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.
traditional math 
Reblogged this on Nonpartisan Education Group.
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Linda Gojak is a past president of NCTM with a, BSEd, Elementary Education and Teaching, from Miami University.
She is not even certified to teach math in high school. Our state now requires certification in math to teach in 7th and 8th grades. That is one reason why we finally got rid of CMP in middle school and replaced it with proper Glencoe textbooks for Pre-Algebra and Algebra that offered a curriculum path to geometry in ninth grade for many students who have parents who help them recover from repeated partial learning Everyday Math in K-6. Parental or tutor help at home is now a requirement for modern Common Core math which only has a K-12 slope to no remediation in college algebra.
Kids struggle in math because schools don’t enforce mastery of basic skills in K-6, no matter how much talk of understanding and in-class group work they offer – which has now been going on in K-6 for 2+ decades! All proper skills require and ensure some understanding. After that, students still might have understanding/flexibility issues. The solution is not top down, but bottom up from mastery of scaffolded skills, and Ms. Gojak has no clue what we mathematicians, scientists, and engineers went through and really know about the many levels of understanding. We don’t expect kids to be able to add and subtract in binary or octal, even though they already know something about dozens and 60 minutes in an hour. Do we expect them to know why months have different numbers of days?
There is no math curriculum problem or controversy in most high schools, where AP/IB math dominate and are the classes and grades that all colleges look for. While there are real problems in K-12 math education, they don’t revolve around a lack of vague conceptual understandings or ability to apply “mathematics to a variety of situations” – outside of the many problem variations provided in proper math textbooks. It’s as if these educators have never really looked at what’s inside a proper math textbook. They need to first ensure individual mastery of homework P-sets in K-6 (which they supposedly believe in) and then we can talk about higher levels of understanding that might be missing. However, Common Core proficiency on a slope to no college algebra remediation is NOT proper math proficiency for skills OR understanding.
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