My Earliest Math Memories

When I start teaching a new group of students, I often ask them to share with me their "Math Autobiographies", a brief written description of their best, worst, and earliest memories of doing math.  Reading these helps me get a better understanding of where my students come from, and who they are at this point in time as math students.

I don't usually share my Math Autobiography, but I thought this blog would be a good place to start.  So here's one of my earliest math memories.  I'll share some of my best and worst math memories later.

When I was in second or third grade, I remember doing lots of rote problems for classwork and homework.  Multiple-digit addition and multiplication sticks in my brain for some reason.  I also remember doing many long division problems, but those probably came later.  Anyway, I remember not really enjoying doing lots of addition and multiplication, but there were these problems at the bottom of the page in a brightly colored box, with a little cartoon monkey hanging on the side.  These were the "challenge" problems, and I can remember rushing through the rest of my work, just to see what the challenge monkey had in store for me.  I think there was one that showed a line of squares, with common edges, and the question was something like how many sticks are needed to make a line of five squares?  Ten squares?  100 squares?  Maybe I'm just making that problem up from another memory, but the excitement I felt about that challenge monkey and the more interesting problems it signaled was real.

I tried to do an internet search for the text book, but not knowing anything other than the years I might have used the book, I wasn't able to find an actual example of the monkey and his challenge problems.  I do still enjoy challenge problems, however, and I will still happily work through some "grunt work" if I know it will help me reach something interesting at the end.

Skillful Teaching

Last week, I was in Massachusetts attending several days of training through Research for Better Teaching on how to teach their "Studying Skillful Teaching" course.  One of their instructors taught a class of about forty teachers, and my teaching partner and I observed, then debriefed the lessons afterward.  I'd been through the training before and I've taught the class for several years at my high school; my teaching partner will be teaching the class with me for the first time in the fall.

Throughout the week, I was struck, again, about how important it is for teachers to maintain their "learning chops" if they want to do a good job in the classroom.  Ann, the instructor leading the training, always modeled a learning frame of mind when teaching the class.  "Modeled" isn't quite the right word there, since it implies a not-quite-real thing.  Ann really lives the learning frame of mind, and tries to make it explicit to the teachers she works with.

One day, it was apparent that a number of the teachers taking the course had not really understood an idea about formative assessment that Ann had presented earlier in the day.  During the debriefing at the end of the day, Ann and the rest of us observing looked at the responses on the exit slips and tried to come up with reasons for the misunderstanding.  A couple of us wanted to go right to solutions and how to fix the mistake, but as a group we persevered in looking at the teachers' work to really try to understand the misconceptions they had.  We thought about what the teachers who did show understanding might need, and we talked about the context of the next day, in which time for reteaching would be tight.  In the end, because we spent time digging into the errors and trying to match the reteaching strategies to the students, to the constraints of the day, and to the flow of the content, Ann was able to really address the mistakes, and the responses of the teachers the next day showed improvement.

I mention this example because it really illustrated for me the teacher-as-learner frame of mind.  At no point in the discussion did any of us put on our "expert faces" and say "this is how you should teach this".  Rather, we asked lots of questions and listened to each other thinking out loud.  As a result, the analysis of student work, exploration of alternatives, and collaborative synthesis of a reteaching strategy produced a much more powerful and effective lesson the next day.

As I teach my classes, I try to put myself into a learner frame of mind, and examples like this inspire me to keep working at it.  So thanks to Ann, Jon, Ganae, Karen, and Nancy, and to all the teachers who participated in the course last week.  I appreciate the chance to hear from all of you; your questions, challenges, and insights help me deepen my thinking about what it means to be a skillful teacher, and my students will be better for it.