The Inner Curriculum I define the outer curriculum as the information students learn. The inner curriculum is the skills for understanding, retaining, using, and appreciating the outer curriculum.

Basic Number Concepts Some problems. For the toddler, the concept of zero; for the mathphobic adult, the real numbers.

Proofs Proof as explanation, understanding, and some rigor.

Definitions How to define a concept, such as "wall". This is actually a thinking skill, but it is similar to the mathematical problem of defining a circle.