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Funny, I read this paper for the first time last weekend after a family discussion about public school math sent me searching. I thought about posting it here m

Funny, I read this paper for the first time last weekend after a family discussion about public school math sent me searching. I thought about posting it here myself, but I noticed that prior submissions didn’t generate much discussion. He identifies people that were told they were “‘good at math’ [but] in fact they have no real mathematical talent and are just very good at following directions.” I fit into that group and it served me all right, but I hope I can find ways to give my kids a more intuitive sense and curiosity as he describes

xboxnolifes 3y ago
> “‘good at math’ [but] in fact they have no real mathematical talent and are just very good at following directions.” Ain't that the truth. I was always told the same thing, but I was awful at most math concepts past high school algebra. I didn't realize it until after college, but the misunderstanding seems to stem from the fact that, for most people, being good at math means being fast at arithmetic and remembering the algebra strategies. That's all their experience in math is, so it's all they can comment on.
Buttons840 3y ago
I think I was good at easy math, and I refused to follow directions. I saw that arithmetic and early algebra had a lot of generally useful principles and I avoided memorizing and would just "think really hard" and I did well enough. I struggled with factoring polynomials (I think it was), and then really started to struggle in Calculus 2. I wish someone had sat me down and said "look, you're not learning universally applicable tools anymore, you just need to memorize these tricks, know that they only work sometimes in the real world, but they will work on the test, just follow the directions!" https://xkcd.com/2117/ https://xkcd.com/2117/
- macintux 3y ago
  Yeah, basically I crashed and burned there and have been stuck ever since. I was studying at a university where CS was treated effectively as a second math department, which is fine, but not when I had a mental block for integration.
nohaydeprobleme 3y ago
There was an interesting discussion about this quote on r/math about a year back: https://old.reddit.com/r/math/comments/obipos/academics_when_did_you_know_you_were_good_enough/ https://old.reddit.com/r/math/comments/obipos/academics_when... The main counter-argument presented was that if a student makes it all the way to graduate school in mathematics while following instruction, they must have some base level of mathematical talent. Then, continued hard work and persistence can set you up for a strong career in mathematics, without necessarily being brilliant. The perspectives shared there were quite interesting. There were quite a few users who have worked as professional mathematicians—some very successfully—who talked about how they didn't really worry about whether they had mathematical talent, but just worked hard at their goals to become mathematicians because it's what they wanted to do. So, in many cases, it's a valid approach to work hard at mathematics without worrying if you have enough mathematical talent, and eventually find challenging and interesting work along the way. ~~ Separately, there was an interesting Medium post discussed on Mathstodon and r/math a while back, about a father encouraging curiosity for his daughter to learn about the definition of the derivative: https://sunilsingh-42118.medium.com/the-death-of-the-mathematics-i-knew-2255693c87cd https://sunilsingh-42118.medium.com/the-death-of-the-mathema... I liked the second part of his essay more when he talks about his approach in encouraging intuition. He wrote about creating a sense of mystery by rolling a marble up and down a curve to introduce the idea of a tangent line and the concept of a slope, then got his daughter curious about finding ways to numerically calculate the slope. I thought that was an interesting approach for kindling a innate motivation to learn mathematics for a person new to mathematics, rather than focusing on physics, engineering, or economics applications like many textbooks too. Though motivating students to learn calculus for applications can also be interesting (especially for different types of students), it's a bit rarer to find ways for educators to motivate students to learn mathematics for the sake of itself, especially for students learning calculus for the first time.

xboxnolifes 3y ago

> “‘good at math’ [but] in fact they have no real mathematical talent and are just very good at following directions.” Ain't that the truth. I was always told the same thing, but I was awful at most math concepts past high school algebra. I didn't realize it until after college, but the misunderstanding seems to stem from the fact that, for most people, being good at math means being fast at arithmetic and remembering the algebra strategies. That's all their experience in math is, so it's all they can comment on.

Buttons840 3y ago

I think I was good at easy math, and I refused to follow directions. I saw that arithmetic and early algebra had a lot of generally useful principles and I avoided memorizing and would just "think really hard" and I did well enough. I struggled with factoring polynomials (I think it was), and then really started to struggle in Calculus 2. I wish someone had sat me down and said "look, you're not learning universally applicable tools anymore, you just need to memorize these tricks, know that they only work sometimes in the real world, but they will work on the test, just follow the directions!" https://xkcd.com/2117/ https://xkcd.com/2117/

macintux 3y ago
Yeah, basically I crashed and burned there and have been stuck ever since. I was studying at a university where CS was treated effectively as a second math department, which is fine, but not when I had a mental block for integration.

nohaydeprobleme 3y ago

There was an interesting discussion about this quote on r/math about a year back: https://old.reddit.com/r/math/comments/obipos/academics_when_did_you_know_you_were_good_enough/ https://old.reddit.com/r/math/comments/obipos/academics_when... The main counter-argument presented was that if a student makes it all the way to graduate school in mathematics while following instruction, they must have some base level of mathematical talent. Then, continued hard work and persistence can set you up for a strong career in mathematics, without necessarily being brilliant. The perspectives shared there were quite interesting. There were quite a few users who have worked as professional mathematicians—some very successfully—who talked about how they didn't really worry about whether they had mathematical talent, but just worked hard at their goals to become mathematicians because it's what they wanted to do. So, in many cases, it's a valid approach to work hard at mathematics without worrying if you have enough mathematical talent, and eventually find challenging and interesting work along the way. ~~ Separately, there was an interesting Medium post discussed on Mathstodon and r/math a while back, about a father encouraging curiosity for his daughter to learn about the definition of the derivative: https://sunilsingh-42118.medium.com/the-death-of-the-mathematics-i-knew-2255693c87cd https://sunilsingh-42118.medium.com/the-death-of-the-mathema... I liked the second part of his essay more when he talks about his approach in encouraging intuition. He wrote about creating a sense of mystery by rolling a marble up and down a curve to introduce the idea of a tangent line and the concept of a slope, then got his daughter curious about finding ways to numerically calculate the slope. I thought that was an interesting approach for kindling a innate motivation to learn mathematics for a person new to mathematics, rather than focusing on physics, engineering, or economics applications like many textbooks too. Though motivating students to learn calculus for applications can also be interesting (especially for different types of students), it's a bit rarer to find ways for educators to motivate students to learn mathematics for the sake of itself, especially for students learning calculus for the first time.