I’m finishing my evening, reflecting on my math brains. This morning I took the GRE Subject test in Mathematics [PDF] (on the chance that I want to apply to any post-graduate programs in the next 5 years), and I prepared by taking one Math GRE a day for the last week. What I found was that everyone must think that math is boring and gross. I believe that this couldn’t be farther from the truth. This is probably more a comment on standardized tests, but out of all of the disciplines, I would hope that the mathematicians could make word problems interesting.
I am probably not allowed to comment on what was and wasn’t on today’s exam, but I can say that it was practically the same material as the practice exams I took: there were people in committees, students waiting in line for lunch, dice being cast (although of the two problems, at least one involved a dodecahedron), coins being flipped–there was a differential equation, but none of the group theory questions had any context, and definitely not the set theory or topology. Linear algebra and complex analysis were context free as well, and even the geometric questions were as bland as “here is an object, apply divergence theorem” or “here is a circle, compute some chords”.
During the week that I was studying / practicing / drilling / training* I accumulated the following (amazing) sample of material in my feedly, which is wholly opposite that material I was working on: These are engaging, interesting, and intellectually challenging accounts instead of numbing drills:
- Data Visualization of Every Person on Earth from @DataPointed
- Organization Emerging from Chaos, Merging Bubbles, and Gravitation Field Lines from @Matthen2
- Wilkinson’s Matrices from Cleve Moler @MATLAB
- A beautiful Tribute to Math Craft from @make and @MoMath1
- Integration by Parts from xkcd
What a roundup! What if the material generated _just_this_week_ was the kind of stuff that the GRE tested people on? What if we could ask people how to think _creatively_ about _new_ problems? Write programs instead of deciphering them? How many times will students be asked to identify the programmatic output of a Collatz Sequence or Euclid’s Algorithm? Obviously, it’s hard to standardize good problems, but we’ve had over 150 years of Residue Calculus–can’t someone come up with a complex function with poles that means something?
Anyway, I’m not really ranting. I thoroughly enjoyed brushing up on my math. Wronskian? Adjugate? L’Hôpital’s Rule (to the max)? These are things I don’t use in my day job. Lie groups and matrix invertibility, FFTs and signal processing, and, every once in a while, some Fundamental Theorem (of Algebra, Invertible Matrices, Calculus, &c), but not much, and not in very wide company. But diving into the tips and tricks was actually a joy for me–and that’s because of where I come from. My personal (Math Nerd**) and educational (Math Mudder) backgrounds get me excited about what are, truly, “Math Tips and Tricks”. But wouldn’t it be great if we didn’t test our future mathematicians on those, but instead on exciting, engaging material? What if people learned something from standardized tests, and what they learned was that they _want_ to answer hard problems with interesting techniques? I know that should be happening in the classroom (in person), but why can’t we manage to make it happen on paper, too? Don’t mind the rhetoric too much, and let me know if I’m way off base here. I hope, in either case, that either the Tips and Trick become interesting on their own to everyone, or we all work very hard to make questions about thinking, and not about Tips and Tricks.
* I was actually doing these tests on my train commute to work, half on the way there and half on the way home. Happily, everyone was very considerate and didn’t bother me with book, paper, pencils, and countdown timer spread across the tables. Sadly, no one engaged me about what I was doing so I couldn’t teach any lay-residue theory or integration by parts.
** This is the book I did an independent study with in High School to continued my jump-started career in math (kicked off in earnest by Mr. Sisley’s introduction to Spivak and Mr. Robinson’s introduction to Chaos and Dynamical Systems in 11th and 12th grades, respectively).