Children who learn maths working in markets and children who learn maths only from school were both unable to transfer their skills to new contexts, highlighting a need to reconsider how maths is taught in school.
I’ll be honest, it’s surprising to me. I recently finished my doctorate in math and taught undergrads for much of that time, and I’m wondering how many of my “bad” students would have been great at the same fucking things if I’d presented them differently. This feels, to me, like a huge finding, and a very puzzling one. Why do similar problems hit people’s brains so differently based on context? To the point where accomplished arithmeticians can lose all of their skill if the problem is stated in a different context? It’s really weird, actually, in my mind.
Maybe this is a generational thing. When I was learning in stuff like grade school or whatever you’d constantly get problems like “Sally has 3 apples. She gives 2 to Jared. How many apples does she have left?” Obviously, I didn’t get as many of those doing like diff eq, but the whole reason you learn subjects like those is to apply them in the sciences, and you just don’t take the course if you don’t intend to use the math. That said, you absolutely can apply this outside of just arithmetic - trig and calculus you can 100% turn into practical problems. Even stuff like Calc 3 and Linear Algebra you can very easily think of more physical examples for. I remember using both in Electromagnetics!
I’ll be honest, it’s surprising to me. I recently finished my doctorate in math and taught undergrads for much of that time, and I’m wondering how many of my “bad” students would have been great at the same fucking things if I’d presented them differently. This feels, to me, like a huge finding, and a very puzzling one. Why do similar problems hit people’s brains so differently based on context? To the point where accomplished arithmeticians can lose all of their skill if the problem is stated in a different context? It’s really weird, actually, in my mind.
Maybe this is a generational thing. When I was learning in stuff like grade school or whatever you’d constantly get problems like “Sally has 3 apples. She gives 2 to Jared. How many apples does she have left?” Obviously, I didn’t get as many of those doing like diff eq, but the whole reason you learn subjects like those is to apply them in the sciences, and you just don’t take the course if you don’t intend to use the math. That said, you absolutely can apply this outside of just arithmetic - trig and calculus you can 100% turn into practical problems. Even stuff like Calc 3 and Linear Algebra you can very easily think of more physical examples for. I remember using both in Electromagnetics!