Here are two of the clues to America’s current mathematics problem:
1.”Student-centered” learning (or “constructivism”)
2.Insufficient practice of basic skills
The article then goes on to say, of constructivism:
In small doses, constructivism can provide flavor to classrooms, but some math professors have told me the approach seems to work better in subjects other than math. That sounds reasonable. The learning of mathematics depends on a logical progression of basic skills. Sixth-graders are not Pythagorus [sic], nor are they math teachers.
That’s right. Constructivism, when used with the right kinds of students and in the right ways, can be quite effective. But it’s important to remember that not all students are ready for this, and not all material is taught effectively this way. When I teach geometry to junior and senior math majors, it’s almost entirely constructivist, because the process of mathematical investigation and discovery is precisely what I am trying to teach them (through the medium of Euclidean and non-Euclidean geometry). But I’d be crazy to try constructivism at that level on, say, a precalculus class full of students who have little skill in and absolutely no taste for math at all. Those students aren’t dumb, but they need structure and guidance a lot more than they need the supposed thrill of mathematical discovery.
And then, about drill and practice:
Another problem in math classrooms is the lack of practice. Instead of insisting that students practice math skills until they’re second nature, educators have labeled this practice “drill and kill” and thrown it under a bus.
I wish I had a dollar for every time I heard that phrase. It’s a strange, flippant way to dismiss a logical process for learning. Drilling is how anyone learns a skill. [...] Everyone drills – athletes, pianists, soldiers, plumbers and doctors. Drilling is necessary.
It isn’t good or bad – it’s simply what must be done.
I’ve said it before here: No human being can do meaningful creative work until they are completely fluent in the rudiments of what they are working with. Musicians, athletes, and skilled workers all know this. For some reason, there’s no outcry among music educators that we need to just hand new musicians a saxophone and try to get them to discover how to play it all by themselves. This fact — that drill and mastery precede creative work — is so painfully obvious that I feel a little embarrassed for my colleagues in math instruction who don’t seem to get it.
Constructivism and drill/practice are pedagogical tools, not religions. You look at your class, your students, and the material to teach, and then choose the right combination of tools for the job. To hear some proponents, and opponents, of constructivism, you’d think that you’re supposed to choose sides and swear undying allegiances instead.