I’ve just finished a week doing number theory with 23 wonderful teachers, pre-K though high school, and three other instructors, also wonderful.

This time around we asked each participant to write a short (ten-minute) reflection each evening on his or her learning that day.  Having read that metacognition — “awareness and understanding of one’s own thought processes” — enhances one’s retention, I thought this might be a useful break from the hectic pace that is a VMI week. What I didn’t anticipate is how much I would get out of reading teachers’ reflections.

Teachers have often told me that in being students at VMI, they find some empathy for their own students’ struggles.  Some of the written reflections made that observation in more detail, specifically mentioning place value and coin conversions, for example.  (One of the week’s activities involved fictional coins with silly names, and early-grade teachers wondered if their students have more trouble with nickels, dimes, and quarters than we realize.)

Other parallels that teachers drew with their own classrooms included the importance of verbalizing math ideas, and the value of working together and seeing other people’s approaches. Several teachers had new creative ideas for treating particular topics with their own students, and at least one noted that she would now be more careful to use vocabulary that her students will use in later grades.

Some comments were more specific to the teachers’ own mathematics learning.  One teacher appreciated that colleagues shared their errors and false starts with the group; it was reassuring to see that “good mathematicians” can make mistakes.  Another found “an entirely new way” to look at a familiar topic.  Several were disappointed in their performance on the post-test from a previous course, and one wanted to go straight to the notes for that class and refresh his memory.  The same teacher, and several others, wrote about the satisfaction of solving a challenging problem — the word “fun” appeared more than once (though I may have primed* them for that on the first day, when I described number theory as fun).

It was a pleasure, really, to read these comments.  Several of the teachers are natural writers, which I don’t usually get to see.  More to the point, though, this was yet more evidence that these are committed professionals who want to do their best for their students.  Sometimes it’s hard to convince them that they can enjoy the math they’re learning without always seeing a direct connection to their own grade levels, and that it will still benefit their students in the long run.  “I can’t be a good teacher unless I’m also learning,” a fellow college professor once told me.   Thank you, VMI 2012 cohort, for giving your instructors a new look at your own learning.

*Sorry for the number theory pun; it really was the best word.


About Priscilla Bremser

Professor of Mathematics Middlebury College
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One Response to Metacognition

  1. Priscilla Bremser says:

    Update: here’s what a teacher got when she asked her high school students for end-of-course reflections (right after the final exam — how brave!):

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