## Friday, July 23, 2010

### Changing the Way We Teach Math - 3 Good Books

I've been reading math teacher books for years. Most of them refer to elementary education, and I've struggled to see how I could use their insights in my college classrooms. Reading teacher blogs over the past year or so has given me lots to think about, much closer to my situation.

Of course there weren't any blogs to be found 15 years ago, when I started teaching full-time. There were two very special books though, which addressed both elementary and secondary math.  I read both volumes of What's Happening In Math Class, edited by Deborah Schifter, about 12 years ago, and have been re-reading them this week. Both books are full of wonderful teacher stories, and totally remind me of my blog reading, except that there is more of a mix of elementary and high school level teachers writing these. (I've searched for elementary teachers blogging about math, and haven't found much.)

It was wonderful to re-read these and rediscover the treasures that have been living in the depths of my memory all these years. This is where I first heard of the Green Globs program (are any of my readers using that still?) and XMania (an extended exercise in creating and using a base 5 number system, used in a number of teacher ed programs).

As I reread ‘Third Graders Explore Multiplication’, by Virginia Brown (volume 1, page 18), I suddenly remembered reading this story so long ago. Remembered the group of kids who figure out the commutative property of multiplication, that 3x9 will be the same as 9x3, and in fact this re-ordering will work for any numbers. Before reading this the first time, I had always thought that was obvious. But it’s not obvious to most kids, and it can be an exciting discovery.

These books also introduced me to good questioning as a method of teaching mathematics. Almost every one of the teacher chapters in these books includes lots of dialogue, both between students and between teacher and students.

Between the two volumes, 22 teachers tell their stories, of working to change their classrooms, and of lessons that engaged the kids and taught them more about how their students learn math. Reading these books, like reading teacher blogs, reminds me that the teacher is always learning in a good classroom, right alongside the students.

Volume 1 focuses on what a good mathematics classroom might look like, and volume 2 focuses more on the struggle the teachers went through as they attempted to change the way they taught. Ruth Heaton wrote (volume 2, page 74), "In the culture of teaching, it is unusual to find practitioners willing to discuss how confused and frustrated they feel about their work." Ahh, but that has changed dramatically with the current crop of teacher blogs! Plenty of teachers are baring their souls, discussing their bad days, their confusions, and their ongoing struggles. So many of us have been hungry for this, and technology has given us our wish. Now we can read more teacher stories than we have time for, and can then narrow it down to the ones that really speak to our personal struggles.

I sometimes find that I think better when I'm reading a book than when I'm reading online. So these two books have been a great resource. I found one more gem, written by Deborah Schifter and Catherine Fosnot, Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform. Like volume 2, this book shows teachers struggling to change the way they teach, although this time through the eyes of Schifter and Fosnot. All three books came out of the SummerMath for Teachers Institute, held at Mount Holyoke College. This institute is described (page 106 of Reconstructing...) as an entirely new experience for the elementary teachers attending:
At SummerMath Institute … many [teachers] experience mathematics for the first time as an activity of construction, evaluation, and exploration, rather than as a finished body of results to be stored away. And for the first time they sense that mathematics instruction can be an invitation to the exploration of ideas, rather than a laying on of facts, rules, and procedures.

Let's all explore ideas in our math classes this fall, and if you're struggling, these books are good company to have (along with all your blogger friends, of course).