I'm continuing my reading of the UW College of Education's little treatise on mathematics education. The author(s) are writing about multiple-choice testing on page 25, such as many standardized tests:
Taylor’s research shows that, although males tend to perform well on multiple-choice questions, females do not. The test questions that are most effective for non-Asian minorities and females are conceptual math problems... show how they arrived at their solutions.Allow me to deconstruct:
These “performance-based” questions offer partial credit for partial understanding...
“The kind of algorithmic math traditionally taught in middle and high school might make sense — with no further explanation — to future theoretical mathematicians, but it seems a fairly elitist thing to push algorithmic math as mathematics instruction for all students.”
“Most kids are not going to become mathematicians, but they are still going to need to use mathematical ideas. What happens is that the largely abstract mathematics instruction becomes a turn-off for many students so they drop out of mathematics. We are one of the very few nations in the world where it’s acceptable to say, ‘I don’t do math.’”
- Again, another false dichotomy. The type of tests that one uses is mostly independent of the way one teaches, and one could use either "show your work" or "choose the correct answer" testing (or even other testing approaches) with either "traditional" or "modern" math.
- Just another straw-man argument meant to equate "traditional" math with what the author(s) consider poor math practices, whether or not such a connection actually exists.
- I'm not sure what to make about the statement that women and minorities don't do as well on multiple-choice tests. Even assuming this is true, this is not necessarily an argument for modifying testing (assuming there are good reasons for such tests). Instead, it would seem to me to be motivation for getting at the underlying reasons and addressing those. And what are these students supposed to do when they hit a point in their education that requires them to take a standardized, multiple-choice test? Bitch and moan about how unfair things are? Well, yes, the world is unfair. Complaining rarely helps. This is a recipe for setting these children up for failure later in life.
- Algorithmic thinking is just for theoretical mathematicians?!? Algorithmic math is elitist?!? What about chefs; they write and follow algorithms all the time. Are they elite mathematicians? The process of computation (which is what we're talking about at the lower grades) is algorithmic; there is no other kind of computation. This is simply incomprehensible, and smacks of someone who doesn't understand what an algorithm is (yes, this is quite a nerve to hit for me as a computer scientist).
- Very few students will become mathematicians? Strictly speaking, this is true; allow me to neglect to discuss what fraction may actually need math beyond those who become mathematicians. The problem is, which ones will go on to need the math? Not so easy to answer. What if the alternative approach to instruction rules out mathematically intensive careers for a good chunk of students? I submit that that's what has been happening: the absolutely brightest students, with parents who have the resources to help them go beyond "modern" math instruction, will do OK, students who will actually never need math may not be harmed one way or another, and a big group in the middle who would struggle under "traditional" math but gain sufficient mastery to continue onward in their studies will be shut out of a wide range of careers.
- The overall tone of the quote implies a mind-set (like much of this document) that "math is hard", "math is irrelevant to everyday life", "math is for mutant theoretical mathematicians", "math is elitist". A wise colleague of mine once said, "Mathematics is a social justice issue." I certainly agree. We need to stop treating math, including algorithms, like something so complex that only Star Trek-like disembodied brains can understand and start treating it as a common human birthright and the only truly international and intercultural language.
- I especially like the last sentence in the quote. After giving a bunch of reasons why algorithms aren't central to mathematics, why certain groups of children need alternative approaches to testing, and why most children won't need "abstract" or "algorithmic" mathematics ("school math" earlier in the brochure), Taylor bemoans the acceptability of people saying that they don't do math! Wait a minute... OK, I've banged my head against the wall, and that still seems like a contradiction of the thesis of the earlier material ("certain types of math are too hard for most children").