| 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... 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-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. |