Sometimes I curse my graduate professors for enabling me to see the issues in math education so clearly. It makes me feel a great weight of responsibility. Of course, most math educators believe that they see the issues clearly and their ideas are the solutions to the problem so I may just be deluded. But I’ve spent years thinking about it and have read a lot of research to back up my beliefs, so I’m just going to go out on a limb and say that I went to a National Science Foundation education conference this weekend and realized that there are math education professors and policy-makers who have less of an understanding of how students learn math than I do. And I credit this in large part to the mentoring I’ve been given at Arizona State by Pat Thompson, Luis Saldanha and Marilyn Carlson. And I’ll say that I don’t know how to use my knowledge to help others teach better-there are a lot of the pieces of the puzzle I’m unsure about.

I feel a little overwhelmed with this knowledge. I knew that as a result of graduate school I started actually being able to understand why kids struggle so much in math and how negatively our traditional methods of teaching affect their understanding. (See the Teaching Gap for details and research based evidence).

I knew that as a teacher I explained poor math scores in many ways. They didn’t learn it in middle school. They didn’t do their homework. We didn’t have a book. The state test isn’t aligned to our curriculum. But I didn’t see that students were approaching math as if the game was to memorize a complicated set of procedures that had no quantitative meaning. I didn’t realize that some of them didn’t understand speed as a ratio of distance and time. I didn’t see that some thought graphs were pictures of situations like the curves in the road and not information about two quantities related by a function. I know I’m not explaining these concepts well enough here-but it took me awhile to grasp how differently students saw math than I did. And it was horrifying.

Now all I have to do is ask a Calculus student to write a problem where you would use division to solve it and see how confused they get to know that to them, division is largely the procedure they learned to divide without a calculator. If you really want to know what I mean, read a seminal work in math education Benny’s Rules and Answers in IPI Mathematics Program.

It might be the spark to change the way you look at math education. It should be required reading for all new math teachers.

So when I went to this education conference and realized that there were people providing professional development to teachers and writing tests of mathematical knowledge for teaching that completely ignored the fact that kids understand math differently than mathematicians I was a little floored. Marilyn pointed out how important it was that we go into research so that million dollar projects are headed up by people with better understandings of the issues involved. I saw huge projects trying to assess if they improved teaching by seeing if superficial features of instruction had changed. Features that have never been linked to increased performance, and features unrelated to the quality of mathematical content. There were people who believed that mathematicians could teach teachers how to teach math even though the failure rate in Calculus classes, taught by mathematicians is at 50%. The majority of university calculus tests written by mathematicians are awful in terms of alignment with math education research knowledge(my fellow student is publishing on this now). As a result of what I’ve learned by careful study of students, I feel not only obligated to help teachers, but other researchers. And I was not expecting that. I didn’t expect to feel like I knew more about something than a room full of professionals. But when I listened to their talks and saw the flaws in what they were doing and assessing I knew that I was using what I learned by careful study of both research and students.

I know I can’t change the world. My brilliant professors have changed thousands of kids lives but still haven’t fixed the big problem. In their work lies some solutions, and some powerful messages for anyone who has the time to read and think. (And yes, there are many other brilliant math education researchers and teachers elsewhere-Steffe, Harel, Ball, Kaput, Lesh, but I’m partial to my professors!)

Oh my,

I appreciate your new understanding, but come on. It took a PhD program to enlighten you to the fact that kids memorize procedures rather than understand the theory/concepts? I guess that you’re a math lover, so perhaps you have been a bit disconnected from the realities of those who don’t love math.

I don’t mean to bash, but there is a place for both memorization and learning concepts. The real question is what should we should be doing. Math teachers and politicians need to get off their high horses and admit to themselves that for most people, MATH ISN”T IMPORTANT. They don’t use anything beyond arithmetic and they don’t need to. Some people find this absurd – the knowledge economy needs people who know math, they say. No, it doesn’t. It needs a few people who know math to do it for the rest, and there are plenty who understand who can fill this need. Should everyone have to understand chemistry? Botany? Auto repair? What makes math special?

I looked the “Benny” interview, and it is telling not just for Benny’s thinking, but for that of the interview. Take the very first question “How would you write 2/10 as a decimal or decimal fraction?”

1) I have a math degree and have no idea what a decimal fraction is.

2) What you’re asking the kid to do – in the interview – it to think of something procedurally. Perhaps the question should have been “What does 2/10 mean”? Some answer like 2 parts out of 10 or 2 divided by 10 would have made sense. That Benny can’t convert 2/10 to .2 is troubling, but really, not surprising. My wife teaches 4th grade and many kids don’t know they basic multiplication or division facts.

3) Trying to generalize from one kid is silly.

4) Many elementary teachers don’t understand the stuff that you’re expecting the kids to know in middle school. It’s not about curriculum – if you don’t really understand it, how can you convey the ideas to your students? I mean, can we please dispense with the division sign they use (dots over and under a bar). It disconnects the notion of operation from number.

In the end, increased “performance” isn’t what’s important. What’s important is that everyone has access to the compelling ideas of math if they are interested and that everyone else can do the very basic math necessary to live your life after school.