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Just to add, building intuition is the same thing as struggling to solve a problem. The process creates solution shaped holes in your brain, in which the formal
by mathgradthrow 3y ago
Just to add, building intuition is the same thing as struggling to solve a problem. The process creates solution shaped holes in your brain, in which the formalism and abstract algebra fit naturally.
But it is important to actually give the formalism and abstract algebra at this point. Unless your child is an age defining genius, they will benefit from some handholding, and theres not much of that that can be done without having access to it yourself.
- rramadass 3y ago> building intuition is the same thing as struggling to solve a problem. Not necessarily. Intuition (borne out of Imagination) is for understanding the domain concepts even before there is a problem to solve. This is the reason i am against the oft repeated advice "solve a lot of problems to learn Mathematics" which merely leads to mechanical "plug and chug problem-solving" with no real understanding. Instead one should spend a lot of time trying to grasp the concepts well, map them to the appropriate notations used and then study a few fully-worked out problems to grasp the "applications".
- mathgradthrow 3y agoThe point is that definitions and theorems are learned backwards. First you dig the hole and then you fill it.