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What he fails to account for is the fact that math
education is so poor that many people don't truly
understand what math is. Beyond arithmetic and algebra,
they think it's some really complicated stuff with big
numbers and funny symbols that geeky people with glasses
do -- it's practically a foreign language to them,
except it has a reputation for being much harder.
I can attest to this. Academically, I am a reasonably able person, but I found math simply baffling at school. Arithmetic and algebra were fine. Rudimentary geometry made sense. When we got to trigonometry, things just fell apart for me. We were taught sine, cosine and tangent in the context of how they could be used to derive angles from other angles, not what they were and how they worked. They were presented as tools that could be used in particular ways that had to be memorized. To me, it felt like trying to teach an alien from another dimension to use a hammer without the alien having any intrinsic understanding of mass or momentum or kinetic energy or friction.In fact, if I'm totally honest, I'm not 100% I completely understand the sine function now. And it wasn't just math. In physics, current, voltage, resistance etc. were taught as inputs to formulas. I know it must be challenging to teach about these kinds of principles that lack concrete macroscopic analogs, but I can't help but feel they could have done a better job than they did. In chemistry too, I remember being taught about valency and how you could work out the valency of an element by its position on the periodic table. I asked what valency actually was, either didn't understand or wasn't satisfied with the answer, asked again, and the teacher brushed off my question and carried on the with the lesson. "Oh well," I thought, "I guess I don't understand chemistry." That was when I was about 12 years old, and I didn't study chemistry after that. I studied biology until I was 16 because I had a teacher who took the time to actually explain things. The worst part is, I went to a pretty good school. It must be absolutely dreadful at bad schools. Most of this happened before I had regular access to the internet and the chance to learn about these things for myself. I can't help but feel the whole course of my schooling and advanced education might have been different had I had better (or at least different) teachers of hard science and math at an early age. |
Last week, my son had a "Chapter 9" math test here in a top-ranked Silicon Valley public school. His teacher pointed us to an official study guide PDF, which we went over carefully. I was not at all surprised to find that it covered a random grab bag of unrelated topics: sorting a half-dozen fractions, each with different denominators, two different silly algorithms for multidigit multiplication, how many $2.30 widgets can you buy for $9.00, and a few others.
This incoherent, random presentation of unrelated topics within a single chapter is totally characteristic of the "reform math" so beloved by our "progressive educators." They despise the approach of methodically working through a small number of carefully sequenced topics, making sure that the foundation of layer N is solid before getting to work building the closely related layer N+1 on top of it. They call it, "drill and kill," "soul-crushing," and "creativity destroying."
Instead of mastering a few closely-related concepts each year and systematically building expertise, they prefer "exposing" kids briefly to lots of unrelated math ideas, trusting that some kids will get some of it, and telling the rest to "trust the spiral," meaning trust that when they hop, skip, and jump over multiple topics the following year and the year after that, most of them will eventually "get" most of the stuff.
The result is that many parents just teach their kids real math outside of school. Many in our neighborhood send them to Chinese school, which teaches them math in addition to Chinese. The Chinese school buses line up in front of all of our local elementary schools at the end of each school day. (A lot of blond kids board those buses.) Some send them to Kumon, which is getting to be as common a sight around here as McDonalds or Starbucks.
I teach mine myself, using non-US curricula (Chinese, Japanese, and Singaporean in my case.) I feel terrible for the kids who don't have parents doing the schools' job for them, whose math skills are limited to what they can pick up from their classmates in "group discovery" sessions, since the "professional educators" have now decided that kids learn best what they discover for themselves and now serve merely as "guides on the side" in edu-speak.
My son took his Chapter 9 test and reported to me that, with the exception of testing the two different, useless multiplication algorithms, the test was a DIFFERENT grab bag of unrelated math topics, bearing little resemblance to the study guide. Totally typical of "reform math." He did fine, but only because he had learned all of it outside school. His friends who rely on what they learn at school think he's a genius.
So kids go through this ridiculous joke of a math education and can't do math. The school points at their friends who did just fine (because--shh!--they learned math elsewhere), the school takes credit for having taught them so well and tells the others and their parents, "well, not all kids are equally good at math, but many of your classmates learned quite well," clearly implying that the kids who didn't are somehow defective.
The result is that those kids will soon be saying, "I'm just no good at math." What a disgrace.