Making Mathematical Discourse Worth Your While
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This is a very useful article for math teachers at all levels, and teachers will need to pay attention to the details to have as much success as these authors apparently had, such as letting students describe their method of solution without interruption. The discussion about the many answers that students share is given after the answers are all described and listed.
From the brief biographies the authors are not actually elementary school teachers, but they describe this sharing task as if they do it all the time in their “class”. At any rate, I will concur that the process works because I have actually done this type of sharing and discussion of answers with first year Algebra students, many of whom were taking it for the second time. So from my experience, I would make one modification to the listing of possible answers. Instead of having students volunteer their answers and methods, because as teenagers they will poke fun at those whose answers are wrong, I listed the possible answers myself from a list I created while I walked around the room observing student work. Then I would ask how a student might get each of the answers. Sometimes I would have to describe a method when no student volunteered, and sometimes I would just let an outlier not be spoken about.
However the sharing occurs, this is a great method for encouraging discourse and helping students understand how errors can occur. We don’t do enough of error analysis in our teaching, and this is a great way to embed it in teaching.
Putting a twist on a popular mathematical tool, this collection
of activities shows how putting a number 1 in the bottom-left cell and a 100 in
the top-right cell can better support student reasoning.