I was going to file this under “Articles I Never Finished Reading, Dept” but I felt that “Shut the Hell Up” was more apt, considering this quote:
“Often what’s lacking for U.S. students, and Massachusetts students as well, is a conceptual understanding,” Chester said. “They may learn the mechanics, but without that conceptual understanding it’s not as clear to those students how that math gets applied.” Mitchell agrees. It’s the skills to apply math that are lacking. She says students need to be taught how to think with math and not just memorize.”
Given that this has been the complaint for the past 28 years or so, don’t you think the excuse that “we’re just not teaching reform math right” sounds a little lame?
On the issue of “understanding” vs “procedures”, a math teacher I communicate with in New Zealand has this to say:
“I tell them that when their exam papers are marked there are no marks for “understanding”. I follow that up with saying that understanding will inevitably follow in time, provided that they could do the skills, but that it would not follow if they couldn’t do the skills.
“Now that isn’t to say that I don’t teach the reasons for things — I teach invert and multiply explicitly, but I also explain why it works. What I don’t do is fret about whether they understood my explanation, and I don’t let them not do something because they “don’t understand”. I most certainly do not try to teach understanding of a procedure to a student who can do it accurately.
“Some students find that truly liberating — they can get on with learning the Maths without any pressure to have to understand the whole picture first. Most just do what they always have done, which is do what the teacher asks them to do and not worry about understanding. Most kids really don’t want to understand very much. Every now and then I have a student who refuses to learn a new skill until they “understand” it — and that causes problems, largely because they learn so unnecessarily slowly as a result, which I find difficult as a teacher.”
I recognize that this quote will cause cognitive dissonance. That’s OK. Productive struggle is good for you.