In the comment section below, share at least one "aha" moment (evidence) and "why." Read comments by other group members and respond to posts by at least two other teachers.
The aha moment from chapter 7 for me was on p. 138 about students understanding underlying math concepts vs. fact retrieval. The author compared fact retrieval in math to spelling in literacy- if a student can spell but cannot write an essay, the spelling does them little good. It seems to go back to the analogy of practicing swimming strokes outside the pool...
I thought that all of the information in Chapter 7 regarding short term, long term, and working memory made a lot of sense. I especially was interested in the section about how we help our students move some of their learning out of working memory and into long term memory. It makes sense that if our students have so much in their working memory, they get lost in math problems, that the don't have enough "brain space" to handle all of the elements. This in turn creates stress which further inhibits the function of working memory. Their suggestions for helping the students were especially helpful.
I also appreciated the support that they give for allowing students to use ther resources that they need to be successful. When our students have tried and tried to memorize facts and continue to be unsuccessful, it is often time to give them resources that will enable them to move on. Many of these students are great at problem solving and other types of mathematics, but they never get the opportunity to demonstrate their thinking because we keep them stuck at the basic fact level.
I'm a little windy, but I like this book. Last!! I appreciate their format in Chapter 8 for lesson delivery. Differentiating when students apply their knowledge of the lesson is SO helpful to all students.
I have learned about having students get information onto paper to help ease working memory difficulties, and chapter 7 was a good reminder, with illustrations. I like that the book supports using explicit instruction when a student is first learning how to use representations, but with the goal that he or she will learn to use it on his own.
I really like the idea of providing students with explicit instruction to make representations or drawings or notes in general to help support their working memory. I know that this is a trick that I have always used....but I do not necessarily remember where I came up with it. I know that I sometimes take for granted the idea that I know how to take notes and how it helps me remember information. For some of our learners getting help with this is only going to help them be successful.
I agree with having students write and draw important information immediately. It helps them (and me!) to figure out "what we know" and " what we need to find out" for the problem and cuts out all of the unnecessary verbiage that bogs students down.
My aha moment was also about the fact retrieval. That you don't need to know all your facts to be able to know how to process mathematical equations. I also liked the idea of giving an ADD student putty to help them concentrate.
This chapter reminded me of the Summer Institute session with Dr. Ricomini on fluency. The point being that fluency is what allows us to free-up the working memory for more problem solving. This makes sense to me, but I also agree with the book that if we are assessing problem solving, give the student tools to solve the details without committing so much of their working memory for the task. The other important point made in the book is understanding the limits of our working memory. If we overload the working memory, the student will shut down. I was guilty of this my first year of teaching as I continued to try to cram too much information into every lesson. Most students tuned out and little was learned.
I'm also reminded here about what Dr. riccomini said about overloading working memory in multi step problems. He said that instead of having students to three problems in succession (problem one:step one, step two, step three)----he said to line all three problems up across the page and do just step one on all three problems....then do step two on all three problems.....and then do step three on all three problems. Frees up working memory because while we are typically demonstrating step two, many students are still processing step one!
One of many aha moments in this chapter is about math anxiety and self-talk. I stopped a lesson a few weeks ago and talked about how what you say to yourself affects your thinking and that if the students notice poor self-talk that they should address it and change it into something positive. They had not thought about that---and it's working, because I have a few students who no longer say "I can't" or "(I'll never get it."). We talked about the sorts of things that pop into their heads and how they can change those things around to be positive for themselves. Those self-fulfilling prophecies can be powerful focused in either direction.
(Sorry for the typos---after re-typing and "losing" my posts several times, I'm wary of moving my cursor to go back and make corrections!!)
That is a great idea and probably forces you to be more conscience of the way you see yourself as a mathematician. It will be interesting to keep note of how many parents make comments about their own self-talk during upcoming parent/teacher conferences.
I agree that this is important. Changing negative self-talk about a student's ability or perceived inability to understand math can be difficult, especially when parents have similar views ("I was never good at math either" or "I don't get the new way you're teaching math") Taking the time to address students' math anxiety may be a better intervention that many of the things we try by really freeing up their working memory resources to learn.
I agree that some students have a math anxiety where something has happened or has been said and now he/she doesn’t believe that they can do the math and be successful. I like the quote” In math, there are no extra points for understanding quickly. The real goal is to understand thoroughly.”
This chapter confirms the power of making connections in our brain. Whether it be used when reading, solving math or just learning any new concept we naturally must find a way for that new learning to connect to something we already know. The concept of chunking also uses connections to help store information. I appreciated the power of math games and even some video games are more beneficial than drill and kill procedures. The mastering of Math facts continues to be a debate. The CCSS Math calls for Math Fact fluency, specifically being accurate. Does this mean students must recall facts fast or accurately, or both? Another reason I enjoyed this chapter is it spoke of good overall teaching practices. The ADD strategies would not just be utilized during Math instruction, but over the course of the day.
The aha moment from chapter 7 for me was on p. 138 about students understanding underlying math concepts vs. fact retrieval. The author compared fact retrieval in math to spelling in literacy- if a student can spell but cannot write an essay, the spelling does them little good. It seems to go back to the analogy of practicing swimming strokes outside the pool...
ReplyDeleteI agree. When I read that part I highlighted it and put exclamation marks by it. It really makes a lot of sense.
DeleteI agree. I never thought of fact retrieval that way.
DeleteI thought that all of the information in Chapter 7 regarding short term, long term, and working memory made a lot of sense. I especially was interested in the section about how we help our students move some of their learning out of working memory and into long term memory. It makes sense that if our students have so much in their working memory, they get lost in math problems, that the don't have enough "brain space" to handle all of the elements. This in turn creates stress which further inhibits the function of working memory. Their suggestions for helping the students were especially helpful.
ReplyDeleteI also appreciated the support that they give for allowing students to use ther resources that they need to be successful. When our students have tried and tried to memorize facts and continue to be unsuccessful, it is often time to give them resources that will enable them to move on. Many of these students are great at problem solving and other types of mathematics, but they never get the opportunity to demonstrate their thinking because we keep them stuck at the basic fact level.
I'm a little windy, but I like this book. Last!! I appreciate their format in Chapter 8 for lesson delivery. Differentiating when students apply their knowledge of the lesson is SO helpful to all students.
I also liked how this book made differentiating lessons look so easy. In some methods, it was just the wording of the question you ask the student.
DeleteI have learned about having students get information onto paper to help ease working memory difficulties, and chapter 7 was a good reminder, with illustrations. I like that the book supports using explicit instruction when a student is first learning how to use representations, but with the goal that he or she will learn to use it on his own.
DeleteI really like the idea of providing students with explicit instruction to make representations or drawings or notes in general to help support their working memory. I know that this is a trick that I have always used....but I do not necessarily remember where I came up with it. I know that I sometimes take for granted the idea that I know how to take notes and how it helps me remember information. For some of our learners getting help with this is only going to help them be successful.
ReplyDeleteI agree with having students write and draw important information immediately. It helps them (and me!) to figure out "what we know" and " what we need to find out" for the problem and cuts out all of the unnecessary verbiage that bogs students down.
DeleteMy aha moment was also about the fact retrieval. That you don't need to know all your facts to be able to know how to process mathematical equations. I also liked the idea of giving an ADD student putty to help them concentrate.
ReplyDeleteThis chapter reminded me of the Summer Institute session with Dr. Ricomini on fluency. The point being that fluency is what allows us to free-up the working memory for more problem solving. This makes sense to me, but I also agree with the book that if we are assessing problem solving, give the student tools to solve the details without committing so much of their working memory for the task. The other important point made in the book is understanding the limits of our working memory. If we overload the working memory, the student will shut down. I was guilty of this my first year of teaching as I continued to try to cram too much information into every lesson. Most students tuned out and little was learned.
ReplyDeleteI'm also reminded here about what Dr. riccomini said about overloading working memory in multi step problems. He said that instead of having students to three problems in succession (problem one:step one, step two, step three)----he said to line all three problems up across the page and do just step one on all three problems....then do step two on all three problems.....and then do step three on all three problems. Frees up working memory because while we are typically demonstrating step two, many students are still processing step one!
DeleteOne of many aha moments in this chapter is about math anxiety and self-talk. I stopped a lesson a few weeks ago and talked about how what you say to yourself affects your thinking and that if the students notice poor self-talk that they should address it and change it into something positive. They had not thought about that---and it's working, because I have a few students who no longer say "I can't" or "(I'll never get it."). We talked about the sorts of things that pop into their heads and how they can change those things around to be positive for themselves. Those self-fulfilling prophecies can be powerful focused in either direction.
ReplyDelete(Sorry for the typos---after re-typing and "losing" my posts several times, I'm wary of moving my cursor to go back and make corrections!!)
That is a great idea and probably forces you to be more conscience of the way you see yourself as a mathematician. It will be interesting to keep note of how many parents make comments about their own self-talk during upcoming parent/teacher conferences.
DeleteI agree that this is important. Changing negative self-talk about a student's ability or perceived inability to understand math can be difficult, especially when parents have similar views ("I was never good at math either" or "I don't get the new way you're teaching math") Taking the time to address students' math anxiety may be a better intervention that many of the things we try by really freeing up their working memory resources to learn.
DeleteI agree that some students have a math anxiety where something has happened or has been said and now he/she doesn’t believe that they can do the math and be successful. I like the quote” In math, there are no extra points for understanding quickly. The real goal is to understand thoroughly.”
ReplyDeleteThis chapter confirms the power of making connections in our brain. Whether it be used when reading, solving math or just learning any new concept we naturally must find a way for that new learning to connect to something we already know. The concept of chunking also uses connections to help store information. I appreciated the power of math games and even some video games are more beneficial than drill and kill procedures. The mastering of Math facts continues to be a debate. The CCSS Math calls for Math Fact fluency, specifically being accurate. Does this mean students must recall facts fast or accurately, or both? Another reason I enjoyed this chapter is it spoke of good overall teaching practices. The ADD strategies would not just be utilized during Math instruction, but over the course of the day.
ReplyDelete