How does Andrew define “the art of mathematical rhetoric”? How does his example of “a gallery of student work” demonstrate concrete ways students can practice this art and get better at it?
How can you lead your math students from the point of observing and critiquing individual students’ work into the exercise of recognizing common techniques from multiple samples, and drawing generalizations from them? Could the Socratic method be used here?
Did you or your group pause and attempt to figure out the chicken and cow problem? If so, did you come up with the algebraic argument or the pictorial argument—or was there another way of finding the answer? Did you discover anything about yourself or your group? Did you or the group think outside the box, and did you find the more creative solutions more appealing?
Andrew’s challenge is for teachers to give more opportunities in the classroom for students both to present their own ideas well and to critique or assess other students’ arguments. How might some of the methods given in the lecture (“a gallery of student work,” nominating another student, competing for the most compelling argument presented for the same correct answer) provide you with a springboard for taking up this challenge? If your students are younger, how can you adapt these ideas to begin to develop their practice of rhetoric?
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