For people who want to learn or teach mathematics on the basis of reason …
What does learning mathematics mean?
J. Piaget started as a biologist and got interested in epistemology, that is in characterizing what the meaning of "to know" is and, since he found it to go through four stages,
he coined the term Genetic Epistemology.
- Sensorimotor stage
- Pre-operational stage
- Concrete-operational stage
- Hypothetico-deductive stage
Piaget described in detail his---very simple---experiments and by repeating them, anyone can check that children indeed go through these four epistemological stages. But, while this showed that "learning" occurred, Piaget never tried to analyze what was occurring and what moved individuals through these four epistemological stages. In particular, and as a result, he speciﬁcally warned against trying to hasten the stages.
More generally, Piaget defended himself from being a psychologist---and was probably not even aware of the existence of educologists.