I’ve been reading blog posts about math like this one, in which a common theme is that we need to return to “basic” or “regular” math skills and dispense with the constructivist programs that were so popular in the last decade or two. I’ve read about people who are frustrated with the idea that children should have to reconstruct the math theorems that evolved over the last 2000 years or so, and it makes sense that they shouldn’t have to do this. Some people turn to Saxon Math, which I have taught, or Singapore Math, as the solutions that teach…
A New York Times Magazine article titled Building a Better Teacher appeared last March. It’s an excellent contribution to the debate about what makes a good teacher. As the article describes, it’s not enough to care a lot; there are many caring teachers who can’t get their students’ attention to teach them anything. Being a good teacher is not strongly correlated with the graduate schools they attend, their teacher test scores, or particular personality characteristics. None of these predicts teacher effectiveness well. Merit pay and high pay incentives, haven’t worked to improve teacher quality (or test scores) either. In fact,…
The Urban Word of the Day today was “cerebral bulimia,” defined as “binging and purging of the brain.” Doesn’t that sound familiar? It calls to mind all the useless studying in which facts are crammed into temporary storage in the brain, dumped out on paper (or computer) for a test, and promptly forgotten. This can, of course, include math algorithms and formulas. How different it is when, like an athlete learning what works best for her body, we learn the fundamental concepts behind new ideas first. Then the algorithms and formulas follow logically. It can even be possible to recreate…
New York State is putting teachers and students under more pressure by revising the required scores on standardized tests for students to achieve proficiency. Why are they doing this? Apparently it is because despite passing Regents tests, almost 25% of the students need extra support once they reach college. How will they afford “remediation” for all the passing students who are now failing? One more sign of why it is so important to put conceptual understanding ahead of rote application of algorithms. It is easy to forget what one learns by rote, but not deeper conceptual understandings. Here is a…