"Pitääkö ymmärtää voidakseen tehdä, vai päinvastoin?"

lähde: Nescher, P., 1986, Are mathematical understanding and algorithmic performance related? For the learning of matehmatics, 6 (3), ss. 2 – 9

"Konseptuaalinen tieto on edellytys etenemiselle proseduraalisessa tiedossa."
[[$$\mathbb{P}\subset\mathbb{C}\subset\mathbb{P}_{\text{sof}}$$]]

lähde: Haapasalo, L. & Kadijevich, D., 2000, Two types of mathematical knowledge and their relation, Journal für Mathematikdidaktik, 21 (2), ss. 139 – 157

1. "I can identify the subject, what it is and what it includes."
2. "I can point out the main essential matters."
3. "I understand it."
4. "I know how to summarize it."
5. "I know how to teach it to the others."
6. "I know how to apply this in action."

lähde: Bloom, B. S.; Engelhart, M. D.; Furst, E. J.; Hill, W. H.; Krathwohl, D. R. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: David McKay Company