I get the feeling a lot of people are surprised when they find out you can _understand_ math.. it isn’t just a series of random facts and some Rube Goldberg machinery.

I think this problem must start quite early in school, and get enforced so often it becomes a belief system.   For example its rare that the distributive rule is related to areas of rectangles.. but that’s such a good visual explanation, it should be the default way of introducing the idea :


After a couple of these diagrams you can mention it works for any rectangle with sides of length a+b and c+d , namely :  (a+b)(c+d)=ac+ad+bc+bd.

Maybe with tablet computers we can make Math more intuitive,  when good visualizations can be seen by most students.

I wonder if teachers are so constrained to teach the points of the curriculum, handle admin tasks and control the class, that there is no time left for cultivating Math ‘understanding’ ?  But surely its faster to learn / teach by understanding?

If you never get that little rush of endorphin from understanding, I could see how Math would be very boring and random.. because its not really math then, its something else ( and that’s not good, is it Precious?   Not at all.. no it isn’t.. Precioussss… hmm… ghollum ! )