- Sep 2021
What if we taught art and music the way we do mathematics? All theory and drudgery without any excitement or exploration?
What textbooks out there take math from the perspective of exploration?
- Inventional geometry does
Certainly Gauss, Euler, and other "greats" explored mathematics this way? Why shouldn't we?
This same problem of teaching math is also one we ignore when it comes to things like note taking, commonplacing, and even memory, but even there we don't even delve into the theory at all.
How can we better reframe mathematics education?
I can see creating an analogy that equates math with art and music. Perhaps something like Arthur Eddington's quote:
Suppose that we were asked to arrange the following in two categories–
distance, mass, electric force, entropy, beauty, melody.
I think there are the strongest grounds for placing entropy alongside beauty and melody and not with the first three. —Sir Arthur Stanley Eddington, OM, FRS (1882-1944), a British astronomer, physicist, and mathematician in The Nature of the Physical World, 1927
- Jul 2021
Play may trump problem solving. When working on a problem without a specific goal, the student can try lots of things to figure out what works. In contrast, only one answer is needed to solve a problem with a single goal. A playful, exploratory mindset may map out the patterns of interactions better than a narrowly, solution-oriented perspective. As an example of this, Sweller asked students to solve some math problems. One group was asked to solve the problems for a particular variable, and the other group was asked to solve for as many variables as they could. The latter group did better later, which Sweller explained in terms of cognitive load.4
exploratory play >> problem solving
How does this compare to the creativity experience of naming white things in general versus naming white things in a refrigerator? The first is often harder for people, while the second is usually much easier.