I could so relate to the beginning of Leinwand's discussion pertaining to memorizing formulas/equations. I remember simply memorizing formulas and completing numerous equations using each formula but never had a grasp on if my answer was correct based on estimation or what made sense. I thought the idea of having students in older grades figure out how much skin would be needed for a skin graph is perfect. I also thought giving the students a number as a referent (1000) was a great idea....by the way I always thought this was a reference not a referent. For younger grades, they could figure out how much gauze would be needed to make a mummy Halloween costume.
Jeanne, I love your idea for the younger grades! I was thinking something like what Leinwand gave his class would be much too traumatic for younger students. This would be awesome to do with younger students! It would probably be a longer process and project though!
It definitely would take a long time, but if children got the concept it would probably be much more beneficial and meaningful to them than doing a bunch of calculations/problems on paper. The problem is so often teachers need to teach the math program that their town has adopted. I wish that teachers could just teach the topics listed in the standards in their own way. As long as activities and assessments are measurable, do we really need a text book to teach?????
I also like the Halloween costume idea. I agree that a lot of times the school system is rigid about what the teachers should be teaching. Luckily my school encourages hands-on teaching and the new evaluation tool for teachers allows teachers to basically create their own units based on the standards. Having the textbook as a guide as opposed to the lesson plan has always been more effective in my experience.
I really like the way Leinwand asks the questions, How big? How much? How far? Occasionally, I have heard teachers ask one of these questions when I am in the classroom and it always seems to make a difference in helping the students to really understand the size and scope of the problem being discussed. The skin grafting example was perfect for 7th graders. Once again, he is also making the math relevant and authentic as well. Giving students a word problem that they could care less about will not entice them to work hard to figure it out. However, giving them a situation in which they care about the outcome helps motivate them to do their best work. Students need to be able to determine the exact amount of things but also to estimate the outcome as well. I really enjoyed reading about the different ways the students answered the skin grafting question. Having the groups discuss their answers and how they came up with them is a great tool for helping all the students learn other ways to solve the same problem. We have discussed in class how bad US students are in regard to measurement so I agree with Leinwand that we need to make measurement an ongoing part of the daily instruction. Measurement is a math concept that is incredibly important to science as well.
Lyanne, I completely agree with you that students need to be able to determine the exact amount, but I like that the estimation the students used in their solutions were more about concept rather then getting an exact answer because it helped them to formulate an idea or plan of action. Then Leinwand sent home homework sheets with the formula and questions, which I thought was a great follow up, so they have time to think at home about the problem to get the exact amount instead of feeling pressured to think about it and get the "right" answer at school.
To this day, when I see a formula in any class I think to myself "start memorizing that now." In school memorizing a formula was only to help me pass the test, and then I would forget about it, and move on to memorizing for the next chapter. I would have to say that is one of the reasons that I have had trouble with math in my adult life- because it was only for the test when I was in school.
If a teacher had asked me questions or gotten me to think about how I could relate something to real life when I was in high school I would probably feel so much more successful in math today because I would feel I knew how to apply formulas to my life situations.
At first when I was reading about his skin graft question, "wow that's a bit traumatic for students to be worrying about" were the words that came to mind. After reading why he presented that problem like that I understand the method to what seemed to be madness. It was exciting to the students, and important to them to figure out, and they could do so in their own way. I thought this was a refreshing way to go about teaching mathematics because it gives a problem, and it allows the students to apply mathematics and use whatever strategy they want to solve something that relates to them. This makes them try harder to do so, and put more thought into their solution. A very smart tactic.
I agree that just allowing students to use their tools and try to solve a problem is much more effective than just using a formula and having students do worksheets. The real-life application is also effective because it gives students a context for the math they are using.
Tori - I had the same thought when I first read about the skin graft but agree with you that the students seemed to love it and it really made the problem solving more personal. When you are able to apply a strategy and solve a problem that has meaning to you it is almost always easier. I remember being able to bring in a index card with formulas written on it for tests in high school algebra and writing so small so I could fit them all on it. Having the formulas provided on tests would allow students to show what they understand and not just their ability to memorize formulars.
I enjoy the strategy the book provides of using real-life questions to approach a math concept. Seeing how the students reacted to the skin graft problem surprised me, because I know my kids would have freaked out. This is one of those cases where knowing your students would help when presenting them with a real-world example. It's always interesting to see how much students are able to show they understand wen they are given basic information and a problem to solve. I think too often teachers think they need to give the students all of the information instead of seeing what they can already figure out. Giving students a consequence-free problem (as in not grading whether it is right or wrong) can help take away the pressure and encourage students to guess.
I could so relate to the beginning of Leinwand's discussion pertaining to memorizing formulas/equations. I remember simply memorizing formulas and completing numerous equations using each formula but never had a grasp on if my answer was correct based on estimation or what made sense.
ReplyDeleteI thought the idea of having students in older grades figure out how much skin would be needed for a skin graph is perfect. I also thought giving the students a number as a referent (1000) was a great idea....by the way I always thought this was a reference not a referent. For younger grades, they could figure out how much gauze would be needed to make a mummy Halloween costume.
Jeanne, I love your idea for the younger grades! I was thinking something like what Leinwand gave his class would be much too traumatic for younger students. This would be awesome to do with younger students! It would probably be a longer process and project though!
DeleteIt definitely would take a long time, but if children got the concept it would probably be much more beneficial and meaningful to them than doing a bunch of calculations/problems on paper. The problem is so often teachers need to teach the math program that their town has adopted. I wish that teachers could just teach the topics listed in the standards in their own way. As long as activities and assessments are measurable, do we really need a text book to teach?????
DeleteI also like the Halloween costume idea. I agree that a lot of times the school system is rigid about what the teachers should be teaching. Luckily my school encourages hands-on teaching and the new evaluation tool for teachers allows teachers to basically create their own units based on the standards. Having the textbook as a guide as opposed to the lesson plan has always been more effective in my experience.
DeleteI really like the way Leinwand asks the questions, How big? How much? How far? Occasionally, I have heard teachers ask one of these questions when I am in the classroom and it always seems to make a difference in helping the students to really understand the size and scope of the problem being discussed. The skin grafting example was perfect for 7th graders. Once again, he is also making the math relevant and authentic as well. Giving students a word problem that they could care less about will not entice them to work hard to figure it out. However, giving them a situation in which they care about the outcome helps motivate them to do their best work.
ReplyDeleteStudents need to be able to determine the exact amount of things but also to estimate the outcome as well. I really enjoyed reading about the different ways the students answered the skin grafting question. Having the groups discuss their answers and how they came up with them is a great tool for helping all the students learn other ways to solve the same problem.
We have discussed in class how bad US students are in regard to measurement so I agree with Leinwand that we need to make measurement an ongoing part of the daily instruction. Measurement is a math concept that is incredibly important to science as well.
Lyanne, I completely agree with you that students need to be able to determine the exact amount, but I like that the estimation the students used in their solutions were more about concept rather then getting an exact answer because it helped them to formulate an idea or plan of action. Then Leinwand sent home homework sheets with the formula and questions, which I thought was a great follow up, so they have time to think at home about the problem to get the exact amount instead of feeling pressured to think about it and get the "right" answer at school.
DeleteThis comment has been removed by the author.
ReplyDeleteTo this day, when I see a formula in any class I think to myself "start memorizing that now." In school memorizing a formula was only to help me pass the test, and then I would forget about it, and move on to memorizing for the next chapter. I would have to say that is one of the reasons that I have had trouble with math in my adult life- because it was only for the test when I was in school.
ReplyDeleteIf a teacher had asked me questions or gotten me to think about how I could relate something to real life when I was in high school I would probably feel so much more successful in math today because I would feel I knew how to apply formulas to my life situations.
At first when I was reading about his skin graft question, "wow that's a bit traumatic for students to be worrying about" were the words that came to mind. After reading why he presented that problem like that I understand the method to what seemed to be madness. It was exciting to the students, and important to them to figure out, and they could do so in their own way. I thought this was a refreshing way to go about teaching mathematics because it gives a problem, and it allows the students to apply mathematics and use whatever strategy they want to solve something that relates to them. This makes them try harder to do so, and put more thought into their solution. A very smart tactic.
I agree that just allowing students to use their tools and try to solve a problem is much more effective than just using a formula and having students do worksheets. The real-life application is also effective because it gives students a context for the math they are using.
DeleteTori - I had the same thought when I first read about the skin graft but agree with you that the students seemed to love it and it really made the problem solving more personal. When you are able to apply a strategy and solve a problem that has meaning to you it is almost always easier. I remember being able to bring in a index card with formulas written on it for tests in high school algebra and writing so small so I could fit them all on it. Having the formulas provided on tests would allow students to show what they understand and not just their ability to memorize formulars.
ReplyDeleteI enjoy the strategy the book provides of using real-life questions to approach a math concept. Seeing how the students reacted to the skin graft problem surprised me, because I know my kids would have freaked out. This is one of those cases where knowing your students would help when presenting them with a real-world example. It's always interesting to see how much students are able to show they understand wen they are given basic information and a problem to solve. I think too often teachers think they need to give the students all of the information instead of seeing what they can already figure out. Giving students a consequence-free problem (as in not grading whether it is right or wrong) can help take away the pressure and encourage students to guess.
ReplyDelete