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RE: https://mastodon.gamedev.place/@shana/116526661413699845
One of my most fervent education takes is that we should be teaching programming earlier, and more than manual arithmetic. By high school, no student should be carrying the 1 on a math test.
@mttaggart The Discourse aside, this is an amazing visual aid and I am contemplating getting a tattoo of that sigma and the associated program, but not sure if the color-coding would come through legibly
@mttaggart I have long thought the concept of algorithms should be more specifically discussed when multiplication is introduced. Rather than making kids memorize times tables, we should show them how algorithms lead to patterns, then how to take a pattern and identify the kind of algorithm which can produce it. How to run algorithms. How to write algorithms for others to run.
It all concretely ties into geometry and trigonometry, too, so we don’t have to change the order in which things are taught, just how parts are emphasized.
@bob_zim One of my favorite demos in my old intro programming classes for middle schoolers was showing how multiplication was repeated addition and integer division repeated subtraction. That was a great way to introduce loops and demystify those two operations at the same time.
@mttaggart Which is why I think the concept of algorithms should be introduced even earlier, at the same time as multiplication. We teach kids that multiplication is repeated addition, but we don’t teach them what this “repeated ____” pattern is called or what else it can do.
Introduce the concept early with multiplication and division.
Reinforce it when introducing functions with the slope of a line and graphing.
Reinforce it when introducing geometry with the construction of regular shapes.
Reinforce it when introducing exponentiation and roots.
Reinforce it in trig with, e.g, approximating a circle by carving triangles away from a square.
Which segues right into limits and precalc.
@mttaggart you had me until that last sentence. Being able to do arithmetic unaided is a life skill. It's not a skill to be discarded, it's for building upon. Yes, teach programming (actual programming, not vibe) as part of maths curricula but as supplement not substitute.
@cczona @mttaggart attempting to momentarily suppress my bias (as a late-diagnosed ADHDer who loves learning, and, it turns out, math, but whose academic career was absolutely ruined early on by secondary school’s pathological obsession with tedious manual arithmetic) for the sake of curiosity: when do you think it is appropriate for students to stop being evaluated on such skills? do you still regularly practice manual arithmetic on large numbers as an adult?
@cczona @mttaggart like this strikes me as bizarre in the same way that it would be bizarre for someone to say it would be a good idea for college entrance exams to focus heavily on identifying animals and colors.
Being able to do arithmetic unaided is a life skill.
Simple operations, sure. Nobody needs to factor polynomials manually in their day-to-day lives. That's why I tagged the ages and grades I did. Once you get to pre-algebra and algebra, you need to be testing conceptual understanding, not those skills. However, in the traditional pedagogy, one is a stand-in for the other, and often a limitation to learning.
@mttaggart maths symbology defenders lean on "it was designed for technical precision & compactness" but it was more designed & adopted for knowledge/discipline gatekeeping
@hrbrmstr Is Newton/Leibniz notation like tabs/spaces?
@mttaggart only if we agree Leibniz's are spaces b/c only monsters use tabs 🙃
If you think it's ridiculous that writing is judged on spelling instead of content, you also think manual arithmetic is a poor measure of mathematical understanding. They are distinct skills, and have been conflated for far too long.
@lastdinosaur One doesn't predict the other. As a data point, F. Scott Fitzgerald submitted drafts of Gatsby rife with spelling errors. He couldn't spell worth a damn, but he knew something profound about how to shape language.
I failed 8th grade algebra. Straight up F. I was told I was bad at math through high school and college, and believed it. I barely got through remedial precalc in my senior year. As an English major, I fulfilled my "quantitative reasoning" course requirement by taking Formal Logic, which I aced.
Then I taught myself programming. Then I taught myself calculus, partially through programming. It was then I realized that I suck at arithmetic, but not math. In fact, I had barely been taught math but for arithmetic.
@mttaggart same, only a discrete mathematics course taught by a great teacher stopped the slide.
@mttaggart just curious but do you have Aphantasia? I do and algebra sucked for me even though I tutored one teacher in programing while I was in HS, applied math was always relatively easy. And I got in trouble in HS Geometry for asking why we didn't prove Axioms. https://en.wikipedia.org/wiki/Aphantasia
@mttaggart Sometimes it's just the approach. I failed calculus in college, passed Physics (basically applied calculus), then went back and aced calc - same teacher - by just sitting for the tests.
Practical visualization is huge. One can certainly help you understand the other.
@mttaggart math is/was taught to me like every child will grow up to be a mathematician.
Teachers could fix this, but oh how society loathes teachers.
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