The most obvious reason for “ferreting out the math zombies” is to identify who needs help. The zombies we should worry about are those whose understanding of the material is insufficient for advancing to the next level of math.
In the Edworld, unfortunately, much of the testing and scoring seems to be an end in itself. These assessments, rather than giving teachers feedback about what sorts of help different students need, often simply serve to brand certain students as “unready” or deficient, and to block them from taking certain classes or enrolling in certain schools or programs.
Education Realist takes this even further. First, s/he identifies a sort of math zombie that s/he feels is valued by a certain sort of teacher: the sort of teacher who, s/he feels, agrees with what Barry and I wrote in our article. Such teachers:
rip through the material, explaining it both procedurally and conceptually but focus on procedural competence. They assign difficult math problems in class with lots of homework. Their tests are difficult but predictable.For the record, Barry and I do underscore the virtues of procedural competence. But, in terms of focus, what our article was doing was weighing the virtues of having students practice procedures with having them explain answers in words and diagrams. We haven’t made any blanket statements about the ideal balance between procedural practice and mathematical concepts. Nor have we advocated that teachers “rip” through the material: we’ve simply proposed that it’s more efficient to have students spend more time doing problems that challenge them mathematically and less time explaining answers to problems that don’t challenge them mathematically.
But moving back to the sort of teacher who rips through material and focuses on procedural competence and whose tests are difficult but predictable, this sort of teacher, apparently, values students who:
diligently memorize the cues and procedures, and obediently regurgitate the procedures, aping understanding without having a clue.Leaving off the “aping understanding without having a clue” qualifier, I'm guessing that the post-1960s textbooks I mention in my previous post favor this sort of student. But I lack Education Realist’s certainty that such students are valued by material-ripping, procedure-focusing teachers. Nor am I so sure that students who memorize and regurgitate procedures have, ipso facto, no clue. In fact, one way to develop an understanding of what underpins procedures is to see them in action, and one of the best ways to see them in action is to enact them yourself. I can think of many examples where people, myself included, started out by applying procedures that we didn’t truly understand, and only in the course of doing so developed an understanding of the underlying meanings or concepts (whether in math, computer programming, or some sort of mechanical project).
But back to these memorizing and regurgitating students. Education Realist feels that such students are completely lacking, not just in conceptual understanding, but also in intellectual curiosity and academic ethics:
The students don’t care in the slightest. They are there for the A… [They] simply go through the motions, stuffing procedures into episodic memory with nothing making it to semantic, all to be forgotten as soon as the test is over.And not only are teachers who emphasize procedures valuing and rewarding such students; so, apparently, is the AP, because, apparently, “AP Calc tests reward zombie math.”
At this point, one might expect Education Realist to cite studies showing the percentages of students who (1) earn 4s and 5s on AP calculus tests and (2) can’t handle the college level math classes they place into. But such statistics matter only if your prime concern is helping students who are unready for the next level of math.
Education Realist’s concern, it seems, is a bit different. S/he feels that we’re living in a time of math zombie-favoritism, and that this, plus the increased drive for calculus for all and AP testing, means that the zombies are (somehow, despite all the downsides of being a zombie) undeservedly winning, and that:
smart, intellectually curious non-zombies bow out of the game, decide they’ll go to a state school or community college.I, too, am concerned about how today’s schools marginalize the smart and the intellectually curious. But I say the most likely culprit isn’t the teacher who focuses on procedural competence over conceptual understanding: as I noted earlier, the first (via “discovery learning,” in the best sense of the term) can lead to the second. Nor is the culprit the AP. No, the most likely culprits are (1) a dumbed down, post-1960s math curriculum that favors formulaic breadth over conceptual depth; (2) NCTM and Common Core-inspired requirements that students spend significant amounts of time working in groups and explaining their answers in words and diagrams to mathematically under-challenging problems. And even if (2) is still relatively rare in high schools, it's increasingly common in K8, particularly in those schools that are otherwise relatively functional, and this only further entrenches (1), which is all too common throughout K12.