Fractions are often named by adults (and depicted in cartoons) as a dreaded math topic. Why do you think this is true? How might your fraction instruction alter this perception for your students?
Fractions get a Bad Rap simply because many teachers don't take the extra time to teach the concepts of fractions before teaching the procedure of the problem. Students, like me in elementary school, who learn the procedure of "doing" fractions will many times misunderstand the concept of the problems they are faced with because they didn't learn how to "see" the fraction conceptually, thus leading to a dislike of the subject. As with most subject students learn, it is ones that are made relevant and personal that are cemented in the student's brain and ultimately loved. For example, teachers of young students could discuss fractions as they relate to eating an ice cream cone or a box of doughnuts. For older students, teachers could use the concept of money students might acquire from their parents or find on the street as the concept for understanding fractions. I would enjoy teaching fractions as they relate to a service learning project. My idea would be to have students develop a food drive plan in which they collect food for four food pantries. The students will divide the food many different ways depending upon many different scenarios. The students will use area models, grid paper and visual concepts to understand the concepts of their project. After the conceptual and planning work is complete the students will actually get to do this service learning project for real. There are many different ways to teach fractions, but it must be taught conceptually first.
I would reiterate Katherine's use of models, and Rachel's use of student-understood contexts as two important approaches to use when teaching fractions. Before learning the procedures to manipulate fractions in various ways (add, subtract, multiply, etc.) students must have opportunities to work with fractions, understand the relationship between the whole and the equal parts, and realize through continues use of context and manipulatives how unit fractions are comparable to the number 1 (see my comments in other post for this week). What student, no matter the age, wouldn't want to divide donuts or brownies.
I think Rachel's idea of incorporating fractions into a service learning project is a great idea. Students may be more engaged learning about fractions when they know that their work is going to help others. It also gives students a great opportunity to represent their progress of understanding fractions from area models to grid paper to actually dividing up the food for the food pantries. I also agree with Dean that through this project students can compare how unit fractions are comparable to 1 which is an important step in students understanding and comparing fractions.
Why are fractions the ugly step child of math? When something is not understood it is not favored. Katherine and Rachel quickly pointed out how difficult understanding fractions were for them and how difficult they can be conceptually. On the other hand I did not think any negative thoughts about fractions and remember using them to divide players in to halves for two teams or measuring wood to cut. I cooked and measured partial cups or amounts and remembering seeing a clock had quarters every fifteen minutes. It was not a problem for me that two numbers made one number in a fraction. I try to visual math a lot and found it was easy to realize with 1/5 and 1/10, that 1/5 was a bigger piece and that it meant the bigger the denominator the smaller the unit size in one whole. Or when I would add 1/4 and 1/4 I knew I would get a larger fraction and 2/8 was the same as 1/4, while 2/4 was equal to a 1/2 and that was larger than 1/4. The biggest part of this reading for me was the occurrence of formative assessments. This was important because the students from my experience learn fraction concepts at greatly varying rates. It was important because the assessments were quick and easy to assess. And they also would allow the small group instruction that area models, set models and equivalent models that provides the conceptual understanding for those who struggle with fractions. I am always thinking that when books talk about the formative assessments they never talk about the group that is moved on and how the two groups come back together! The article about progression of Common Core State Standards was of interest because the reality of where students are and where they should be is truly a lousy idea. I believe and the reality is that you take students from where they are and move them forward. The sixth grade students I worked with for fractions this year where all over the place with incorrect knowledge and inability with fractions. I could not say I will only teach them the 6th grade standards. If as educators we find ourselves saying that we are only responsible for these standards we as an institution will be in big trouble. The students will learn at different rates and be ready for information early or late! So again I come back to the formative assessment and the ability to use that well.
I think this is true because fractions are not well understood by many. We run into fractions almost every day and yet they remain a dreaded topic. If fractions are not explored and deeply understood by students, they may have a false understanding of how they work which could leave to math difficulties down the road and into adulthood. Just after reading chapter 15 I felt that I was able to look at fractions in a different way.
To help students gain a better understanding of fractions I think it is crucial that teachers explain the similarities and differences between fractions and whole numbers. The book points out that students often overgeneralize their knowledge of whole-numbers and apply that to fractions. Next, teachers should incorporate models into lessons to give students a visual of what they are learning. These models allow students to see 1 whole compared to 1/2 and eventually move onto partitioning fractions with visuals. The problems used in the classroom should have context that students can easily relate to; such as sharing food among the class evenly. In my instruction I hope to show students that fractions are very important in their lives and with practice and understanding they are something that students will become more confident using.
Jennifer Brown I think the portion of this chapter that stood out the most for me was was the concept of making the math accessible to the student's by using their informal understanding of partitioning and equal sharing. For instance, the example on page 347 with the pizza is an excellent visual for students. I also think this could be done using connecting blocks to represent a chocolate bar. For instance, students could make different size bars and ask a partner whether they want half of the big one or a whole small one. This would be a fun way to assess their understanding of fractions, collaborate with their peers, and create visual models for the math they are solving. The Chapter then goes on to describe the concept of equal sharing and again relate it to the student's life experiences. This allows for the opportunity for students to see the reason for why this kind of mathematical understanding is important in everyday life, allowing for a deeper learning experience. I also think that the concept of partitioning and equal sharing are easy to differentiate depending on the shapes or sizes and numbers used.
While I can get by, I am not entirely comfortable with fractions. Thinking back on my mathematics career, however, I realize this discomfort has less to do with actual fractions than with math in general. Similar to many of you, I was taught that there was only one way to do math. I could always do the algorithms but I didn’t necessarily understand the how’s and the why’s, which, as it turns out, are pretty important! At this point, I feel that I do not have a great number sense and doing mental math is difficult. I tend to revert back to lining numbers up vertically and looking at digits. No wonder why fractions are hard for me! There is a possibility that my math teacher did not really understand it, or just didn’t notice that I didn’t because I was still getting the right answers. I will definitely check to make sure my students understand important concepts and that they can explain and justify their answers. Having discussions and assessing student’s understanding will be very helpful. I think that the problem is that some students stop understanding how to do math by 3rd or 4th grade when it goes beyond simple addition and subtraction. Not having a solid base makes learning future concepts unrealistic. I wonder if the concepts I missed have to do with place value? I do not remember ever using models, but I now know how important this is in aiding understanding. I will use any kind of manipulative I can and encourage students to try them all to develop their own ways of solving problems. Making fractions a part of every day will help. Fractions are all around, and shouldn’t be so scary. I like the game we played in class today, like the one suggested in our text, that makes it fun and easy to see the connection between numerator and denominator. Having fraction puzzles at morning meeting might be helpful. Once students see how fractions work, fractions will not be so dreaded. Working to solve problems and succeeding will give students a sense of mastery and confidence.
Rachel and Tiffany's thread about service learning project makes sense. When we truly think about fractions they are every where in our students world. Making it real from time (quarter til three), cooking, win-lost fraction, grade on an assessment 17/20 correct and so much more. Students understanding of one is so important as many have mentioned, but it surprises me how many students say they understand what one is but then forget to define what one is with a particular problem.
Fractions get a Bad Rap simply because many teachers don't take the extra time to teach the concepts of fractions before teaching the procedure of the problem. Students, like me in elementary school, who learn the procedure of "doing" fractions will many times misunderstand the concept of the problems they are faced with because they didn't learn how to "see" the fraction conceptually, thus leading to a dislike of the subject. As with most subject students learn, it is ones that are made relevant and personal that are cemented in the student's brain and ultimately loved. For example, teachers of young students could discuss fractions as they relate to eating an ice cream cone or a box of doughnuts. For older students, teachers could use the concept of money students might acquire from their parents or find on the street as the concept for understanding fractions. I would enjoy teaching fractions as they relate to a service learning project. My idea would be to have students develop a food drive plan in which they collect food for four food pantries. The students will divide the food many different ways depending upon many different scenarios. The students will use area models, grid paper and visual concepts to understand the concepts of their project. After the conceptual and planning work is complete the students will actually get to do this service learning project for real. There are many different ways to teach fractions, but it must be taught conceptually first.
ReplyDeleteI would reiterate Katherine's use of models, and Rachel's use of student-understood contexts as two important approaches to use when teaching fractions. Before learning the procedures to manipulate fractions in various ways (add, subtract, multiply, etc.) students must have opportunities to work with fractions, understand the relationship between the whole and the equal parts, and realize through continues use of context and manipulatives how unit fractions are comparable to the number 1 (see my comments in other post for this week). What student, no matter the age, wouldn't want to divide donuts or brownies.
DeleteI think Rachel's idea of incorporating fractions into a service learning project is a great idea. Students may be more engaged learning about fractions when they know that their work is going to help others. It also gives students a great opportunity to represent their progress of understanding fractions from area models to grid paper to actually dividing up the food for the food pantries. I also agree with Dean that through this project students can compare how unit fractions are comparable to 1 which is an important step in students understanding and comparing fractions.
DeleteWhy are fractions the ugly step child of math? When something is not understood it is not favored. Katherine and Rachel quickly pointed out how difficult understanding fractions were for them and how difficult they can be conceptually. On the other hand I did not think any negative thoughts about fractions and remember using them to divide players in to halves for two teams or measuring wood to cut. I cooked and measured partial cups or amounts and remembering seeing a clock had quarters every fifteen minutes. It was not a problem for me that two numbers made one number in a fraction. I try to visual math a lot and found it was easy to realize with 1/5 and 1/10, that 1/5 was a bigger piece and that it meant the bigger the denominator the smaller the unit size in one whole. Or when I would add 1/4 and 1/4 I knew I would get a larger fraction and 2/8 was the same as 1/4, while 2/4 was equal to a 1/2 and that was larger than 1/4. The biggest part of this reading for me was the occurrence of formative assessments. This was important because the students from my experience learn fraction concepts at greatly varying rates. It was important because the assessments were quick and easy to assess. And they also would allow the small group instruction that area models, set models and equivalent models that provides the conceptual understanding for those who struggle with fractions. I am always thinking that when books talk about the formative assessments they never talk about the group that is moved on and how the two groups come back together!
ReplyDeleteThe article about progression of Common Core State Standards was of interest because the reality of where students are and where they should be is truly a lousy idea. I believe and the reality is that you take students from where they are and move them forward. The sixth grade students I worked with for fractions this year where all over the place with incorrect knowledge and inability with fractions. I could not say I will only teach them the 6th grade standards. If as educators we find ourselves saying that we are only responsible for these standards we as an institution will be in big trouble. The students will learn at different rates and be ready for information early or late! So again I come back to the formative assessment and the ability to use that well.
I think this is true because fractions are not well understood by many. We run into fractions almost every day and yet they remain a dreaded topic. If fractions are not explored and deeply understood by students, they may have a false understanding of how they work which could leave to math difficulties down the road and into adulthood. Just after reading chapter 15 I felt that I was able to look at fractions in a different way.
ReplyDeleteTo help students gain a better understanding of fractions I think it is crucial that teachers explain the similarities and differences between fractions and whole numbers. The book points out that students often overgeneralize their knowledge of whole-numbers and apply that to fractions. Next, teachers should incorporate models into lessons to give students a visual of what they are learning. These models allow students to see 1 whole compared to 1/2 and eventually move onto partitioning fractions with visuals. The problems used in the classroom should have context that students can easily relate to; such as sharing food among the class evenly. In my instruction I hope to show students that fractions are very important in their lives and with practice and understanding they are something that students will become more confident using.
Jennifer Brown
ReplyDeleteI think the portion of this chapter that stood out the most for me was was the concept of making the math accessible to the student's by using their informal understanding of partitioning and equal sharing. For instance, the example on page 347 with the pizza is an excellent visual for students. I also think this could be done using connecting blocks to represent a chocolate bar. For instance, students could make different size bars and ask a partner whether they want half of the big one or a whole small one. This would be a fun way to assess their understanding of fractions, collaborate with their peers, and create visual models for the math they are solving. The Chapter then goes on to describe the concept of equal sharing and again relate it to the student's life experiences. This allows for the opportunity for students to see the reason for why this kind of mathematical understanding is important in everyday life, allowing for a deeper learning experience. I also think that the concept of partitioning and equal sharing are easy to differentiate depending on the shapes or sizes and numbers used.
ReplyDeleteWhile I can get by, I am not entirely comfortable with fractions. Thinking back on my mathematics career, however, I realize this discomfort has less to do with actual fractions than with math in general. Similar to many of you, I was taught that there was only one way to do math. I could always do the algorithms but I didn’t necessarily understand the how’s and the why’s, which, as it turns out, are pretty important! At this point, I feel that I do not have a great number sense and doing mental math is difficult. I tend to revert back to lining numbers up vertically and looking at digits. No wonder why fractions are hard for me! There is a possibility that my math teacher did not really understand it, or just didn’t notice that I didn’t because I was still getting the right answers. I will definitely check to make sure my students understand important concepts and that they can explain and justify their answers. Having discussions and assessing student’s understanding will be very helpful. I think that the problem is that some students stop understanding how to do math by 3rd or 4th grade when it goes beyond simple addition and subtraction. Not having a solid base makes learning future concepts unrealistic. I wonder if the concepts I missed have to do with place value? I do not remember ever using models, but I now know how important this is in aiding understanding. I will use any kind of manipulative I can and encourage students to try them all to develop their own ways of solving problems.
Making fractions a part of every day will help. Fractions are all around, and shouldn’t be so scary. I like the game we played in class today, like the one suggested in our text, that makes it fun and easy to see the connection between numerator and denominator. Having fraction puzzles at morning meeting might be helpful. Once students see how fractions work, fractions will not be so dreaded. Working to solve problems and succeeding will give students a sense of mastery and confidence.
Rachel and Tiffany's thread about service learning project makes sense. When we truly think about fractions they are every where in our students world. Making it real from time (quarter til three), cooking, win-lost fraction, grade on an assessment 17/20 correct and so much more. Students understanding of one is so important as many have mentioned, but it surprises me how many students say they understand what one is but then forget to define what one is with a particular problem.
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