11/29/12 Reading

The tips offered by Reinhart in “Never Say What a Kid Can Say,” seem like they would be helpful in developing problem solving in students. Another way I’ve heard his key piece of advice is, “the person doing in the talking is the person doing the learning.” I think part of the value of getting kids to explain why they have made a choice about a math problem is building vocabulary and putting language to their thought process. I find that students often lack the ability to explain even their own questions when they are confused. Students are very imprecise with language and mathematics tends to be a language and subject that requires precise language.

Finding the right questions is challenging. When students have struggled with a problem I have to keep backing up within the thought process in order to figure out where they got messed up. Also finding the right questions becomes more difficult the larger the gap is between the student skill set and the level of problem being solved. I’m really struggling with questioning when reviewing for the EOC in my Algebra 2 classes. Many times students just don’t even know what the question is asking and it’s like pulling teeth to get them to start before they give up once they have become frustrated. When I can get to the sweet spot where they are not overwhelmed by the learning they really do like participating.

I like the tip about asking more process questions than product questions, I try to strive for that in the classroom. Students will directly go to answers and I’m always asking “why” they made the decision to do something in order to get at the problem solving process. With out understanding the process math looks like a bag of magic tricks, which is probably why so many kids already think that.

A few tips that I do a poor job of in my classes is providing wait time, not repeating student answers, and I do carry a pencil with me. The hardest one for me to do will be not holding a pencil. Many kids will be able to pick up on individual explanation when they are struggling, but some of them really won’t and they will try writing down what I say word for word, like if I say “f of x” they will write that, and I will show them the notation. Some of the kids have been trained to just wait of the answer rather than talking with me about the problem. I have some students really have a difficult time following dialog. However, now I’m thinking of one student I have that can hold a perfectly mathematically valid conversation with me when I am questioning him, but when he tries to write it down on his own it becomes suddenly more complicated for him. Sometimes I think they are just confused by the notation of the mathematical language.

Also, I know that the new way of teaching is all about letting kids problem solve themselves, but doesn’t there need to be lessons and lecture also? They are not going to intuit everything themselves. I just wonder where the balance is. I sort of think of activities as a way to peak interest or introduce a concept or to be a hook, but then there has to be leading also at some point. And manipulatives are great, but aren’t we also striving for the ability to abstract? Sure I can come up with problems that can be solved by drawing and manipulatives, but eventually students have to take the mental leap and use the math like a tool, because that what it is. It’s a tool that helps me figure out things that would take me too long to figure out with manipulatives, or too complicated to figure out through some tangible way.