TITLE: Perfectly Reasonable Deviations AUTHOR: Eugene Wallingford DATE: April 08, 2011 6:07 AM DESC: ----- BODY: I recently mentioned discovering a 2005 collection of Richard Feynman's letters. In a letter in which Feynman reviews grade-school science books for the California textbook commission, I ran across the sentence that give the book its title. It stood out to me for more than just the title:
[In parts of a particular book] the teacher's manual doesn't realize the possibility of correct answers different from the expected ones and the teacher instruction is not enough to enable her to deal with perfectly reasonable deviations from the beaten track.
I occasionally see this in my daughters' math and science instruction, but mostly I've been surprised at how well their teachers do. The textbooks often suffer from the ills that Feynman complains about (too many words, rules, and laws to memorize, with little emphasis on understanding. The teachers do a reasonable job making sense of it all. It's a tough gig. In many ways, university teachers have an easier job, but we face this problem, too. I'm not a great teacher, but one thing I think I've learned since the beginning of my time in the classroom is that students deviate from the beaten track in perfectly reasonable ways all the time. This is true of strong students and weak students alike. Sometimes the reasonableness of the deviation is a result of my own teaching. I have been imprecise, or I've taught using implicit assumptions my students don't share. These students are learning in an uncertain space, and sometimes they learn differently than I intended. Of course, sometimes they learn the wrong thing, and I need to fix that. But when their deviations are reasonable, I need to recognize that. Sometimes we recognize the new idea and applaud the student for the deduction. Sometimes we discuss the deviation in detail, using the differences as an opportunity to learn more deeply. Sometimes a reasonable deviation results simply from the creativity of the students. That's a good result, too. It creates a situation in which I am likely to learn as much as, or more than, my students do from the detour. -----