I’ve claimed many times in conversations over the last two weeks that I believe many parents and educators misconstrue the relationship and causality direction between being skilled/fluent at mathematics and being fast at computations. Read that latter as student accomplishment defined by skill on speed testing as done in many, many schools. Here is a post from Stanford’s Jo Boaler on math anxiety created by timed testing.
Here’s my thinking: When we watch someone perform at a very high level in anything, that person appears to perform complex tasks quickly and effortlessly, and indeed, they do. But . . . they are fast because they are good, and NOT the other way around. When you learn anything very well and deeply, you get faster. But if you practice faster and faster, you don’t necessarily get better.
I fear too many educators and parents are confusing what comes first. From my point of view, understanding must come first. Playing with ideas in different contexts eventually leads to recognizing that the work one does in earlier, familiar situations eventually informs your understanding in current, less familiar settings. And you process more quickly in the new environment precisely because you already understood more deeply.
I think many errantly believe they can help young people become more talented in mathematics by requiring them to emulate the actions of those already accomplished in math via rapid problem solving. I worry this emphasis is placed in exactly the wrong place. Asking learners to perform quickly tasks which they don’t fully understand instills unnecessary anxiety (according to Boaler’s research) and confuses the deep thinking, pattern recognition, and problem solving of mathematics with rapid arithmetic and symbolic manipulation.
Jo Boaler’s research above clearly addresses the resulting math anxiety in a broad spectrum of students—both weak and accomplished. My point is that timed testing–especially timed skill testing–at best confuses young students about the nature of mathematics, and at worst convinces them that they can’t be good at it. No matter what, it scares them. And what good does that accomplish?