In theory, this is great, and previously I've actively encouraged such cooperation. After all, what better way to learn to communicate math, sharpen argumentative skills, look at concepts and methods from different perspectives - well, y'all know the drill. Every modern text on teaching and learning mathematics seems to wet itself with excitement over group work. A classroom full of quiet students working alone with their (gasp!) textbook is, or should be, a remnant of older and more ignorant days.

But now I'm starting to change my mind. I see how students use each other as crutches, easy support instead of the harder work of figuring something out by oneself. Two main negative effects from this: students believe that they have mastered and understood something which they really haven't, and also that they are deprived of the chance to build thinking, memory and confidence by single-handedly struggling with math problems and concepts.

But now I'm starting to change my mind. I see how students use each other as crutches, easy support instead of the harder work of figuring something out by oneself. Two main negative effects from this: students believe that they have mastered and understood something which they really haven't, and also that they are deprived of the chance to build thinking, memory and confidence by single-handedly struggling with math problems and concepts.

In an ideal world students would be doing this kind of individual work as homework. This is not an ideal world.

So I'd like to incorporate more of that quiet individual work in class, but at this point I'm not sure how to fit that in with the explorations we frequently have going on. It's a matter of priorities, I'm sure, but even without individual work we're struggling against the clock every lesson. Right now I'd just really like a structure that I can use for each (or at least most) lessons and which includes a brief warm-up review of the previous lesson, an exploration, discussion/summary, group practice, and individual practice. But unless these components on average take less than 10 minutes each (they don't), something's gotta give. It's a pretty nasty dilemma and I welcome any and all suggestions.

One thing that I want to implement is something my co-worker does. She is a Biology teacher, and her routine is, the day after a unit test, students bring in their textbooks, and do reading/questions about the next chapter. I'm not sure what the questions are -- obviously not the end-of-chapter questions! But it seems to be a good way for students to overview the chapter independently, maybe think of prior knowledge, and since it's a class routine, the teacher doesn't even tell them to bring their books -- they know. (or else...!)

ReplyDeleteNancy

NJ

Sounds like a good way to introduce a new topic, I might try it in psychology. I wonder how that could be adapted in Math though.

ReplyDeleteI’m assuming you are talking about your honors or regular math classes: in my remedial or “basic” math level classes, the goal is often to get them to work together rather than giving up at the first bit of difficulty or waiting until I notice they’re struggling.

ReplyDeleteMy goal is for all of my students to solve problems without a net: no notes in front of them, no classmate with the answer when the solution doesn’t come easily. If they can’t, then they’re not ready for the test. Unfortunately, too many students do the homework with their notes in front of them and then are baffled when they bomb the quiz/test.

While I’m checking homework, I send up two students to solve one of the challenging problems at the board without any notes. I would love to have a student work the problem at the board without a partner, but in the USA, the student would feel embarrassed if they got the problem wrong in front of their classmates. For many of the students, this is an eye-opening experience if they did the homework correctly (with their notes) and then find themselves completely clueless as to what to do when at the board (without their notes).

Beyond that, I have no easy answers. On the one hand, it is wonderful for the students to ask each other for help when they hit a wall, especially as there is only one of me to help everyone needing assistance. On the other hand, like you, I want them to struggle for a bit longer if it translates into their figuring it out for themselves.

Paul Hawking

Blog:

The Challenge of Teaching Math

Latest post:

Dear Parents Letter

http://challenge-of-teaching-math.blogspot.com/2011/02/dear-parents-letter.html

Paul, sorry for the late reply...

ReplyDeleteThis goes in all my classes, honors to "remedial" (just a lower level, really) as well as psychology. The lower level students in particular are reluctant to let go of each other.

I give mini-quizzes every lesson instead of having students up at the whiteboard, but I've been meaning to try out what you're suggesting. How do you get the other students (not at the board) to focus on the math at that point though?

I talk about my bellwork procedure in detail here

ReplyDeletehttp://challenge-of-teaching-math.blogspot.com/2011/02/remember-shy-kids-in-class.html

but basically, at the bell, students are working on a warm-up problem while I check the homework. If they complete the warm-up before I finish checking homework, they have a minute or two to watch the pair at the board or to chat with a neighbor: it doesn't really matter to me. If the pair is really stuck, I'm usually willing to allow them to "phone a friend" for help, but I'm just as likely to say, "No, keep thinking and if you can't figure it out by the time I'm done with checking homework, that's okay."

Once I'm done with the homework check, I collect the warm-ups and then I have everyone give their undivided attention to the pair at the board while they present their work to the class. It usually doesn't take any more time than if I had worked the solution and explained it to the class, so it doesn't cost me anything, i.e. I don't have to cut my lesson to fit in the daily pair work.

This assumes of course that the rest of class isn't going to get out of control when they finish the warm-up problem and have idle time on their hands. I have had classes that were so inclined, and having them do 5 or 6 warm-up problems or a mini-quiz to keep them occupied, until I finished checking homework, was the better option.

Paul Hawking

Blog:

The Challenge of Teaching Math

Latest post:

Jo Boaler and The Railside Report

http://challenge-of-teaching-math.blogspot.com/2011/03/jo-boaler-and-railside-report.html

Thanks, Paul. If I do decide to assign specific homework problems (I usually just tell them "this is what you should master/understand") I'll probably do just like you're suggesting.

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