My post last week about the MATHCOUNTS competition for middle school students attracted some comments (verbal, email and others) criticizing my opinion that creativity in teaching math were being squeezed out by the drill-and-kill approach to test preparation. What I don’t understand, however, is why so many people seem to believe that we must teach the mechanics of math before we teach problem solving skills. It makes absolutely no sense to teach one without the other.
I spent many years teaching Algebra I to high school freshmen (and other grades, higher and lower) and I started my career with the premise that students must learn the mechanics before they could grasp the problem solving. But we usually ran out of school year before getting that far. For the most part the kids learned the processes just well enough to pass the next test and found working through the algorithms boring. Frankly, I was bored with that approach as well. When I flipped the order of things and came at it from the direction of "here’s a problem, what do we need to know to solve it", it made much more sense to all of us. We also had a lot more fun (fun? in math class?), and the kids still passed the end-of-year standardized test.
Having never taught elementary school, I can’t comment on the process of teaching math at that level. But a school yard blog seems to be right on target in her comments related to this topic.
If the only idea a student has of the number 6 is the symbol and not the quantity or area, it makes math hard for too many later on. It creates the math phobic. If you drill on the flashcards before the concept is established the brain skips right to an answer before looking to see the picture or the story. You need the picture and story to see math go from one-dimensional to three or four-dimensional later on.
Which brings me back around to the problem solving skills being developed in MATHCOUNTS. Of course the kids need know their basic skills in order to do well in the contest. However, it’s far more important – not to mention more interesting – to develop the concepts along side of the mechanics. The same thing is true of learning math at any level.
By the way, the ESPN broadcast of the MATHCOUNTS finals was a little flat but still interesting. However, it won’t do for this event what Spellbound did for the Spelling Bee.