different models for the multiplication of fractions.
@ Elizabeth Sills I agree with you. However I really like fractions but I am very scared of teaching fractions. I did do fractions for my mini HOT lesson and I was super nervous! I will definitely refer back to this book when it comes time for me to teach strategies for fractions! Have you ever seen the Everyday math curriculum taught? They teach it is with so many different variations that help all students pick up on the concepts!
Chapter 15 was about developing fraction concepts. When starting this chapter it honestly made me a little nervous because I remember how much of an issue fractions always seemed to be when they were brought up in my math courses. It seems that no matter how well students are doing with the concepts things get more difficult to understand when fractions are brought in.
I liked how the book gave many examples of how to use manipulatives to help students with the concept of fractions. I remember using some of these manipulatives in the classroom but others are new to me but are very impressive, because they give students different ways of looking at the same information. I also liked the activities that were given for students to use fractions. As I watch some of the students in my internship struggle with addition and subtraction it sometimes worries me about how they might handle more difficult concepts in the future. I do think that these activities will be helpful to them though. I am surprised more and more every time I look for new books by how many good math books there are out there for students.
Chapter 16 is about fraction computation. Seeing the fractions within the equation scares students, but having to actually solve the problem is the tricky part. There are so many different rules for fractions that are different from whole numbers, that it can be hard to remember what to do and when. Luckily there have been many strategies created that make the solutions easier to come up with. According to the book fraction circles are the most widely used strategy however they can be difficult to use if the students are not careful. If the circles are not perfect and the partitions do not show equal parts the students can easily come to the wrong conclusions and come up with the wrong answers.
I have not yet seen fractions used in my internship classroom but know that the teacher has many manipulatives ready to help the students when it is necessary.
I had also never thought about using pattern blocks as a fraction manipulative. However, after looking through the book and seeing the strategies to use I am very confident in the fact that the pattern blocks could help students that may be having trouble. However, just like any other manipulative used students must understand that they are math tools and not toys.
I won’t lie… When I started reading chapter 15 all I was thinking was, “Yuck… Fractions!” At the end of this chapter though I was relieved because it seemed a lot easier than I was making it seem.
The fraction constructs were new to me – not the actual fractions, but the names. It seems I have learned all of these constructs that are given throughout the book, but I never know the actual name that goes with it. Would it be beneficial for students to know the names like “part-whole” or “ratio” instead of some other term that a teacher may use?
Manipulatives are my favorite part of this book. I love that for fractions there are several different types of manipulatives that can be used. I think all students need to be familiar with all of them, but once they understand a concept I think it would be okay to let them use what works best for them!
Chapter 16 was also about fractions, only this time it involved the computation aspect. This textbook does an excellent job of giving examples and showing you how to teach and solve problems. In addition to the book, a little clarification from Dr. Stramel during lectures made it a lot easier to understand. I can say that I’m not as scared to teach fractions as I originally thought I would be!
I think we all agree that the concept of fractions makes us nervous. I was never bad at math (until high school) but I always second-guessed myself when working with fractions. I would hate for this trend or attitude to continue when I find myself up in front of my class one day teaching fractions.
I love the manipulatives and the ideas the textbook gives us. All of these ideas are things we need to keep in mind when we do have to teach fractions. I also agree that the manipulatives and ideas could definitely benefit the students that may struggle a bit with concepts in math that are crucial to go further (like adding and subtracting to add and subtract fractions, etc.).
As opposed to many who have posted here, I love, love, love fractions! I guess this is because I had a wonderful teacher who explained in depth the concepts. While reading chapter 15, I kept thinking, "yep, I did that, and that, too!" My teacher introduced several fraction models so that every student could relate to at least one model.
The ideas in these chapters that has impressed me the most is the writing integration. Two subjects combined equals greater learning and success for the students.
The part of the chapters that I would like to see develop a little further is the use of food in the classroom. Every other page seemed to have a problem dealing with some sort of food. Please remember some students may have diseases that prevent them from participating in food related lessons. Yes, I do agree, students can relate to pies, fruit, and candy bars, but I would hate to see any student left out.
In response to Emily: I too love to incorporate manipulatives into lessons. Honestly, I didn't think they were too important until this internship. My mentor teacher uses manipulatives in every lesson, and her students just seem to get that "I got it!" look every lesson! The students love math because they get to get their hands on something.
To Kristie C: I don't mind simple fractions but when they start getting odd and big my brain gets confused. I am glad that you are going to stress fractions in your classroom instead of avoiding a topic that makes you uncomfortable. I don't remember being taught fractions with manipulatives, so I found this interesting in the chapter.
Fractions, Fractions, Fractions. I think this word makes many people uncomfortable. Personally for me I learned fractions the old way. Adding and subtracting involved find the common denominator. Multiplying was simple straight across and division was flipping and multiplying. Therefore, I found this chapter very interesting and took a lot of good information on how to teach elementary students fractions using manipulatives. I felt like this chapter had a lot of good activities that I can use in my classroom.
Chapter 16 More Fractions....This chapter discussed fractions more and included many good examples. What I took from this chapter is that students may grasp a better understanding of fractions if the teacher uses real life situations. I like the the example in the book that uses the Ben and Jerry example. Yum. I think it would fun to do a real life example in the classroom so the students could participate. I feel like it would be a good memory of learning fractions.
To Lacey K: That is great that you had a good teacher. I think there are many ways to implement fractions in the classroom. It just takes a little creativity on the teachers part. Kids get excited doing all kind of things.
Oh the joyous fractions! I can honestly say that fractions are not my favorite concept to learn let alone teach! These chapters were very informative offering numerous strategies and methods to use when teaching fractions in the classroom. There were many terms and ways of figuring fractions that I had never heard of. Many of the phrases I remember learning while being taught fractions are not even used anymore and our text even says that these phrases can be very confusing for students such as “reducing fractions.” Even when I am working with my students today I use this term, I now know that is more confusing to students than helpful. I have to remember to use the term simplified and not reduced. I was also not familiar with the term iteration; while I have heard the term I did not know its actual meaning. I loved the concept on page 295 that stated “the top number counts the bottom number tells what is being counted.” I do not know why I had never thought a fraction in that way before. I love the idea of having numerous manipulatives to use while teaching fractions. Fractions could be a very good unit for visual and tactile learners due to the fact that the best way to learn the basics of fractions is to “see” the examples by using different manipulatives with the students.
I believe the use of manipulatives in teaching fractions is very important and I also like the example you gave that was shown in your ed psych class. These manipulatives make the understanding of fractions so much greater than just writing the examples on a piece of paper and only drawing circles. I also found the estimation method of figuring fractions to be quite interesting. I had never thought of completing fraction problems in this way! Factors are very important for students to know when working with fractions and I believe that in that concept is where many students begin to fail the understanding of fractions simple because they do not know the basics needed when it comes to understanding and working with fractions.
Chapter 15 – Developing Fraction Concepts This chapter talks about the importance of our understanding of fractions AND all the possible concepts that can be represented by a fraction. I know that fractions can be scary but I feel like this chapter helped go deeper and help us to see we can just know that a fraction is part of a whole – in fact it is, but we need to know what it REALLY means. We need our kiddos to be able to cross over the information they are learning to real life scenarios. Our terminology is important as well. We have to be careful as to not confuse the student any more than they might already be. We have to be able to help students build on their prior knowledge of whole numbers. When talking about the concept of fractions the text says it important that students understand that a fraction is one number and that all parts are equal sized. I thought the different models the book showed us were handy. Some of them I was familiar with and then there were some I was not as familiar with, but I felt like it was great information to have. Fractions don’t have to be scary, but they are important to gain the deeper knowledge as our students are learning. They need to know what the fraction really is telling them, what does it mean? They need to know the proper vocabulary to help with this understanding. All of this is our job as educators to make sure is happening. To do this we need to make sure we are assessing our students by presenting exercises and asking questions.
Chapter 16 – Developing Strategies for Fraction Computation This chapters takes us deeper into the importance of our fraction knowledge. I love that at the very beginning the text states “…learning rules without reasons, an unacceptable goal.” Development of number sense is just as important when dealing with fraction as with dealing with whole numbers. The text talks about strategies for adding and subtracting fractions. I can remember using the fraction circles. Seems like many teachers use the idea of a pie cut into piece or a pizza. I like the idea of using the ruler or a number line. The fraction bars are a new manipulative to me and we used them in class. I liked using them because you can really get the idea of add or subtracting fractions without having to find a common denominator. This chapter really made me see the importance of using manipulatives. I don’t remember using manipulatives much but I know that they help a great deal and I plan on using them as much as I can. Overall this chapter was a great deal of help. It does go to show if we don’t do a great job in our early years with our students with whole number adding, subtracting, multiplying, and dividing – we are setting them up for a tough struggle down the road.
@ Lindsay H I am with you that its safe to say many students will and do struggle with fractions. I am pretty sure I did when I was learning them. I would hope that teacher can find ways to help limit this struggle. The manipulative and activity suggestions in these 2 chapters should really help with this. I think if we as educators can push ourselves to think outside the box , then we can really help benefit our student and help ease that struggle with fractions. There are so many other options our there for us to apply to our lessons.
After reading this chapter, I feel a lot better about the topic of fractions. I still don’t like them as they feel very confusing to me, but I feel better learning the many ways I can teach them to my students. I usually cringe when it come to fractions. The mentor teacher I intern with told me I could either teach fractions or graphing for my formal observation, so of course you can probably guess which one I chose, yep, graphing. I felt more comfortable with the topic. I have learned from this chapter that I do not have to feel so overwhelmed when teaching fractions. I always hate dealing with them when it comes to tests. I do real well with probability which is some fractions as well. Not sure why. Maybe part of my problem with fractions is I don’t take my time to deal with them and I have a negative attitude towards learning about them. I do not really feel as strong in this issue anymore after reading this chapter. I will definitely keep this textbook very very close to me when teaching it in my classroom. Who would have known that drawing circle could help with fractions.
In response to Shawna W. – I agree that this chapter was great in going deeper for us to understand fractions a lot better. To know that a fraction is a whole number and the parts are all equal in size. They just make up the whole number in the end. I know this information already, but I still hate when I have to use fractions. When I am cooking, my husband always helps me learn fractions when it comes to the measuring cup. I hate cooking with a fraction I do not already know, but it is a great exercise for me. He loves fractions which is great because he loves math and that is his section he helps our son on in homework and it is English for me.
Chapter 15 and 16 covers Fractions. I have always had problems growing up when we would learn fractions. It was always something I struggled with. After reading Chapter 15 and 16 I feel like I have a better understanding of how to teach fractions and the different ways you use them, the different language that goes along with it as well as the symbols. In Response to April B: I feel the same way about fractions. I felt like these chapters made it easier to understand and apply to different lessons.
Chapters 15 and 16 were all about fractions. Chapter 15 talked about the concept of fractions while chapter 16 talked about developing strategies for fraction computation. I really enjoyed reading about all the different strategies in chapter 16 that teachers can use to teach fractions in their classrooms. I was never a fan of fractions when I was younger and even still today but I believe from this course, I am excited to teach my students this concept. I believe I am so excited because there are so many great resources out there that can be used to teach. There are a number of books, as we learned about in class than can be used as read alouds. Also, I enjoyed listening and watching Dr. Stramel teach us strategies to use.
In response to April B--I completely agree with you, I am not very found of fractions myself but after this chapter I feel I will definitely be more comfortable teaching my students this concept then me learning this concept. There are so many great strategies that can be used to teach fractions that I believe we won't have a problem trying to find ways to teach this concept. Thanks for sharing!
Chapters 15 and 16 discuss developing fraction concepts, as well as developing strategies for fraction computation. My instructional unit was over addition of fractions and so I referred to these chapters many times as I was preparing my lesson plans. These chapters are full of wonderful ideas of how to help students develop a concept of fractions and what they really mean. I wish that I had been introduced to fractions this way. I think that teaching fractions the way these chapters describe could alleviate much of the anxiety many people associate with fractions. Chapter 15 discusses developing fraction concepts, including fractions being parts of a whole, and made up of equal parts. It also discusses the concepts of “sharing” and equivalent fractions. During my formal lesson plan I used manipulatives to review basic fraction addition. After having taught that lesson I am bigger believer in manipulatives than ever before. There were many students who understood after being able to “see” the fractions, that hadn’t understood before. Through the use of manipulatives I was able to teach students many of the fraction concepts discussed in this chapter, including equivalent fractions and simplest form. Chapter 16 discusses fraction computation. It suggests allowing students to use invented strategies first, so that they will develop an understanding of fractions before moving on the standard fraction strategies. It also discussed like and unlike denominators, common multiples, as well as multiplication and division of fractions. Each section includes multiple ways that teachers can help students develop the concept outside of traditional pencil and paper problems. I know that this book is something I will refer to time and time again, and that it will continue to push me further from how I was taught and further into teaching students to really understand mathematical concepts.
I was never very fond of fractions either, but this is what I ended up teaching for my formal observation and I now feel very comfortable with the topic. One of the advantages of developing these instructional units is that you learn a concept inside and out, and I feel I learned a lot about teaching math in a way that is hands on. This is somewhat of a challenge for me because it is so different from how I was taught, but it is also so much more rewarding!
As a young student, fractions always frustrated me. As an adult, I actually enjoy fractions. Fractions can be tricky to teach if the right skills aren't put in place. It is important, and meaningful to students when real life situations are used. For example, using a cake to teach fractions is how I learned. Anything to use to peak students interests about fractions. Manipulatives and visuals are very important when teaching fractions.
In response to Lindsai S.: You said, "There were many students who understood after being able to “see” the fractions, that hadn’t understood before. Through the use of manipulatives I was able to teach students many of the fraction concepts discussed in this chapter, including equivalent fractions and simplest form." That is so great! I agree that manipulatives can make a world of difference in the process of teaching fractions. It really is something that truly needs to be visualized before true comprehension can easily take place. Most math topics are more easily understood while using manipulatives, but if I were only allowed to use them during one topic throughout the school year, I would definitely choose fractions.
Jena Simms: "Why didn't I have a teacher who taught me this information?" I feel that way about most of what we have learned in this class! I feel like I would have been much more able to do math is it had been as okay to explore different ways of doing problems as it is in this class. Every time Dr. Stramel shows us another way for students to do something and says, "it's OK if students do it this way" it makes me smile and I have "aha" moments about math every week.
Chapters 15 and 16 both deal with fractions. Chapter 15 discusses developing fraction concepts and chapter 16 discusses developing strategies for fraction computation. The definition chapter 15 gives for fractions is rather interesting. It says fractions are critical foundations for students because they are used in measurement and are essential for the study of algebra and advanced mathematics. We really do associate fractions with measurement the most; whether the measurement is for cooking or for measuring on a ruler. One of the things I have the hardest time with is fractions when it comes to measuring with rulers. When we did the activities in class I developed a better understanding of fractions. But I’m still nerves about teaching them. How do we teach something when we are so unsure of it ourselves? Chapter 16 shows an example of how to multiply fractions using grid paper. I remember when we did that activity in class. I have never multiplied fractions in that way, but I could see how it would help children who are beginning with multiplying fractions. We often frown upon teachers who are stuck in one way of teaching. Those teachers who just teach the traditional way and refuse to bring in something knew. I think they do this because they themselves do not understand the concept fully. I mean, my high school math teacher was one of the smartest people I’ve met in the mathematics field, but he was so strict on how to do each problem. You had to do it his way or else it was wrong. I feel like he did not know any other way of doing the problem and he was afraid to learn a different way.
Chapter fifteen talks about building on whole number concepts and how important it is to help students see how fractions and like and different from whole numbers. It says to avoid saying “three out of four” unless talking about ratios and proportions and not to “three over four.” I did say 3 over 4 some in my mini-teach. I was thinking about when students are first introduced to writing the fraction and what it looks like. But I think I said, 3 over 4 or ¾, and I think it would have been more effective to say 3 over 4 IS ¾ or to say: when you see a number written as something over something (3 over 4), the number is~ and then state the fraction (three-fourths). Does that even matter? Will we need to make distinctions and help students identify this, or will their everyday life give them plenty of exposure? Sometimes I realize that I give too much information instead of letting students driving the learning. I just want them to “get it” so badly that I “help” them, which I have also noticed looks really ugly when I see other teachers do it. I liked what the chapter said about fractions telling about the relationship to the whole, they don’t tell the size of the whole. The text gave the illustration of choosing ½ of a pizza or 1/3 of a pizza. Because the pizza that offered 1/3 was larger than the one that was cut in 1/2, the person who chose the 1/3 of a pizza got more pizza. Chapter 15 also gives some good examples of students justifying their work and explaining how they found their answers. This is something I really appreciate about this text. This seems to me to be the most important thing about mathematics- that the student is able to explain HOW they came to the right answer. And sometimes they may have the wrong answer do to a simple error but when they explain it, the teacher knows that they understand the concept. This helps both the student and the teacher and develops the students understanding while giving the teacher an assessment of the students understanding. Chapter 16 starts out by discussing number sense and fraction algorithms, and states that conceptual development takes time. Dr. Stramel stressed this in class and said, do you remember that from being in school? It takes time to understand the concept. That hit home with me. I know I am not alone when I say that for me to learn math takes a lot of practice and just doing it over and over until it makes sense. The concepts in this chapter make more sense to me because we did them in class also. I was able to understand the idea of developing a fraction algorithm when I pair the information in the text with what we did in “class.” Sometimes I feel like watching the adobe connect does not connect me to the teaching at all and sometimes I learn so much. In this class when the on-campus class works math problems, I learn too. This is really valuable to me!
In response to Kymberly: I loved working with numbers all my life, from grade school to high school. Fractions, however, were not my strong point, but I got by. I remember taking an industrial arts woods class all four years of high school. I had the hardest time reading a tape measure (I know that sounds horrible, but its true). I had to have my teacher help me every time I was to measure something. After reviewing fractions in class in math methods, I feel so much more confident about fractions.
My instructional unit was on the conversions of fracions/decimals/percents. It was developed out of my confusion in my past experiences. Conversions are very common in life and I wanted to teach it in a way that makes it fun and applicable. Our textbook recommends a book titled "The Man Who Invented Parks" Even though the book was somewhat boring it was a good tie into my lesson. The students had to opportunity to create their own park on grid paper in small groups. From their, the students had to determine what part or percent of the park would be what. The students had a lot of fun applying fractions/decimals and percents to an relevant activity.
The most important take away for me is the need for manipulatives in this subject area. Dr. Stramel did some great exercises with manipulatives. By allowing us to participate in the use of these manipulatives made all the difference to me. You can read all about the importance, but until you get your hands on them that is when you really understand their value.
@Shawna I'm so glad that you brought up using rulers. My mentor teacher has done some amazing activities with rulers and fractions. I would have never thought to tie the two of them together, but they go hand and hand. Addition and subtraction of fractions can be easy with a ruler.
Chapter 15 and 16 discussed developing fraction concepts and strategies for fraction computation. I thought that it was important that the text stated, "A fraction tells us about the relationship between the part and the whole." I can understand why some students struggle with fractions because sometimes even I have to really think to determine which out of two fractions is actually larger. I enjoyed doing the activities in class with the fraction bars and circles. The fraction bars were very useful because you could see exactly what 2/4 looks like as well as the fractions that were equivalent. Using these types of manipulatives will definitely help students to better understand exactly how one-half is larger than one-third. Some students may also need to draw pictures in order to represent the problem and this should be encouraged. The drawings that we did on the graph paper were helpful. As we were comparing fractions in class, it was very tempting to use the traditional algorithms and find the common denominators, but the students will not automatically think about doing this. It's important for teachers to show them other ways that they can determine which fraction is larger/smaller.
Having students estimate the answer to an addition problem involving fractions can help them to better grasp the concept of what exactly 12/13 looks like and that it's close to 1. There are so many ways that fractions are used in everyday life including baking, driving, measuring, etc. These are important concepts that we should make sure that our students understand because they will be using them even after they are finished with school.
I completely agree with you! I wish that I had been taught about fractions using the methods that have been shown to us in class. I think I'm definitely more of a visual person and they could have helped me to understand some of these concepts much better. I'm glad that the Common Core Standards emphasize the importance of using manipulatives and I think it's a great way for students to demonstrate that they really understand the material.
Chapters 15 and 16 are all about teaching students fractions. I remember being introduced to fractions as the teacher wrote them on the chalkboard. We never used any manipulatives or models that I can recall. I had a hard time understanding fractions until I had that “aha” moment when I realized that the bigger the bottom number, the smaller the fraction was. After that they seemed to make sense, but I always wondered why my teacher didn’t explain that to me to begin with. I think using the methods outlined in these two chapters in combination with real life situations and use of manipulatives is a much better and more effective way to help students understand what fractions are and how to use them.
Brandi S., I agree with you that the need for manipulatives when teaching fractions is very important. Like you, I am grateful that Dr. Stramel showed us how to use them in so many different activities. I don’t remember using manipulatives hardly ever when I was in grade school. It is nice to see them in use.
Elizabeth: I don't remember using manipulatives to help learn fractions. I love how Dr. Stramel incorporates math manipulatives during class this help me learn because I'm a hands on learner.
Fractions were harder for me to learn. We didn't have math manipulatives to help us understand them during school. I like using the math manipulatives because I think its easier for students to see.
Chapters 15 and 16 were all about fraction. I, like most others in this class, am not a fan of fractions. I have always liked math and been fairly good at it, but I have avoided fractions like the plague! I would never work a problem with a fraction in it. As soon as I saw a fraction, I automatically converted it to a decimal. The fact that I have all of the commonly used fractions’ decimal equivalents memorized is a clear indicator of this. I realize now that fractions are not the enemy; they just need to be taught correctly. I will have to get over my avoidance of fractions so that my students can learn to use them without being afraid. When thinking about how I learned fractions, I really don’t remember using any sort of model or manipulative. I just remember the numbers and maybe a circle here or there. Had I been introduce to fractions with number lines, fraction towers, or fraction circles, I might have had an easier time understanding them. Like any subject, when completing computations with fractions, it is important to apply real-world uses. No one walks down the street and is asked how much of a circle is shaded in. However, there are many situations such as dividing food or materials among people that do happen and involve fractions. The use of fractions is a very important math concept that every student needs to understand. If we start teaching fractions in a better way, maybe the concept will become less horrifying to students.
I am the same way, I don't ever remember being shown fractions with a model or any kind of manipulatives. I just remember the teacher writing fractions on the board and explaining how to find common denominators, or cross multiply, or flip and multiply for division. I definitely think if I had gotten to use a manipulative I would have understood fractions better and more quickly.
Chapter 15 and 16 were about teaching fractions. I honestly have never liked fractions and it is so funny to hear our whines and sighs in class when Dr. Stramel tells us that is what we are doing for the day! I will say using the manipulatives have been such a great help, especially for me! They are so much fun and we can visually see how many different ways of creating fractions. It is funny when we get stumped in our groups with the deer in the headlights look! Then it comes together and we have a blast. I never got anything with fractions other than a teacher and chalkboard! I think that all of the new manipulatives not only makes fractions fun for students, but it also gives so much of a better understanding. I have leaned so much these past few weeks in class!!
I agree with you that fractions are not the enemy and that it is so important that they be taught well for a good understanding. As much as we whine in class it is fun once we get going to see all of the varieties of fractions we can come up with. I know I need more knowledge in fractions when it comes to me actually teaching them to give this much of a variety, but at least now I feel comfortable in saying that I can understand what I am teaching!
Fractions have always come easy to me, unlike many people. I am not sticking my nose up in the air, on the contrary, because they have made sense to me I find it extremely difficult and at times frustrating if the student is having a difficult time. I have worked with many students who just can not conceive of the idea. If I ask for half of an orange, they can give me half, but to ask them how much is 1/2 plus 1/2 they have no idea. To me it was simple, you cut one orange into 2 pieces and take one of the two. you have 1/2. Now if I take another orange and do the same (take one of the two) and put that half with my first half, I have one whole. But my student may say I have 2 oranges! Our text indicates that the fraction language is very important and maybe that is the key! I am anxious to try it out.
Jeremiah Gramkow When you mentioned that we need to be careful not to assume the student knows something is so right on. I work with special ed students and to assume a 16 year old knows how to multiply or divide because they are classified as being in 10th grade is a horrible mistake. Many students will not speak up and say "I don't know how", they will just go on in total confusion. That is something I need to remind myself often. Great post.
I have always needed paper and pencil to figure out fractions as I cannot do the problem in my head unless, of course, I estimate. With that said, chapter 15 and 16 gave good examples and ideas to use for fractions. Using manipulatives, grids, dot paper or even paper folding are great things to use when figuring out a fraction problem. I didn’t even think about the vocabulary words when working with fractions, but like the book said when discussing fractions it is a good time to introduce new words such as fourths. Chapter 16 talks about the four guidelines to use when developing computational strategies for fractions which are: 1) begin with simple contextual tasks, 2) connect the meaning of fraction computation with whole number computation, 3) let estimation and informal methods play a big role in the development of strategies and 4) explore each of the operations using models. These guidelines are great when working with fractions and I will have to keep them in mind when I begin teaching.
It is always hard when students do not understand what you are trying to teach them, but try putting yourself in their shoes. They don’t have all the background knowledge you have so you make have to break it down even more for them to understand. Also going over the same problem again and again is key as well as having them know the language of fractions. Bring real word problems into the classroom and model what you are wanting them to do.
Ch. 15: In the first part of 15 they talk about how fractions are often the most confusing thing for young students.I remember that I didn't know how to tell which fractions were bigger. For instance when I saw 50/100 and 1/2 I automatically thought that 50/100 was bigger because it had bigger numbers. I think this is a popular occurrence with many students and I definitely understand how it would be confusing. Ch. 16: Putting fractions together was an even harder concept for me, when learning fractions. With out going through the whole process of changing denominators and working through every step I couldn't figure it out. It was hard enough for me to learn how to add, subtract, multiply, and divide whole numbers much less fractions. Now I think I understand fractions in a way that is easier to teach. I know more strategies to teach and ways to help them remember.
In response to Ashley L: I agree with you on figuring out fractions without paper and pencil- it's so hard. I think I've gotten better at it in this class because I've learned how to estimate better. Also, those steps seem like they would work great and it's good to remember these things to use while teaching.
Chapter 15 introduces us to developing fraction concepts. This has ALWAYS been an area I personally struggle with! In fact when taking my PPST test I actually feared having to do them! That was the only area I was truly nervous about! I think that having these issues will make me a better teacher because I will go above and beyond to make sure that my students know fractions and are comfortable with them! If they don't get a good understanding of them from the get-go they are going to struggle with them for a lifetime! I agree with the text on the importance of using manipulatives to introduce fractions (or pieces) to students. Having students make a shape out of smaller shapes and count how many pieces there are and how many pieces there are if you take away one or two. This gets their brains thinking! Possibly my favorite section in the chapter was on assessing understanding as this is SO important!
ReplyDeleteChapter 16 is about developing strategies for fraction computation. The text stresses the importance of giving students ample opportunity to develop fraction number sense prior to and during instruction about common denominators and other procedures for computation. If students don't have a good sense of fractions, they are going to have a terrible time trying to solve them. I think that it is great when educators find ways to help students solve them. "Dividing fractions is as easy as pie, flip the second and multiple" I can still hear my 7th grade math teacher saying this!
In response to chapters 15 and 16 there were several times when I thought to myself, “If only my teachers had approached fractions and decimals in this way.” When I was in elementary school, many years ago; I had a very difficult time developing these concepts, I believe that if my instructors had spent more time working on developing the concept- and less time forcing the computations- my understanding of these concepts would be more established and complete. In fact, in chapter 16 the book says, “it makes sense to delay computation and work on concepts if students are not conceptually ready.” I think that is one of the most brilliant ideas ever- however; I find it hard to institute in this age of standards and assessments. We automatically expect that just because a child is in a certain grade that they have the conceptual understanding required to understand fractions and decimals and it is not always the case. As teachers I feel this puts us in a bind- do we do what is right for our students and focus on developing the concepts- or do we focus on the computations in order to prepare them for the assessments we know they will encounter? It is a tough question.
ReplyDeleteI think in previous chapters in this book they offer several ideas for implementation in earlier grades- that if fully developed and built upon, will leave the student more capable of understanding these larger more complex ideas. I think the primary thing we as mathematics educators must focus on in fostering a numeric sense in students, giving them a firm foundation in reasoning and understanding why at an early age. Then later down the road- when confronted with more complex ideas- the students will not shut down, but rather embrace the challenge of more complex ideas because they feel confident in their mathematical abilities.
I realize I didn’t say much in regard to content within these chapters, while reading them I just kept coming back to this ‘big idea’. I feel very strongly that mathematics education in our country is struggling, and the ideas presented within this text, if implemented correctly along with the NCTM guidelines, could really help our students perform better in mathematics.
In response to Kristle C.
ReplyDeleteI too was fearful of fractions on my PPST test, I have always struggled with them as well; probably because I did not have a firm conceptual knowledge of them prior to being forced to compute them using the traditional algorithms. I understand what you were saying about this inspiring you to do a better job in educating your students when it comes to these ideas because I feel much the same way. It is embarrassing to be an adult and still struggle with things you should have learned well as a child- and I don’t want children in my class to go through their life with that sense of embarrassment. It makes me want to give each student more than what I had and I think you are right on target, along with the text, when you suggest the use of manipulatives to achieve this understanding. I also liked the suggestion in the text about always working with manipulatives in more than one way (this might have been covered in lecture) but I believe the premise is sound. I may not understand it one way- but if shown an alternate way I may have a light bulb moment. That is part of the reason why this text is so enlightening to me and I think each one of us, it provides multiple ways to access each student- increasing the chances of creating an ‘I get it’ moment.
Thanks for sharing the remarks of your teacher, I wrote that one down for future use- I think it is great!
Adrianne- I just re-read what I wrote and meant to write "multiply" but you probably caught on to that! Lol. I agree with you on the embarrassment of not being comfortable with things like fractions as an adult! I hope that having issues like this will indeed help us better educate and prepare our students!
ReplyDeleteAfter reading the topic for chapter 15, developing fraction concepts, I wanted to close my book and fun away. I usually do ok with fractions, but the thought of them scare me! I think the main thing for me and for all students is that if fractions are put into a real world situation it will be so much easier to understand. I also think the use of manipulatives is so important to help students understand fractions. I know they help me. The topic that I found the most interesting in this chapter was using number sense to compare. This section discussed how only 21 percent of fourth graders could explain why one fraction was larger or smaller than another. This is because the actual size of a fraction is hard for students to imagine. It said that they must have a strong mind-set about numbers to be able to do this. It said to help students notice that the larger bottom numbers mean smaller fractions, but this idea must be revisited so students have this information reinforced.
ReplyDeleteChapter 16 is equally as terrifying to me because it is about developing strategies for fraction computation. I found it interesting that having students draw circles is considered to be the best model for students to develop mental images of fractions. I feel like this is the most common used model, and easiest for students to understand by telling them it's a pizza or a pie. The book also suggested using a number line to model adding and subtracting fractions. I have never seen students use this for this purpose. Mixed numbers and improper fractions is what I feel like I would have the most trouble with. But, the book provides strategies for solving these problems. There were tons of wonderful activities throughout both chapters to help students with fractions. This chapter will be revisited when I am a teacher.
In response to Kristle, like you, fractions scare me. I think this might be because I never really understood the ins and outs of them. I also think this will make me a better teacher. I want all students to really get it, that way they will be ready for the next step, and won't shy away from fractions their whole life.
ReplyDeleteChapter 15 Developing Fraction Concepts
ReplyDeleteFractions are such an everyday use just like money. I think it’s very important that children understand how many ways in real life we use fractions. I think saying three over four is a common thing to say and it will probably be hard to break when using fractions. I say that there are (denominator) pieces and we are using (numerator) pieces. I just have a thought, when teaching measurement with a ruler; we divide it up into fourths and eighths, could we use a printed ruler that has marks that are different colors? Color the ¼, 2/4, ¾ and 4/4 all the same color, that way they can visualize the marks better. I say this because many times they seem as though they can’t see the difference in the marks. I also love the Elmo’s because they really let you enlarge them for teaching. I really liked all the manipulative we have in our kits to help us teach fractions.
Chapter 16 Developing Strategies for Fraction Computation
This chapter started me off thinking that some of our teachers have a tool kit for each student’s, such as a zippered pencil bag. They contain certain things they will need for math; some coins, templates. I thought of making number lines, hundreds charts, and other templates laminated. I really used the pause and reflect and I think they are very effective teaching tool in this chapter. Fraction computations not only require you to add and subtract them but you have to understand them to begin with, if they don’t get fractions then adding or subtracting them only makes it more difficult.
In response to Adrianna, your right it can be very uncomfortable as an adult and not knowing fractions well. It is very important for them to understand them because we just continue to build onto the basics as we go along. They need to feel comfortable learning. I think teaching has changed so much. It used to be drilled into us, forced on us. We didn't have ways to teach children that were not only fun but, where we could apply to everyday use and visually see.
ReplyDeleteChapter 15 talked about the different strategies that can be used for computation with fractions. When it came to adding and subtracting the one strategy that I really liked was the number line. The reason that I liked it so much was because it could be related to using a ruler and measuring things that I build is where I use fractions the most. A number line, such as a ruler, can help students get a better grasp of adding and subtracting fractions because they can visually see what it is they are adding. An example would be 3/4+1/2. If the student knows that there is two 1/4’s in a 1/2 then the student can count the two 1/4 on the number line to find the answer. It personally helped me out the most when I could use the number line and actually see it when I was learning how to add and subtract problems.
ReplyDeleteTammy M
ReplyDeleteI completely agree that children need to understand how they will be using fractions in everyday life. Whether it’s with money, using a ruler, etc. The more ways that information can be related to everyday life the more willing students will be to learn the material. I know that is what worked the best with me. Knowing that I was going to be using the information someday helped me to focus more on the material.
I have to begin by saying, "Why didn't I have a teacher who taught me this information?" I feel better now. Again my favorite part of this chapter was the literature connection at the end of the chapter. Maybe this section continues to be my favorite because I love literature. When I can make a connection between literature and math in my classroom I will have a smile on my face. I believe that using the appropriate language when teaching fractions can cut down on much of the confusion that I felt when I learned about fractions. Many teachers use different terminology and this is a point of concern for me. In my classroom I will make sure to call a fraction bar what it is: a division sign. Increasing the number sense when teaching fractions is also another key objectives for me. Continuing to expand the number sense even with fractions is critical to connecting the dots for students. Chapter 16 is another chapter I found to be exceptionally well written and focused on developing strategies for fraction computation. I find that 6th grade students that I test have a hard time with this concept. Changing a fraction to decimal and mixed numbers is a skill that needs to be practiced and practiced. Showing students how one fact relates to another fact is key to making the connection between decimals and fractions. I especially like figure 16.8 and how the author shows the starting amounts, shows the fraction of the starting point, and shows the solution. Woo Hoo for the literature connection at the end of the chapter.
ReplyDeleteIn response to Adrianne Hoefler: I feel the same way about learning fractions. At no point did I feel confident in my computation abilities pertaining to fractions. I did not fully understand fractions until I was an adult. The strategies in these chapters were always visual. I think this was a big difference in the way I learned and they way I will teach fractions.
ReplyDeleteI related this chapter back to the discussion that we had in class a week or so ago. I’m glad to see that there are many different ways to teach fractions to students. As we said in class, we were taught using a pie or a circle but how often do we actually divide up a circle in real life? When we were presented with fraction problems in class, quite a few of us jumped to solving and illustrating the problem with a circle. I think that the fraction snap cubes are great! They can help visually illustrate a concept that can be tricky for some kids. This chapter helped me realize that we do need to incorporate critical thinking skills more into the classroom. But, we need to do it in a logical way. I liked the activity on page 292 where the student was asked to write out how they came up with the solution. This is a great way for the students to think critically, and explain their answer.
ReplyDeleteIn response to Lane-
ReplyDeleteI also liked using the number line. I don’t think I was shown the number line when I learned how to solve fraction problems. (At least I don’t remember). Your reason and my reason for liking the number line are the same. When you build something, you are either going to have to use a ruler or a tape measure. (You can’t eye ball it!) This would help connect a real world problem to the content.
I think that math is something that every person uses on a day to day basis. It is also something that continues to be built upon as the individual gets older. It can be difficult when a student gets behind but it can be avoided by going the extra mile with the student, which isn't always the easiest or most fun thing to do sometimes. Fractions is one of those areas that can be a little tricky. Using multiple hands-on methods of teaching fractions, I believe, can help those students understand fractions much better. Walking them through each step can be a huge asset as well. Adding and subtracting, multiplying and dividing fractions can be even more of a challenge. I think that adding and subtracting fractions can be even more difficult to teach than multiplying and dividing but the book gives great references and examples. It is fun to teach to students who do not understand a concept. Once the student understands the concept, there is nothing more rewarding than being a part of that.
ReplyDeleteAndrew,
ReplyDeleteI do not know if this is what you were trying to say or not but how elementary teachers teach a concept to students such as adding, subtracting, multiplying, and dividing, they will forever use that strategy once they have found one that works for them. You used the example of pies and circles that we all used in elementary school. That visual is forever in our minds and is the first thing I think of when thinking about fractions.
This week we read chapters 15, developing fraction concepts and chapter 16, developing strategies for fraction computation. These two chapters are very closely related, you must first understand the concept of fractions before you can solve problems with them in it. We spent a lot of time on fractions in class because they are such broad area to cover; and for students to fully understand them students need to see that fractions across many constructs. Students need to see that fractions are more than just parts of a whole; they are also ratios, a part of measuring, division, and operations. The main focus of the first chapter is the variety of ways fractions can and should be taught. Teachers need to go beyond the pie pieces because there are not practical life experiences. How often do we really think about the fraction of pie we ate? I also agree with Dr. Stramel about teaching realistic equations rather than ones that are not practical and just naked number problems. In order for students to want to learn fraction they have to be able to relate them to the real life and 17/8 is not a realistic fraction. Finally I love figure 16.9, it shows how to solve multiplication of fraction problems. I was always taught to just multiply the top numbers, then the bottom numbers, and then simplify, but I never knew why the answer always comes out. This figure shows how to demonstrate it to the students so they can actually see why it comes out this way. I did not have any questions about these chapters; I love the new ways to look at math problems that I have always only done one way.
ReplyDeleteIn response to Joel Stucky,
ReplyDeleteYou are correct that math is constantly being built on, and fractions are one of those concepts that if you don’t understand at the beginning you definitely won’t understand at the end. It is so important that students have a good foundation and understanding of the concepts of fractions before they are asked to use them or add, subtract, multiply and divide. I also thought that multiplying and dividing are much easier to do than adding and subtracting, but the book gives a lot of great ideas for teaching everything.
Katie Coulter
ReplyDeleteChapters 15 & 16
This past week while watching a video for my educational psychology class, I saw a teacher demonstrate fractions in a fun way for a class. He used something they can relate to and had a good time playing with, apples. This teacher used a great manipulative that caught the student’s attention. He actually cut an apple in half and explained how there were two pieces, then wrote it on the board then let students get their pre-cut apples out and show him the two halves. Then he got another apple and cut that into fourths. Explaining how there are 4 pieces, wrote it on the board for them and walked through each amount,1/4-2/4-3/4-4/4. It was a very comprehensive concept and he took his time and allowed the children to also experience holding those amounts. In chapter 15 it mentioned several times about explaining to students that items must be the same size to hold the same amount but the shape doesn’t necessarily matter. I don’t know why I was surprised, I should be used to being corrected for my math grammar but I was taken back when they explain how we should properly say a fraction “three fourths”. The whole chapter was a lot to take in. I felt extremely confused at moments on how they were trying to present each concept. I guess when you have taught one way, doing it another way just doesn’t make sense.
Chapter 16 also confused me. I had a hard time really through the steps of the problem based approach and just felt exhausted after reading the words spelt out instead of the numbers just written when used in the paragraphs. This chapter included estimation which I thought was a little much but soon realized the purpose to allowing students to estimate. It gives students a better physical grasp on the fraction it they can estimate it out to a whole or bigger fraction, especially in length. I guess I don’t remember that day we covered length on our rulers because I still don’t know fractions on a tape measure or whatever. I can do fourths and I only remember that because of the dollar! When they got in to the multiplication and division, I thought it was ironic because this morning in observation students were learning how to compute the Greatest Common Factor in a whole number. Students need to be aware of factors as they begin to work with fractions.
Chapter fifteen discussed fraction concepts and I think the first sentence in the chapter really hit the nail on the head saying that many students find fraction concepts to be a challenge. I subbed one day and taught a math lesson about fractions. It was dealing with parts of a whole and the students were just struggling with it. Finally I used tape to have them make their own number lines on their desk. I had them number it 1-10. The students also drew three tic marks in between each number. This helped them see that when they plotted ¾ the dot would go on the third notch right before the whole number, which would be the fourth notch. It wasn’t the easiest way for me but it was for them so I went with it! I would have preferred a model such as popcubes but the students seemed to do fine with the number line so it goes to show the many different methods that can get through to them.
ReplyDeleteChapter sixteen continued the discussion of fractions only it went in a little deeper to discuss fraction computation. Fractions can be terribly confusing on their own so when computation is involved it just seems like a mess. I liked the section in the chapter that discussed problem-based number sense approach. It discussed the need to go slow with algorithmic procedures so students really have a chance to develop fraction number sense before doing any computing with them. This will give students a change to discover what they can do with fractions before any strict methods are put in their heads. Fractions are a hard concept so when students can come up with self-invented methods that make perfect sense to them then that’s a major aid.
KatieC,
ReplyDeleteI like your example of how when teachers use manipulatives that students are familiar with, or that they can relate to, it sort of helps it click by keeping their attention. I’m a big fan of visual hands on aids in teaching so this apple example sounds great. Chapter sixteen was also a bit confusing for me. It was a lot to take in and I too didn’t really think estimation would be an aid in fraction computation at first. Like you said though, estimation helps students get a better grasp on the fractions. It can give them a better knowledge base on fraction number sense by allowing them to see what fractions are close to what whole numbers. Fractions were hard when we were younger and I think they just continue to be a bit frustrating! Good post!
When reading Chapter 15 over developing fraction concepts I was able to learn lots of useful information to use in my own classroom some day and I was also able to learn information about fractions that I didn’t know beforehand. Before reading this chapter I was unaware that the part-whole model is the most commonly used in textbooks today and now that I stop to think about it makes sense to me. I liked how the book also talked about how it is important to say three fourths instead of saying three over four. I liked the section of the chapter that talked about estimating with fractions which is important in any elementary school classroom. The book gave great examples of what to say to students such as what fraction of our class are wearing sweaters or what fraction of our pick picked spaghetti. These were great ways to estimate in the classroom using fractions. Lastly I liked how on page 306 at the end of the chapter it gave different tips that were found throughout the entire chapter with a total of 10 tips which will be great for me to refer back to when I begin teaching.
ReplyDeleteWhen reading Chapter 16 over developing strategies for fraction computation I was able to learn lots of new information that I will be able to use in my own classroom someday. I liked how the book gave a problem based number sense approach which gave me as the reader four guidelines to follow in order to develop computational strategies. I also liked how the book gave the different ways to develop algorithms which was very helpful. I like how the book pointed out that in order to add or subtract the students don’t have to find common denominators unless they want to or are doing the problem the standard algorithm way. Overall I liked the activity sheet that we did in class which was from figure 16.15 which was dividing the cookies into servings of ½ cookies. I loved the different activities presented throughout this chapter and are planning on using these activities when I begin teaching.
In response to Kristle C.,
ReplyDeleteI agree with you Kristle on the area of being nervous about fractions in relation to chapter 15. I agree with you that you as a teacher will go above and beyond in order to help your students understand the concept of fractions so that they are not as worried and nervous about fractions as you were. The fact that if the student doesn’t understand fractions from the beginning of the time teaching them then they will struggle in it that area of fractions the rest of the time is exactly correct. I believe that if students are struggling in an area that the teacher needs to stop and rethink about what they are teaching and how they are teaching it and adapt their instruction to the needs of the students. This will help the students to possibly understand the idea of fractions in a way that is better fitting to them. I also feel that it is so important to use manipulatives in order to help the students understand the concept of fractions.
I have some of the same views of the topics in chapter 16 that you had. I feel also that students need to have a strong sense of fractions in order to help them to solve the problem. If the students don’t understand fractions at all or not in the right way then the student will not be able to solve problems dealing with fractions. I also agree with you that it is great when educators find ways to help students to solve the problems dealing with fractions and to slowly but surely help the students to develop a stronger fraction sense.
We have been talking a lot about fractions in class the last few class periods and I realized they are very difficult. They are difficult for me. So I know they must be challenging for children. There are so many different ways you can teach fractions and I think that a teacher should try all the ways until they find what works for their class. It doesn’t really mean that one strategy is going to work for all the students in your classroom. This is why learning all of these different strategies for the classroom.
ReplyDeleteI think I can honestly say I hope I never have to teach fractions. I just don’t enjoy them at all and I would much rather teach addition and subtraction. Maybe it is because fractions are still very confusing to me and I wouldn’t feel comfortable teaching it to other students.
In Response to Shannon H.
ReplyDeleteYour insight on teaching fractions is great. I think you are so right in saying that what is easiest for us may not be the easiest way for the children. I think this is why I do not like fractions very much. I do not understand the deeper computations in fractions and it does get very frustrating. Students learn best with a teacher that knows exactly what is going on.
FRACTIONS! What a scary word! Chapter 15's concepts are useful and helpful, however. This whole book gives great tools and examples. It seems that working with elementary students, and from my own experience, that students are usually scared of fractions... I think that they are just misunderstood. I believe with the correct resources, students can and do fall in love with fractions. I know I have mentioned this book before, but FYI (just as Dr.Stramel described) the Hershey's Bar book and the M & M's are great literature for young students to comprehend fractions.
ReplyDeleteI know we have been discussing fractions with our class lately, and they can be overwhelming. I think just with any topic within mathematics, fractions are a system that that domino affect each other. In order to understand what 2 + 3 is, you must understand what "2" is, what "3" is, and what "+" is... and how to put the equation all together. The same for fractions. I think that as long as teachers/students make sure and "break down" the steps within fractions and make them as fun as possible, students won't get so frustrated or discouraged with fractions. With that being said, I also feel that we should not just refer to pizza and pies for fractions. I know that within our HOT kit there are several examples of lesson and tools, such as the fraction towers and fraction circles, that can be used for future reference. I look forward to making fractions fun by incorporating choice of what students will compare and contrast fractions to. I also think that in the beginning of learning fractions, group work will be encouraging versus individually (also to help one another).
In response to AMANDA L.-
ReplyDeleteI too agree, I think that different concepts are meant for different students. Even as an adult, I feel this way with many things. Especially with fractions and their complexities, I think all students should feel comfortable with how THEY comprehend fractions. Whether it's by visually seeing a pizza split into even pieces OR being handed pieces of a chocolate bar OR working it on on paper. There are many ways, and any way is A-Okay. It's finding the concepts that work best that may take time. But I also think along with this idea, it's important to incorporate group work so that students may be able to see how other students comprehend fractions, in turn hoping that they will be able to better attain fractions, too.
Chapter 15 and 16
ReplyDeleteChapter fifteen and sixteen 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. discusses how to teach fractions as well as how students learn about fractions. Fractions are a starting off point for many other concepts in math and if students do not understand fractions it may be hard for them to grasp these other concepts. Van de Walle et al. backs up this statement in chapter fifteen of the textbook by saying in the textbook that “This lack of understanding is then translated into difficulties with fraction computation, decimal and percent concepts, and the use of fractions in other content areas, particularly algebra (Van de Walle et al., 2010, p. 286). Van de Walle also states in chapter 16 that “We can use their prior understanding of the whole-number operations to give meaning to fraction computation. This, combined with firm understanding of fractions, provides the foundation for fraction computation” (Van de Walle et al., 2010, p. 309). These two chapters really explain how so many different concepts come together forming new concepts.
A piece of information that I learned from chapter fifteen of this text was different strategies that I could use to assist students with estimating fractions. This was always difficult for me in school so it is nice to fine different ways that I did not know about before. I liked the different examples that the textbook uses in figure 15.14 on page 299.
A piece of information that I learned from chapter sixteen of Van Walle et al. textbook was a strategy to teach students how to #/# of #/#. This can be a difficult concept for students to understand and I have never done it the way it is described in the textbook on page 319. Figure 19.9 said to start with a fractions and then to divide the other by that fraction. I can think of different manipultives students can use to understand this concept as well.
Something interesting mentioned in chapter 15 of Van de Walle et al. textbook was when to teach students different fraction rules. According to the textbook “if students are taught these rules before they have had the opportunity to think about the relative sizes of various fractions, there is little chance they will develop any familiarity with or number sense about fraction size (Van de Walle et al., 2010, p. 300). Another interesting piece of information mentioned in chapter 16 of Van de Walle et al. textbook that made me think about how I will conduct my classroom is “it is important to give students ample opportunity to develop fraction number sense prior to and during instruction about common denominators and other procedures for computation” (Van de Walle et al., 2010, p. 310). Knowing this will assist me in the long run to know what I need to focus on with me students.
to be continued...
Chapter fifteen and sixteen of Van de Walle et al. made me think about when I was learning about was how I always related to fractions. I would always no matter what would think of fractions as a pie. If I was comparing fractions I would ask me self which piece of the pie would I want and that would usually help me. The bad thing about always using this strategy was that it started to get difficult to do larger numbers. I would often times not divide my pie up correctly and then would get the wrong answer.
ReplyDeleteSomething from chapter fifteen and sixteen Van de Walle et al. that I would like to use in my classroom is having the students use a variety of manipulatives in the classroom. This chapter of the textbook had many different ideas for how to show the concept for fractions to students and they are a great way to find different ways for students to relate to the material. I also really liked all the different activities that were featured in the lesson. These are ones that I would like to use in my classroom.
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 Rachel Curry,
ReplyDeleteI agree with you that fractions are difficult for some students but they don't have to be as long as the teacher explains everything. Fractions always seemed backwards to me and that is why I think it may be difficult for some students. It is just a different way of thinking.
In response to JenniferP
ReplyDeleteI agree that the variety of approaches given in these two chapters is certainly interesting. When it got to dividing fractions and talked about the common denominator method I really had to slow down because I had not worked with that method, just the invert and multiply method
If we make our students only do something in one way we are not doing the m a favor, no matter what way we make them use.
Math is a subject a lot of people do not like, fractions is then the least favorite part of many people's least favorite subject.
ReplyDeleteThese two chapters fit with the rest of the book in that they approach fractions using the same basic approaches the book uses for the other topics discussed. As before it does not spend a lot of time discussing the so called traditional methods, likely assuming that we know them well. I have never really appreciated that assumption, assumptions are dangerous things.
As teachers we should try not to assume our students do or do not know things, that is why we are supposed to use pretests.
These two chapters do a great job of breaking down the topics covered in a way that is easy to understand and will help us to explain the topics to our students in easy to understand ways.
These two chapters are worth all of the time I have given them and more.
I would agree with how chapter 15 starts! I do think that fractions pose a considerable challenge to students. Overall most students show weakness in fractions. I think it is important in order for students to fully understand fractions that they see the fractions in many different ways. Oddly enough I never realized that pattern blocks could be used for fractions. I had never seen them used for this purpose so I think they would be fantastic! I also like the idea of giving emphasis on seeing fractions as division. Personally I love fractions and always have! I think that chapter 16 is super important. Our students have to be able develop the important strategies to figure out how to figure fractions. I really liked model 16.8. It was neat to see the different models for the multiplication of fractions.
ReplyDelete@ Elizabeth Sills
I agree with you. However I really like fractions but I am very scared of teaching fractions. I did do fractions for my mini HOT lesson and I was super nervous! I will definitely refer back to this book when it comes time for me to teach strategies for fractions! Have you ever seen the Everyday math curriculum taught? They teach it is with so many different variations that help all students pick up on the concepts!
Carissa Kruse
ReplyDeleteChapters 15 and 16-BLOG
Chapter 15 was about developing fraction concepts. When starting this chapter it honestly made me a little nervous because I remember how much of an issue fractions always seemed to be when they were brought up in my math courses. It seems that no matter how well students are doing with the concepts things get more difficult to understand when fractions are brought in.
I liked how the book gave many examples of how to use manipulatives to help students with the concept of fractions. I remember using some of these manipulatives in the classroom but others are new to me but are very impressive, because they give students different ways of looking at the same information. I also liked the activities that were given for students to use fractions. As I watch some of the students in my internship struggle with addition and subtraction it sometimes worries me about how they might handle more difficult concepts in the future. I do think that these activities will be helpful to them though. I am surprised more and more every time I look for new books by how many good math books there are out there for students.
Chapter 16 is about fraction computation. Seeing the fractions within the equation scares students, but having to actually solve the problem is the tricky part. There are so many different rules for fractions that are different from whole numbers, that it can be hard to remember what to do and when. Luckily there have been many strategies created that make the solutions easier to come up with. According to the book fraction circles are the most widely used strategy however they can be difficult to use if the students are not careful. If the circles are not perfect and the partitions do not show equal parts the students can easily come to the wrong conclusions and come up with the wrong answers.
I have not yet seen fractions used in my internship classroom but know that the teacher has many manipulatives ready to help the students when it is necessary.
In response to Lindsay H...
ReplyDeleteI had also never thought about using pattern blocks as a fraction manipulative. However, after looking through the book and seeing the strategies to use I am very confident in the fact that the pattern blocks could help students that may be having trouble. However, just like any other manipulative used students must understand that they are math tools and not toys.
I won’t lie… When I started reading chapter 15 all I was thinking was, “Yuck… Fractions!” At the end of this chapter though I was relieved because it seemed a lot easier than I was making it seem.
ReplyDeleteThe fraction constructs were new to me – not the actual fractions, but the names. It seems I have learned all of these constructs that are given throughout the book, but I never know the actual name that goes with it. Would it be beneficial for students to know the names like “part-whole” or “ratio” instead of some other term that a teacher may use?
Manipulatives are my favorite part of this book. I love that for fractions there are several different types of manipulatives that can be used. I think all students need to be familiar with all of them, but once they understand a concept I think it would be okay to let them use what works best for them!
Chapter 16 was also about fractions, only this time it involved the computation aspect. This textbook does an excellent job of giving examples and showing you how to teach and solve problems. In addition to the book, a little clarification from Dr. Stramel during lectures made it a lot easier to understand. I can say that I’m not as scared to teach fractions as I originally thought I would be!
@ Carissa K
ReplyDeleteI think we all agree that the concept of fractions makes us nervous. I was never bad at math (until high school) but I always second-guessed myself when working with fractions. I would hate for this trend or attitude to continue when I find myself up in front of my class one day teaching fractions.
I love the manipulatives and the ideas the textbook gives us. All of these ideas are things we need to keep in mind when we do have to teach fractions. I also agree that the manipulatives and ideas could definitely benefit the students that may struggle a bit with concepts in math that are crucial to go further (like adding and subtracting to add and subtract fractions, etc.).
Lacey Keller
ReplyDeleteAs opposed to many who have posted here, I love, love, love fractions! I guess this is because I had a wonderful teacher who explained in depth the concepts. While reading chapter 15, I kept thinking, "yep, I did that, and that, too!" My teacher introduced several fraction models so that every student could relate to at least one model.
The ideas in these chapters that has impressed me the most is the writing integration. Two subjects combined equals greater learning and success for the students.
The part of the chapters that I would like to see develop a little further is the use of food in the classroom. Every other page seemed to have a problem dealing with some sort of food. Please remember some students may have diseases that prevent them from participating in food related lessons. Yes, I do agree, students can relate to pies, fruit, and candy bars, but I would hate to see any student left out.
Lacey Keller
ReplyDeleteIn response to Emily:
I too love to incorporate manipulatives into lessons. Honestly, I didn't think they were too important until this internship. My mentor teacher uses manipulatives in every lesson, and her students just seem to get that "I got it!" look every lesson! The students love math because they get to get their hands on something.
To Kristie C: I don't mind simple fractions but when they start getting odd and big my brain gets confused. I am glad that you are going to stress fractions in your classroom instead of avoiding a topic that makes you uncomfortable. I don't remember being taught fractions with manipulatives, so I found this interesting in the chapter.
ReplyDeleteFractions, Fractions, Fractions. I think this word makes many people uncomfortable. Personally for me I learned fractions the old way. Adding and subtracting involved find the common denominator. Multiplying was simple straight across and division was flipping and multiplying. Therefore, I found this chapter very interesting and took a lot of good information on how to teach elementary students fractions using manipulatives. I felt like this chapter had a lot of good activities that I can use in my classroom.
ReplyDeleteChapter 16 More Fractions....This chapter discussed fractions more and included many good examples. What I took from this chapter is that students may grasp a better understanding of fractions if the teacher uses real life situations. I like the the example in the book that uses the Ben and Jerry example. Yum. I think it would fun to do a real life example in the classroom so the students could participate. I feel like it would be a good memory of learning fractions.
ReplyDeleteTo Lacey K: That is great that you had a good teacher. I think there are many ways to implement fractions in the classroom. It just takes a little creativity on the teachers part. Kids get excited doing all kind of things.
ReplyDeleteOh the joyous fractions! I can honestly say that fractions are not my favorite concept to learn let alone teach! These chapters were very informative offering numerous strategies and methods to use when teaching fractions in the classroom. There were many terms and ways of figuring fractions that I had never heard of. Many of the phrases I remember learning while being taught fractions are not even used anymore and our text even says that these phrases can be very confusing for students such as “reducing fractions.” Even when I am working with my students today I use this term, I now know that is more confusing to students than helpful. I have to remember to use the term simplified and not reduced. I was also not familiar with the term iteration; while I have heard the term I did not know its actual meaning. I loved the concept on page 295 that stated “the top number counts the bottom number tells what is being counted.” I do not know why I had never thought a fraction in that way before.
ReplyDeleteI love the idea of having numerous manipulatives to use while teaching fractions. Fractions could be a very good unit for visual and tactile learners due to the fact that the best way to learn the basics of fractions is to “see” the examples by using different manipulatives with the students.
In response to Katie C:
ReplyDeleteI believe the use of manipulatives in teaching fractions is very important and I also like the example you gave that was shown in your ed psych class. These manipulatives make the understanding of fractions so much greater than just writing the examples on a piece of paper and only drawing circles. I also found the estimation method of figuring fractions to be quite interesting. I had never thought of completing fraction problems in this way! Factors are very important for students to know when working with fractions and I believe that in that concept is where many students begin to fail the understanding of fractions simple because they do not know the basics needed when it comes to understanding and working with fractions.
Chapter 15 – Developing Fraction Concepts
ReplyDeleteThis chapter talks about the importance of our understanding of fractions AND all the possible concepts that can be represented by a fraction. I know that fractions can be scary but I feel like this chapter helped go deeper and help us to see we can just know that a fraction is part of a whole – in fact it is, but we need to know what it REALLY means. We need our kiddos to be able to cross over the information they are learning to real life scenarios. Our terminology is important as well. We have to be careful as to not confuse the student any more than they might already be. We have to be able to help students build on their prior knowledge of whole numbers. When talking about the concept of fractions the text says it important that students understand that a fraction is one number and that all parts are equal sized. I thought the different models the book showed us were handy. Some of them I was familiar with and then there were some I was not as familiar with, but I felt like it was great information to have. Fractions don’t have to be scary, but they are important to gain the deeper knowledge as our students are learning. They need to know what the fraction really is telling them, what does it mean? They need to know the proper vocabulary to help with this understanding. All of this is our job as educators to make sure is happening. To do this we need to make sure we are assessing our students by presenting exercises and asking questions.
Chapter 16 – Developing Strategies for Fraction Computation
This chapters takes us deeper into the importance of our fraction knowledge. I love that at the very beginning the text states “…learning rules without reasons, an unacceptable goal.” Development of number sense is just as important when dealing with fraction as with dealing with whole numbers. The text talks about strategies for adding and subtracting fractions. I can remember using the fraction circles. Seems like many teachers use the idea of a pie cut into piece or a pizza. I like the idea of using the ruler or a number line. The fraction bars are a new manipulative to me and we used them in class. I liked using them because you can really get the idea of add or subtracting fractions without having to find a common denominator. This chapter really made me see the importance of using manipulatives. I don’t remember using manipulatives much but I know that they help a great deal and I plan on using them as much as I can. Overall this chapter was a great deal of help. It does go to show if we don’t do a great job in our early years with our students with whole number adding, subtracting, multiplying, and dividing – we are setting them up for a tough struggle down the road.
@ Lindsay H
ReplyDeleteI am with you that its safe to say many students will and do struggle with fractions. I am pretty sure I did when I was learning them. I would hope that teacher can find ways to help limit this struggle. The manipulative and activity suggestions in these 2 chapters should really help with this. I think if we as educators can push ourselves to think outside the box , then we can really help benefit our student and help ease that struggle with fractions. There are so many other options our there for us to apply to our lessons.
After reading this chapter, I feel a lot better about the topic of fractions. I still don’t like them as they feel very confusing to me, but I feel better learning the many ways I can teach them to my students. I usually cringe when it come to fractions. The mentor teacher I intern with told me I could either teach fractions or graphing for my formal observation, so of course you can probably guess which one I chose, yep, graphing. I felt more comfortable with the topic. I have learned from this chapter that I do not have to feel so overwhelmed when teaching fractions. I always hate dealing with them when it comes to tests. I do real well with probability which is some fractions as well. Not sure why. Maybe part of my problem with fractions is I don’t take my time to deal with them and I have a negative attitude towards learning about them. I do not really feel as strong in this issue anymore after reading this chapter. I will definitely keep this textbook very very close to me when teaching it in my classroom. Who would have known that drawing circle could help with fractions.
ReplyDeleteIn response to Shawna W. –
ReplyDeleteI agree that this chapter was great in going deeper for us to understand fractions a lot better. To know that a fraction is a whole number and the parts are all equal in size. They just make up the whole number in the end. I know this information already, but I still hate when I have to use fractions. When I am cooking, my husband always helps me learn fractions when it comes to the measuring cup. I hate cooking with a fraction I do not already know, but it is a great exercise for me. He loves fractions which is great because he loves math and that is his section he helps our son on in homework and it is English for me.
Chapter 15 and 16 covers Fractions. I have always had problems growing up when we would learn fractions. It was always something I struggled with. After reading Chapter 15 and 16 I feel like I have a better understanding of how to teach fractions and the different ways you use them, the different language that goes along with it as well as the symbols.
ReplyDeleteIn Response to April B:
I feel the same way about fractions. I felt like these chapters made it easier to understand and apply to different lessons.
Chapters 15 and 16 were all about fractions. Chapter 15 talked about the concept of fractions while chapter 16 talked about developing strategies for fraction computation. I really enjoyed reading about all the different strategies in chapter 16 that teachers can use to teach fractions in their classrooms. I was never a fan of fractions when I was younger and even still today but I believe from this course, I am excited to teach my students this concept. I believe I am so excited because there are so many great resources out there that can be used to teach. There are a number of books, as we learned about in class than can be used as read alouds. Also, I enjoyed listening and watching Dr. Stramel teach us strategies to use.
ReplyDeleteIn response to April B--I completely agree with you, I am not very found of fractions myself but after this chapter I feel I will definitely be more comfortable teaching my students this concept then me learning this concept. There are so many great strategies that can be used to teach fractions that I believe we won't have a problem trying to find ways to teach this concept. Thanks for sharing!
ReplyDeleteChapters 15 and 16 discuss developing fraction concepts, as well as developing strategies for fraction computation. My instructional unit was over addition of fractions and so I referred to these chapters many times as I was preparing my lesson plans. These chapters are full of wonderful ideas of how to help students develop a concept of fractions and what they really mean. I wish that I had been introduced to fractions this way. I think that teaching fractions the way these chapters describe could alleviate much of the anxiety many people associate with fractions.
ReplyDeleteChapter 15 discusses developing fraction concepts, including fractions being parts of a whole, and made up of equal parts. It also discusses the concepts of “sharing” and equivalent fractions. During my formal lesson plan I used manipulatives to review basic fraction addition. After having taught that lesson I am bigger believer in manipulatives than ever before. There were many students who understood after being able to “see” the fractions, that hadn’t understood before. Through the use of manipulatives I was able to teach students many of the fraction concepts discussed in this chapter, including equivalent fractions and simplest form.
Chapter 16 discusses fraction computation. It suggests allowing students to use invented strategies first, so that they will develop an understanding of fractions before moving on the standard fraction strategies. It also discussed like and unlike denominators, common multiples, as well as multiplication and division of fractions. Each section includes multiple ways that teachers can help students develop the concept outside of traditional pencil and paper problems. I know that this book is something I will refer to time and time again, and that it will continue to push me further from how I was taught and further into teaching students to really understand mathematical concepts.
@ April B
ReplyDeleteI was never very fond of fractions either, but this is what I ended up teaching for my formal observation and I now feel very comfortable with the topic. One of the advantages of developing these instructional units is that you learn a concept inside and out, and I feel I learned a lot about teaching math in a way that is hands on. This is somewhat of a challenge for me because it is so different from how I was taught, but it is also so much more rewarding!
As a young student, fractions always frustrated me. As an adult, I actually enjoy fractions. Fractions can be tricky to teach if the right skills aren't put in place. It is important, and meaningful to students when real life situations are used. For example, using a cake to teach fractions is how I learned. Anything to use to peak students interests about fractions. Manipulatives and visuals are very important when teaching fractions.
ReplyDeleteIn response to Lindsai S.:
ReplyDeleteYou said, "There were many students who understood after being able to “see” the fractions, that hadn’t understood before. Through the use of manipulatives I was able to teach students many of the fraction concepts discussed in this chapter, including equivalent fractions and simplest form." That is so great! I agree that manipulatives can make a world of difference in the process of teaching fractions. It really is something that truly needs to be visualized before true comprehension can easily take place. Most math topics are more easily understood while using manipulatives, but if I were only allowed to use them during one topic throughout the school year, I would definitely choose fractions.
Jena Simms: "Why didn't I have a teacher who taught me this information?" I feel that way about most of what we have learned in this class! I feel like I would have been much more able to do math is it had been as okay to explore different ways of doing problems as it is in this class. Every time Dr. Stramel shows us another way for students to do something and says, "it's OK if students do it this way" it makes me smile and I have "aha" moments about math every week.
ReplyDeleteChapters 15 and 16 both deal with fractions. Chapter 15 discusses developing fraction concepts and chapter 16 discusses developing strategies for fraction computation. The definition chapter 15 gives for fractions is rather interesting. It says fractions are critical foundations for students because they are used in measurement and are essential for the study of algebra and advanced mathematics. We really do associate fractions with measurement the most; whether the measurement is for cooking or for measuring on a ruler. One of the things I have the hardest time with is fractions when it comes to measuring with rulers. When we did the activities in class I developed a better understanding of fractions. But I’m still nerves about teaching them. How do we teach something when we are so unsure of it ourselves? Chapter 16 shows an example of how to multiply fractions using grid paper. I remember when we did that activity in class. I have never multiplied fractions in that way, but I could see how it would help children who are beginning with multiplying fractions. We often frown upon teachers who are stuck in one way of teaching. Those teachers who just teach the traditional way and refuse to bring in something knew. I think they do this because they themselves do not understand the concept fully. I mean, my high school math teacher was one of the smartest people I’ve met in the mathematics field, but he was so strict on how to do each problem. You had to do it his way or else it was wrong. I feel like he did not know any other way of doing the problem and he was afraid to learn a different way.
ReplyDeleteChapter fifteen talks about building on whole number concepts and how important it is to help students see how fractions and like and different from whole numbers. It says to avoid saying “three out of four” unless talking about ratios and proportions and not to “three over four.” I did say 3 over 4 some in my mini-teach. I was thinking about when students are first introduced to writing the fraction and what it looks like. But I think I said, 3 over 4 or ¾, and I think it would have been more effective to say 3 over 4 IS ¾ or to say: when you see a number written as something over something (3 over 4), the number is~ and then state the fraction (three-fourths). Does that even matter? Will we need to make distinctions and help students identify this, or will their everyday life give them plenty of exposure? Sometimes I realize that I give too much information instead of letting students driving the learning. I just want them to “get it” so badly that I “help” them, which I have also noticed looks really ugly when I see other teachers do it.
ReplyDeleteI liked what the chapter said about fractions telling about the relationship to the whole, they don’t tell the size of the whole. The text gave the illustration of choosing ½ of a pizza or 1/3 of a pizza. Because the pizza that offered 1/3 was larger than the one that was cut in 1/2, the person who chose the 1/3 of a pizza got more pizza.
Chapter 15 also gives some good examples of students justifying their work and explaining how they found their answers. This is something I really appreciate about this text. This seems to me to be the most important thing about mathematics- that the student is able to explain HOW they came to the right answer. And sometimes they may have the wrong answer do to a simple error but when they explain it, the teacher knows that they understand the concept. This helps both the student and the teacher and develops the students understanding while giving the teacher an assessment of the students understanding.
Chapter 16 starts out by discussing number sense and fraction algorithms, and states that conceptual development takes time. Dr. Stramel stressed this in class and said, do you remember that from being in school? It takes time to understand the concept. That hit home with me. I know I am not alone when I say that for me to learn math takes a lot of practice and just doing it over and over until it makes sense. The concepts in this chapter make more sense to me because we did them in class also. I was able to understand the idea of developing a fraction algorithm when I pair the information in the text with what we did in “class.” Sometimes I feel like watching the adobe connect does not connect me to the teaching at all and sometimes I learn so much. In this class when the on-campus class works math problems, I learn too. This is really valuable to me!
In response to Kymberly: I loved working with numbers all my life, from grade school to high school. Fractions, however, were not my strong point, but I got by. I remember taking an industrial arts woods class all four years of high school. I had the hardest time reading a tape measure (I know that sounds horrible, but its true). I had to have my teacher help me every time I was to measure something. After reviewing fractions in class in math methods, I feel so much more confident about fractions.
ReplyDeleteMy instructional unit was on the conversions of fracions/decimals/percents. It was developed out of my confusion in my past experiences. Conversions are very common in life and I wanted to teach it in a way that makes it fun and applicable. Our textbook recommends a book titled "The Man Who Invented Parks" Even though the book was somewhat boring it was a good tie into my lesson. The students had to opportunity to create their own park on grid paper in small groups. From their, the students had to determine what part or percent of the park would be what. The students had a lot of fun applying fractions/decimals and percents to an relevant activity.
ReplyDeleteThe most important take away for me is the need for manipulatives in this subject area. Dr. Stramel did some great exercises with manipulatives. By allowing us to participate in the use of these manipulatives made all the difference to me. You can read all about the importance, but until you get your hands on them that is when you really understand their value.
@Shawna
I'm so glad that you brought up using rulers. My mentor teacher has done some amazing activities with rulers and fractions. I would have never thought to tie the two of them together, but they go hand and hand. Addition and subtraction of fractions can be easy with a ruler.
Chapter 15 and 16 discussed developing fraction concepts and strategies for fraction computation. I thought that it was important that the text stated, "A fraction tells us about the relationship between the part and the whole." I can understand why some students struggle with fractions because sometimes even I have to really think to determine which out of two fractions is actually larger. I enjoyed doing the activities in class with the fraction bars and circles. The fraction bars were very useful because you could see exactly what 2/4 looks like as well as the fractions that were equivalent. Using these types of manipulatives will definitely help students to better understand exactly how one-half is larger than one-third. Some students may also need to draw pictures in order to represent the problem and this should be encouraged. The drawings that we did on the graph paper were helpful. As we were comparing fractions in class, it was very tempting to use the traditional algorithms and find the common denominators, but the students will not automatically think about doing this. It's important for teachers to show them other ways that they can determine which fraction is larger/smaller.
ReplyDeleteHaving students estimate the answer to an addition problem involving fractions can help them to better grasp the concept of what exactly 12/13 looks like and that it's close to 1. There are so many ways that fractions are used in everyday life including baking, driving, measuring, etc. These are important concepts that we should make sure that our students understand because they will be using them even after they are finished with school.
In response to Lindsay Sabala:
ReplyDeleteI completely agree with you! I wish that I had been taught about fractions using the methods that have been shown to us in class. I think I'm definitely more of a visual person and they could have helped me to understand some of these concepts much better. I'm glad that the Common Core Standards emphasize the importance of using manipulatives and I think it's a great way for students to demonstrate that they really understand the material.
Chapters 15 and 16 are all about teaching students fractions. I remember being introduced to fractions as the teacher wrote them on the chalkboard. We never used any manipulatives or models that I can recall. I had a hard time understanding fractions until I had that “aha” moment when I realized that the bigger the bottom number, the smaller the fraction was. After that they seemed to make sense, but I always wondered why my teacher didn’t explain that to me to begin with. I think using the methods outlined in these two chapters in combination with real life situations and use of manipulatives is a much better and more effective way to help students understand what fractions are and how to use them.
ReplyDeleteBrandi S., I agree with you that the need for manipulatives when teaching fractions is very important. Like you, I am grateful that Dr. Stramel showed us how to use them in so many different activities. I don’t remember using manipulatives hardly ever when I was in grade school. It is nice to see them in use.
ReplyDeleteElizabeth:
ReplyDeleteI don't remember using manipulatives to help learn fractions. I love how Dr. Stramel incorporates math manipulatives during class this help me learn because I'm a hands on learner.
Fractions were harder for me to learn. We didn't have math manipulatives to help us understand them during school. I like using the math manipulatives because I think its easier for students to see.
ReplyDeleteChapters 15 and 16 were all about fraction. I, like most others in this class, am not a fan of fractions. I have always liked math and been fairly good at it, but I have avoided fractions like the plague! I would never work a problem with a fraction in it. As soon as I saw a fraction, I automatically converted it to a decimal. The fact that I have all of the commonly used fractions’ decimal equivalents memorized is a clear indicator of this. I realize now that fractions are not the enemy; they just need to be taught correctly. I will have to get over my avoidance of fractions so that my students can learn to use them without being afraid. When thinking about how I learned fractions, I really don’t remember using any sort of model or manipulative. I just remember the numbers and maybe a circle here or there. Had I been introduce to fractions with number lines, fraction towers, or fraction circles, I might have had an easier time understanding them. Like any subject, when completing computations with fractions, it is important to apply real-world uses. No one walks down the street and is asked how much of a circle is shaded in. However, there are many situations such as dividing food or materials among people that do happen and involve fractions. The use of fractions is a very important math concept that every student needs to understand. If we start teaching fractions in a better way, maybe the concept will become less horrifying to students.
ReplyDeleteElizabeth --
ReplyDeleteI am the same way, I don't ever remember being shown fractions with a model or any kind of manipulatives. I just remember the teacher writing fractions on the board and explaining how to find common denominators, or cross multiply, or flip and multiply for division. I definitely think if I had gotten to use a manipulative I would have understood fractions better and more quickly.
Chapter 15 and 16 were about teaching fractions. I honestly have never liked fractions and it is so funny to hear our whines and sighs in class when Dr. Stramel tells us that is what we are doing for the day! I will say using the manipulatives have been such a great help, especially for me! They are so much fun and we can visually see how many different ways of creating fractions. It is funny when we get stumped in our groups with the deer in the headlights look! Then it comes together and we have a blast. I never got anything with fractions other than a teacher and chalkboard! I think that all of the new manipulatives not only makes fractions fun for students, but it also gives so much of a better understanding. I have leaned so much these past few weeks in class!!
ReplyDeleteIn response to Allison G,
ReplyDeleteI agree with you that fractions are not the enemy and that it is so important that they be taught well for a good understanding. As much as we whine in class it is fun once we get going to see all of the varieties of fractions we can come up with. I know I need more knowledge in fractions when it comes to me actually teaching them to give this much of a variety, but at least now I feel comfortable in saying that I can understand what I am teaching!
Fractions have always come easy to me, unlike many people. I am not sticking my nose up in the air, on the contrary, because they have made sense to me I find it extremely difficult and at times frustrating if the student is having a difficult time.
ReplyDeleteI have worked with many students who just can not conceive of the idea. If I ask for half of an orange, they can give me half, but to ask them how much is 1/2 plus 1/2 they have no idea.
To me it was simple, you cut one orange into 2 pieces and take one of the two. you have 1/2. Now if I take another orange and do the same (take one of the two) and put that half with my first half, I have one whole. But my student may say I have 2 oranges!
Our text indicates that the fraction language is very important and maybe that is the key! I am anxious to try it out.
Jeremiah Gramkow
ReplyDeleteWhen you mentioned that we need to be careful not to assume the student knows something is so right on. I work with special ed students and to assume a 16 year old knows how to multiply or divide because they are classified as being in 10th grade is a horrible mistake. Many students will not speak up and say "I don't know how", they will just go on in total confusion.
That is something I need to remind myself often.
Great post.
I have always needed paper and pencil to figure out fractions as I cannot do the problem in my head unless, of course, I estimate. With that said, chapter 15 and 16 gave good examples and ideas to use for fractions. Using manipulatives, grids, dot paper or even paper folding are great things to use when figuring out a fraction problem. I didn’t even think about the vocabulary words when working with fractions, but like the book said when discussing fractions it is a good time to introduce new words such as fourths. Chapter 16 talks about the four guidelines to use when developing computational strategies for fractions which are: 1) begin with simple contextual tasks, 2) connect the meaning of fraction computation with whole number computation, 3) let estimation and informal methods play a big role in the development of strategies and 4) explore each of the operations using models. These guidelines are great when working with fractions and I will have to keep them in mind when I begin teaching.
ReplyDeleteIn response to Linda McC –
ReplyDeleteIt is always hard when students do not understand what you are trying to teach them, but try putting yourself in their shoes. They don’t have all the background knowledge you have so you make have to break it down even more for them to understand. Also going over the same problem again and again is key as well as having them know the language of fractions. Bring real word problems into the classroom and model what you are wanting them to do.
Ch. 15: In the first part of 15 they talk about how fractions are often the most confusing thing for young students.I remember that I didn't know how to tell which fractions were bigger. For instance when I saw 50/100 and 1/2 I automatically thought that 50/100 was bigger because it had bigger numbers. I think this is a popular occurrence with many students and I definitely understand how it would be confusing.
ReplyDeleteCh. 16: Putting fractions together was an even harder concept for me, when learning fractions. With out going through the whole process of changing denominators and working through every step I couldn't figure it out. It was hard enough for me to learn how to add, subtract, multiply, and divide whole numbers much less fractions. Now I think I understand fractions in a way that is easier to teach. I know more strategies to teach and ways to help them remember.
In response to Ashley L:
I agree with you on figuring out fractions without paper and pencil- it's so hard. I think I've gotten better at it in this class because I've learned how to estimate better. Also, those steps seem like they would work great and it's good to remember these things to use while teaching.