David Bornstein wrote a very interesting opinion article in the New York Times this week. He tells the story about a new way of teaching math called Jump Math. The basic concept is that you teach math by breaking it down to the smallest steps and getting the students to understand these steps. Here is an excerpt of the article
New York Times: Children come into school with differences in background knowledge, confidence, ability to stay on task and, in the case of math, quickness. In school, those advantages can get multiplied rather than evened out. One reason, says Mighton, is that teaching methods are not aligned with what cognitive science tells us about the brain and how learning happens.
In particular, math teachers often fail to make sufficient allowances for the limitations of working memory and the fact that we all need extensive practice to gain mastery in just about anything. Children who struggle in math usually have difficulty remembering math facts, handling word problems and doing multi-step arithmetic (pdf). Despite the widespread support for “problem-based” or “discovery-based” learning, studies indicate that current teaching approaches underestimate the amount of explicit guidance, “scaffolding” and practice children need to consolidate new concepts. Asking children to make their own discoveries before they solidify the basics is like asking them to compose songs on guitar before they can form a C chord.
Mighton, who is also an award-winning playwright and author of a fascinating book called “The Myth of Ability,” developed Jump over more than a decade while working as a math tutor in Toronto, where he gained a reputation as a kind of math miracle worker. Many students were sent to him because they had severe learning disabilities (a number have gone on to do university-level math). Mighton found that to be effective he often had to break things down into minute steps and assess each student’s understanding at each micro-level before moving on.
Take the example of positive and negative integers, which confuse many kids. Given a seemingly straightforward question like, “What is -7 + 5?”, many will end up guessing. One way to break it down, explains Mighton, would be to say: “Imagine you’re playing a game for money and you lost seven dollars and gained five. Don’t give me a number. Just tell me: Is that a good day or a bad day?”
I completely agree. I’ve always felt that we should teach math like we teach sports. If you want to be a good golfer then you should go to the range and hit thousands of golf balls. Almost everyone thinks that they can improve in golf or any sport if they practiced more. Well the same is true for math. If you want to get better you should practice. I’ve always felt that this idea that we need to make math more pertinent to students lives to get them motivated to study it to be completely misguided. From my experience as a former math professor, I found that most students liked to do math for its own sake and didn’t really care if it was useful for their lives (even though it is).