My impression was that with constructivism, the question is not whether the student ultimately achieves a gears-level model, but whether they discover (“construct”) it for themselves.
I agree it’s hard to imagine addition without a gears level model.
Yes, but there can be a lot of nudging towards the discovery.
Like, if you want kids to find out that “a + b = b + a”, you give them hundred pairs of problems like “2 + 7 = ?; 7 + 2 = ?”. That achieves the goal more reliably and more quickly than merely giving them hundred random addition problems.
My impression was that with constructivism, the question is not whether the student ultimately achieves a gears-level model, but whether they discover (“construct”) it for themselves.
I agree it’s hard to imagine addition without a gears level model.
Yes, but there can be a lot of nudging towards the discovery.
Like, if you want kids to find out that “a + b = b + a”, you give them hundred pairs of problems like “2 + 7 = ?; 7 + 2 = ?”. That achieves the goal more reliably and more quickly than merely giving them hundred random addition problems.