Beliefs About “Understanding” in Math, Dept.

Here are some of many beliefs about “understanding” in math.  It was hard to choose from so many candidates, but feel free to add some of your own.  

We shouldn’t be teaching kids algorithms before they have the conceptual understanding.

The belief is that standard algorithms for mathematical operations (like adding/subtracting multidigit numbers, multiplying and dividing multidigit numbers, multiplying/dividing fractions, etc) eclipse the conceptual underpinning.  That is, why the algorithm works.

The standard way used to be taught first, and alternate ways later, after mastery of the standard algorithm. Now it’s other way around in the belief that std algorithms eclipse “understanding”. Side dishes now become the main course and students grow confused—sometimes profoundly so. 

Problems are to be solved in more than one way, in the belief that doing so imparts and gives evidence of “understanding”.  You have students being required to solve simple problems in multiple ways supposedly to enhance…