Types of
Mathematical Knowledge

  1. Facts (maths results)
  2. Perceptual Features
  3. Heuristics
  4. Procedures

At least four different types of mathematical knowledge can be distinguished:
Facts, or mathematical results,
Perceptual features,
Heuristics,
and Procedures or Algorithms.
Mathematical results are the most common form of mathematical knowledge, like a(b +c) = ab + ac.
Perceptual features are possessed by experts to enable them to see a pattern in a result quickly.
Heuristics guide when to apply a result so as to control search.
Finally, procedures have several steps like the algorithm of long division.