Thursday, August 7, 2008
Mathematics and Cognition
Wow! This article is right up my alley as my background is in literacy not math (as any of you who have had the misfortune of working with me this week can attest!) The concept of using these reading strategies: making connections, asking questions, visualizing, inferring and predicting, determining importance, synthesizing and metacognitive monitoring to help students gain a greater understanding of math makes perfect sense. As I will be assisting students in math for the first time this fall, it's comforting for me to know that I can use the same strategies I'm already using in reading. The author's statement that "the quality of most student's work, especially their explanations of the concepts, improved dramatically during the school year"spoke to me as well. If we can help children to verbalize their thinking we've accomplished at lot!
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9 comments:
I had not given much thought about the similarities between teaching students to read and teaching them mathematical concepts. Having read the article it makes perfect sense that the strategies would be universal for teaching any subject. Not liking reinventing the wheel I have to wonder if there is a reliable assessment that can be done quickly to get a sense of which foundational concepts the students have or do not have. For language arts we use a number of assessments such as the Observation Survey, AIMS probes, writing prompt and spelling lists. If the foundational mathematical concepts could clearly be identified, then math support time could be better focused and used more effectively. Any information would be welcome.
Gail, I had the very same feelings.I was very excited reading this article and could make all kinds of connections to it!
I felt a little validated as well about one strategy I thought I made up this year...an approach to "story" problems I use is to ask the students to write down what they know from the problem and then to write down what they need to know (or find out). After that, of course, is the work of figuring out the mathematical processes of solving the problem, but at least I feel I've made a connection for the students between what they do for making meaning from print for reading to making meaning from the print of math. I think that's a powerful first step. I also know I will use the language of the seven reading stragegies a lot more this coming year.
The point in Hyde's article about making personal connections to math story problems to encourage deeper understanding reminded me of our class discussion today about acting out story problems before trying to fit them into an abstract formula. Focusing on the context of the story problem, visualizing it, thinking about what is unknown, and making predictions (like we do with literature) leads to a deeper understanding of the problem and moves the primary focus away from just finding the correct operation and solution.
I was excited to learn that even though I have not taught math for very long, the strategies I have been using with my students in reading can be worked into my math instruction.
I do think like a "math person"!
I'm not sure why I had never made the connection, before reading this article, that the same cognitive strategies that I use in language arts can be applied to mathematics. As Jean says, it makes perfect sense that the strategies would be universal for teaching any subject. I use them regularly in my language arts classes, so why wouldn't I also use them in math?
With the increased emphasis on MEA scores, it makes sense to start applying these strategies to mathematics instruction. On the MEA, in order to gain the greatest number of points, the students have to explain their reasoning...HOW did they arrive at their answer. This seems to be where our students breakdown. With so much emphasis placed on following the steps and arriving at the right answer, students often can not explain how they got their answer. I fell victim to that myself in one of today's activities. I knew my answer was right because I had followed the steps that had been drilled into my head when I was in school, but when the question asked "Why does that make sense?" I was not able to explain why. It gave me a deeper understanding of how my students feel when they take that MEA. If we can apply these cognitive strategies to math consistently, so that it becomes second nature to the kids to ask questions and be able to explain the map that they are following, perhaps we will see an increase in the formal test scores, but more importantly, we will see an increase in math understanding and an increase in math comfort levels.
The most brilliant points are often the most simple. This seemed to be staring us all in the face. This article should be printed and put in faculty rooms around the country.
Reading tonights article make perfect sense but
I am also trying to connect this concept to the students I work with in the resource room. For some of them it is hard to make predictions about a book, I really can't invision them using all the reading strategies. I think the video idea from Jessie's posting could be a perfect solution for when my students do math word problems (and any type of math). They need someone to act out (being a model) what the word problem tells them to do. They need both auditorial and visual. This way they could maybe verbalize how they are solving the word problems.
I use many of the ideas mentioned in the article in my reading classes, but love the idea of using some of those same ideas during math, especially when doing problem solving. I found the article gave me some great ideas to try this coming year. I have sometimes found it difficult to help students develop strategies to use for solving multistep word problems. I love the idea of using the the k-w-c before starting a problem. What a way to pull out the important aspects of a word problem.
Visualizing was one of the seven cognitive strategies listed in the article. I decided to do a bit of research on visualization in Math. Actually I stayed up late last night and got up early this morning!
Maggie commented in class about my use of visualization when measuring the circumfererence of my head.
Walter Whiteley experiences the visual as central to mathematics. He works with teachers What he had to say got my attention. Read the article if you like:
http://www.math.yorku.ca/Who/Faculty/Whiteley/Visualization.pdf
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