I wrote this 4 years ago regarding a column in USA Today. I commented and got into an argument with Linda Gojak, former president of NCTM. She presents the usual obfuscation and claims as evidence that students lack ‘understanding” because they cannot apply procedures in a variety of different problem solving situations. Well, if you ignore the novice-expert spectrum and put an expectation of expert thinking on novices, then yes, there’s your evidence I guess.
Here’s what I wrote four years ago:
Linda Gojak, former president of NCTM, decides to answer my comment on a comment she made in response to someone else and … Where was I? Well, it was a USA Today article proclaiming that Common Core math is not fuzzy.
Here’s what I said: “Linda Gojak Some understanding is critical, but not all. Sometimes procedural fluency leads to that understanding. It works in tandem. “
Her response: “Barry Garelick : I never implied that students need to understand all methods…they understand and use the strategy that makes most sense to them. Kids who struggle in math tend not to develop understanding through procedural fluency — my mathematically talented students sometimes did — and sometimes did not. What they had in common was that they couldn’t apply the mathematics in a variety of problem situations if they didn’t understand it (at the middle school level) The common core calls for a balance of conceptual understanding, procedural fluency/skills and applying mathematics to a variety of situations which is described quite explicitly in the introduction. Past mathematics instruction has focused too much on drill and kill. plug and chug — and the reality is that we have left too many kids hating math and parents bragging that they were never very good in math.”
Good thing I said “sometimes”. Anyway, I find that the weaker kids who understand procedures can actually do problems. As far as applying mathematics in a variety of problem situations–that’s difficult for all students, even ones in Singapore. But shhhh. Don’t tell Linda Gojak that. Let her “discover” it. It’ll sink in better.