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It's interesting to discuss mathematical literacy with primary school teachers, mathematicians, statisticians, data scientists. I do periodically. Primary scho

by ggm 2y ago

It's interesting to discuss mathematical literacy with primary school teachers, mathematicians, statisticians, data scientists. I do periodically. Primary school teachers respect core fundamentals as kids acquire "mental muscle memory" and realize they have to both create some axiomatic knowledge (axiomatic in as much as you know 9x9 is 81 from rote recall, not because of a belief in inductive reasoning) as well as try to begin an uplift to reasoned knowledge (that 2^2 x 2^2 is 2^(2+2) is 2^4) and some coding/transcoding (1/2 == 0.5) Cuisenaire rods come in and out of fashion. Crows can count. Kids are sometimes dumber than crows. Mathematicians are very much in davis/hersh "what is mathematics anyway" -I believe Hersh noted that you can be in a field where only 3 other people worldwide can talk to you cogently about your work, and peer review is meaningless. Statisticians are very comfortable that approximations work, but are less concered with accuracy at times, and very much concerned with methodology. I've had quite remarkable conversations with them about sample size, and how UX people can survive on 5 responses. I neve predict which side of the problem they're going to respond. Data scientists are almost intuitive at times. sometimes the reliance on codified knowledge (numpy/pandas) and a belief in the p-jacked value or an obvious excel error is frightening. I think they divide sheep/goats into the numerate, and the highly visual. I consider myself semi literate, mathematically speaking but in fact, I stumble over basic arithmetic all the time, and I struggle with ideas behind complex numbers, trig. I have to re-prove things which should be known, re-induce belief in things which are based on inductive reasoning, I question commutation all the time. How the hell can 2 x 3 be the same as 3 x 2 there's a fundamental left-right ordering in my brain which at times I ask myself is this inside the farsi or hebrew or thai or boudestrophon flow texts, suggesting that not all right-to-left ordered languages obey it yet alas I do. I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant. I suspect at times it was dividing us into the ones which drink from the hand, and the ones which lap from the stream. Do they teach decimal to octal and hex and binary in primary school yet? Will the world be different when the last of the duodecimal measurement learners have died?

PhasmaFelis 2y ago
> Mathematicians are very much in davis/hersh "what is mathematics anyway" This reminds me of getting my CS degree in the early 2000s, then slowly realizing that my comp-sci program had taught me lots of interesting things about how computers and programs work, and essentially nothing about how to write code for a living. Also reminds me of playing Dominion (the card game) with another student, me saying "Okay, I've got 1 and 2 and 2 and 3, that's 8..." and him gasping "Wow! How did you do that so fast?" Dude was a math grad student. I narrowly restrained myself from saying "Well, you see, I finished the 3rd grade..."
- criddell 2y ago
  I got my degree in the mid 90's and let me tell you - high school guidance counsellors in the 1980's had no clue at all what computer science was. I arrived at university expecting to be writing a lot of programs and was soon struggling with a heavy load of mathematics and proofs. Our introduction to computer programming professor made it clear that that class was the only one where we would be taught to program. Computer science, he said, was mostly done with paper and pencil. It wasn't quite true. We eventually did a lot of programming, but it was nothing like I was expecting.
  - hot_gril 2y ago
    The problem with actually learning to code in school is that you'd spend a lot of time learning specifics that become outdated, which you could've self-studied anyway. Idk what it was like in the 1980s, but in 2015 our CS practice problems and tests were mostly pencil+paper, with actual code only used as a teaching tool in projects and some homework (more in lower divs).
    - criddell 2y ago
      That’s why I think the old SICP-based curricula are so great. Learning Scheme isn’t really the point. It’s all about fundamentals of computation.
      - hot_gril 2y ago
        We used Scheme too, it was a good way of teaching general computation.
  - PhasmaFelis 2y ago
    > high school guidance counsellors in the 1980's had no clue at all what computer science was. My problem was that the fucking college counselors didn't know either. When I signed up, I told the lady I wanted to be a computer programmer, and she said "You'll want computer science, then," and that wasn't true. The CS program was only interested in teaching me how to be a CS professor. A few years in I was scouring the course lists for classes on graphics, web, anything with a GUI even, and there was nothing. It was 100% command line C++, and they didn't even bother teaching us about IDEs and debuggers. Just Telnet, vi, g++. It was like taking a pure math degree to become an architect.
anon291 2y ago
While I can agree that in the later years, the math becomes unnecessarily prescriptive, as a mathematician myself, I am categorically not in the 'what is mathematics anyway' camp, at least not for kids. For children, it is fundamental that they calculate. Learning arithmetic is the first introduction into the idea of infinity, which is a vital concept all children must come to terms with. The natural numbers pop up everywhere and is a basic life skill. Mathematicians and philosophers can pontificate later as to what the exact nature of mathematics is, and if the real numbers are actually real, but none of that means that kids shouldn't learn how to count.
- ggm 2y ago
  Nothing I said, nothing whatsoever was meant to imply kids should not learn to count or acquire the times tables, and learn the fundamentals of mathematics we call arithmetic on the streets. Nothing.
  - anon291 2y ago
    I don't think I said you did say that. It was a response, not an argument.
nerdponx 2y ago
> I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant. Trig is useful for practical problems involving angles, and ubiquitous in applications in engineering and statistics. One year in school we spent a long time on logarithms and trig. Approaching 20 years later I consider it time well spent, and my one regret is that I didn't strive to understand it more deeply at the time, and had to revisit some details later (mostly about logarithms, but same category IMO).

by ggm 2y ago

PhasmaFelis 2y ago

> Mathematicians are very much in davis/hersh "what is mathematics anyway" This reminds me of getting my CS degree in the early 2000s, then slowly realizing that my comp-sci program had taught me lots of interesting things about how computers and programs work, and essentially nothing about how to write code for a living. Also reminds me of playing Dominion (the card game) with another student, me saying "Okay, I've got 1 and 2 and 2 and 3, that's 8..." and him gasping "Wow! How did you do that so fast?" Dude was a math grad student. I narrowly restrained myself from saying "Well, you see, I finished the 3rd grade..."

criddell 2y ago
I got my degree in the mid 90's and let me tell you - high school guidance counsellors in the 1980's had no clue at all what computer science was. I arrived at university expecting to be writing a lot of programs and was soon struggling with a heavy load of mathematics and proofs. Our introduction to computer programming professor made it clear that that class was the only one where we would be taught to program. Computer science, he said, was mostly done with paper and pencil. It wasn't quite true. We eventually did a lot of programming, but it was nothing like I was expecting.
- hot_gril 2y ago
  The problem with actually learning to code in school is that you'd spend a lot of time learning specifics that become outdated, which you could've self-studied anyway. Idk what it was like in the 1980s, but in 2015 our CS practice problems and tests were mostly pencil+paper, with actual code only used as a teaching tool in projects and some homework (more in lower divs).
  - criddell 2y ago
    That’s why I think the old SICP-based curricula are so great. Learning Scheme isn’t really the point. It’s all about fundamentals of computation.
    - hot_gril 2y ago
      We used Scheme too, it was a good way of teaching general computation.
- PhasmaFelis 2y ago
  > high school guidance counsellors in the 1980's had no clue at all what computer science was. My problem was that the fucking college counselors didn't know either. When I signed up, I told the lady I wanted to be a computer programmer, and she said "You'll want computer science, then," and that wasn't true. The CS program was only interested in teaching me how to be a CS professor. A few years in I was scouring the course lists for classes on graphics, web, anything with a GUI even, and there was nothing. It was 100% command line C++, and they didn't even bother teaching us about IDEs and debuggers. Just Telnet, vi, g++. It was like taking a pure math degree to become an architect.

anon291 2y ago

While I can agree that in the later years, the math becomes unnecessarily prescriptive, as a mathematician myself, I am categorically not in the 'what is mathematics anyway' camp, at least not for kids. For children, it is fundamental that they calculate. Learning arithmetic is the first introduction into the idea of infinity, which is a vital concept all children must come to terms with. The natural numbers pop up everywhere and is a basic life skill. Mathematicians and philosophers can pontificate later as to what the exact nature of mathematics is, and if the real numbers are actually real, but none of that means that kids shouldn't learn how to count.

ggm 2y ago
Nothing I said, nothing whatsoever was meant to imply kids should not learn to count or acquire the times tables, and learn the fundamentals of mathematics we call arithmetic on the streets. Nothing.
- anon291 2y ago
  I don't think I said you did say that. It was a response, not an argument.

nerdponx 2y ago

> I also still don't entirely understand why school focussed on trig so much given that very few of us are navigating by sextant. Trig is useful for practical problems involving angles, and ubiquitous in applications in engineering and statistics. One year in school we spent a long time on logarithms and trig. Approaching 20 years later I consider it time well spent, and my one regret is that I didn't strive to understand it more deeply at the time, and had to revisit some details later (mostly about logarithms, but same category IMO).