Battleground schools response

3 stops:

1. The following quote made me laugh, it's so good:

"Those who like mathematics are (generally male) eggheads, nerds, absent-minded professors, and mad scientists, unable to cope with the world of human interactions, and not fully mentally competent (ranging from the mildly autistic to the completely mad)" (393)

I feel like this is totally how people think of "math people." It's been a really strange experience transitioning gender while in mathematics. These days people are more likely to be surprised when they learn I did a degree in math, and more likely to think I'm crazy than smart. It always feels strange when people get intimidated when they learn I enjoy mathematics (men especially do this), or when people say I must be so smart to do that. I don't think you need to be smarter than anyone else to go far in mathematics, I think you just need to have a passion for mathematics, that's all. And people shouldn't feel unintelligent for not being passionate about math! It's so absurd to me. Imagine a world where people who excel at fiber arts like crocheting and knitting are considered the most intelligent, and people who struggle with such things are made to feel like they are missing an essential cognitive capacity...

2.  The next stop is "Complicated but opaque techniques like the infamous 'rule of three'..." (395)

I've never heard of the rule of three, so I looked it up, and I certainly agree it's complicated and opaque. In my experience algebra is one of the harder math topics to teach to high schoolers given the level of abstraction and symbolic opaque-ness. It's somewhat unintuitive to me that so many students struggle with algebra concepts like variables, constants, and rearranging equations, because I've always found these sorts of things intuitive. I will continue to think of strategies as I progress in my teaching journey.

3. The last stop is the last sentence: "Mathematics education has itself become a focal point for a left versus right political standoff that is being played out on many fronts, and there appears to be little public appetite for concepts like balance and consensus" (400). 

If this was true in 2008 when this was published, it's even more true now. Education, and in particular the questions of what should be taught and who should teach it, seems to be a frontline in the ongoing, exhausting culture war. Most of this culture war talk seems to focus on other subjects, especially what should be taught for history, what books should be read in English class, as well as non-curricular fronts like the recent law Alberta passed about pronouns and chosen names. Despite this, math education is not immune.

To me, it seems like there is a massive gulf in the culture of "Mathematics" that mathematicians do, and the culture of math education. In mathematics proper, there has been a huge corpus of work over the last century that has completely changed the foundations of mathematics and the philosophy of mathematics. What used to be seen as a perfectly consistent, rational, deductive system is now known to be much more relative, flexible, and touchy than previously thought. Sure, math is perfectly deductive, up to a change of topos, relative to the axioms you use, and even then there will always be theorems that are unproveable without introducing additional axioms. There has been extensive work in constructive mathematics recently, much of which is still blasphemous to traditional mathematicians. 

In math education, quite on the contrary, it seems many educators, policymakers, and laypeople have a sort of pseudo-Hilbertism-Platonism-Creationism in their minds, that math is this perfect calculation tool, that everything objective can be made math, that math is timeless and unchanging. It is always ironic to me when people say "2+2=4" to mean the prototypical objective fact - because even something as simple as that depends on how we define "2" and "+" and "=" - none of which are a given in advanced mathematics. It seems that math education always lags behind "Mathematics," not just in content (and I'm not advocating for neo-NewMath here), but in philosophy and culture, too.