Back in 1993, the National Council of Math Teachers (NCTM) published standards that changed the way math was taught in schools. The “reform math” movement, as it has come to be called, called for more problem-solving and understanding of why mathematical operations work the way they do, and less “drill and kill” practicing of low-level skills.
It seemed like a good idea at the time.
However, looking at the results twenty years later, several problems have become apparent.
- Because students don’t know their multiplication tables, they can’t do algebra without a calculator. This means they can’t follow a problem, equation, or concept in their heads to see where it goes. This makes higher math much harder for them.
- Because they can’t follow a problem in their heads, they are unable to make estimates, and are therefore unable to see when they have come up with an nonsensical answer.
- Because they can’t do simple math in their heads, they are unable to make change without a cash register to tell them how much to give back to the customer.
- Because of the lack of drilling, they have not developed as much attention to detail. As a result, they make a lot more small-but-significant mistakes.
In response, two systems seem to be gaining favor. Singapore math seems to favor the global, intuitive learner who wants to discover ideas for himself. The method favors initially presenting students with problems and letting them work out how to solve the problems themselves. The problems start out concrete, often with manipulatives, and gradually become more and more abstract. Once students understand the problems at a conceptual level, they are taught and have a chance to practice the skills and procedures that go with the problems.
JUMP math favors the sensing, sequential learner who wants to be shown how to solve problems in a step-by-step fashion. The method breaks down problems into smaller and smaller micro-steps, requiring students to master each micro-step before advancing to the next. Once students get to the final micro-step, they can apply the full set of steps that they have learned, and solve problems.
Clearly either method has the potential to address many of the shortcomings of the reform math curriculum for a subset of students. Sensing learners would be lost in the Singapore system, but intuitive learners would be stifled by JUMP math. I think each works for some learners, but neither works for everyone.
My concern is that, like much of what goes on in American education, everyone wants a single silver bullet that will solve everyone’s problems. Ultimately, if these are the silver bullets we have to choose from, I think schools need a combination of the two methods, with a way for kids to gravitate toward whichever one is better suited to them. In my ideal school, there would be parallel Singapore-based and JUMP-based classes and students would be placed in the one that seems to best match their learning styles.
