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Former math TA* here. What if the pb isn't the $100 barebone calculator but the way/medium by which math is currently instructed in the U.S.? To this day, we'r
by __sy__ 7y ago
Former math TA* here. What if the pb isn't the $100 barebone calculator but the way/medium by which math is currently instructed in the U.S.?
To this day, we're still teaching math with pen & paper, and require students to memorize concepts like how to differentiate functions of the form 1/x, x^2...etc. To test proficiency, well we give pen & paper tests and forbid most notes, but we still provide you a calculator because it'd be almost dumb not to. But given the prior rules about no notes, the calculator that doesn't have fancy note storage & programming wins, even if it costs $100.
But my recollection as a student is that math didn't entirely click until I started playing with Excel and later with Jupyter notebooks. Honestly, nothing quite like coding along a spam filter from scratch to really understand the basic principles at play behind Bayes' theorem.
In summary, I didn't love math in the pen&paper contest, but absolutely loved it when applied using a computer and some visualizations...etc. Based on my TA'ing experience, I am willing to bet most kids feel the same way. Mathematicians have long moved away from using abacus; maybe it's time our education does too.
Context: Former college TA for linear-algebra/vector-calculus/differential-equations.
- lopmotr 7y ago> differentiate functions of the form 1/x, x^2...etc. To test proficiency, well we give pen & paper tests and forbid most notes, Maybe it's a US thing, but that sounds horrible. When I was a teacher, we usually allowed notes and always gave them the differentiation formulas as well as every other formula they might need. Why are you guys getting them to memorize a bunch of specific facts that they'll forget after the exam? You don't learn math by reciting formulas to yourself the way you might learn vocabulary in a foreign language. I'm not even sure you learn languages very well that way either.
- __sy__ 7y agoI completely agree. By the way, I'm not convinced it's just a U.S. thing. I went to high-school in France for 1.5 years. I also have some exposure to Japanese high-school math. In both contexts, rot memorization of derivation techniques was at play.
- SamReidHughes 7y agoTo be productive in math you do in fact need to be able to differentiate 1/x and x^2 without a table.
- agumonkey 7y agoit's true that computers can allow exploratory and multi...dimensional or multi-representations of math concepts in way that can be very very powerful to teach. That said pen and paper is the only thing you need when you think. The current context is mostly absurd because we give useless tools at absurd prices. Make a rpi like pocket calc with a CAS and RPL (hp forever) or even newer ideas like js/glsl canvas.
- iscrewyou 7y ago> That said pen and paper is the only thing you need when you think. Anecdata, I occasionally design with CAD software. Working on details, it's hard for me to draw up(think up) the first draft in CAD. Pen and paper is the only way to get the thing off the ground and running. Basic things require the most basic tools. What i'm trying to say is that you are correct.
- __sy__ 7y agoYeah to actually correct my initial comment, I think pen & paper are still very important & powerful. Nothing quite like deriving Euler's formula on blank pages to see the beauty in it :) But pen & paper shouldn't be the only medium. That's more along of what I meant.
- agumonkey 7y agoTrue but that's for large amount of semi simple things, not conceptual reasoning, right .?
- mixedmath 7y agoWhat are you using "pb" here to mean, in your sentence "What if the pb isn't ..."?