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Re: Learning and Mathematics: Schoenfeld, Metacognition
Posted:
Apr 9, 1996 5:59 PM


Laurie Gerber <lgerber1@swarthmore.edu> wrote: >A new twist is word problems perhaps just a disguise for the usual rote >applying of procedures OR perhaps an attempt to bring real world matters >into the classroom. The children don't know yet so they stick to what they >know which is plugging and chugging through the procedures without >thinking about the context. Would discussing the question first make a >difference? Would generating their own "real life" questions or using math >time to actually answer real questions (like how many papers can we post on >the bulletin board, how many buses will we need for an actual school trip, >what grade do I need on my next test to get an 80% average etc.) help bring >this new message home to kids?
I think that word problems as they are used in many math classes are not much more than a disguise for applying formulas and procedures. Any word problem offers the added challenge of figuring out what procedure to apply in that problem, but that an become just another part of the game. Getting students to generate ÃÂ³real lifeÃÂ² questions and working on ÃÂ³real lifeÃÂ² problems in math class sounds like an excellent idea. I heard of a teacher in Chicago who teaches algebra by using, among other things, problems involving stops on the el trains which many of his students ride regularly. I used a similar approach in teaching a math lesson in New York City, but my lack of detailed knowledge of the subway system hampered my ability to set the questions up correctly. The students seemed to enjoy it, though, and for some of them, it seemed to reinfore the math concept involved.
> Finally, are we ready for this to be the >message? Do we want kids to learn that math is only useful if it helps us >with real world things or do we want them to have a place for (blind?) >procedures as well? If so, should they be taught at the same time, >integrated or kept separate like one day the kids do real life problems >and one day they do book problems? Laurie >
I think it is important for students to learn about the internal logic and patterns of math as well as about its real world applications. I think a certain amount of memorization and drill is useful for learning basic procedures and operations. However, instead of jumping right into the procedure, looking at one or two ÃÂ³real worldÃÂ² problems is often useful in motivating why the students would want to learn the procedure. Basically, I think real world problems, drill work to learn basic operations, and ÃÂ³abstract theoryÃÂ² the patterns and ÃÂ³whyÃÂ¹sÃÂ² of math should be interspersed in the math curriculum so that they reinforce each other.
As others have pointed out, students are often able to solve real word math problems quite well in the real world, but fail to see the connections between those problems and the drill or concepts they encounter in math class. I think math teachers should take up the challenge to help students see these connections. Another thing teachers can do is to encourage students to explore the patterns in math on their own, perhaps by introducing nonstandard topics like number bases. My fourth grade math teacher used a creative lesson to introduce that concept to us, and I started exploring it on my own. ItÃÂ¹s been a topic that has interested me ever since, and it has come up repeatedly in classes and other problemsolving situations in high school and college.
Matt Reed



