Investigation and Discovery


  • Steven P. Meiring Ohio Department of Education (retired)


Problem solving


Investigation and discovery are how mathematics is applied outside the classroom. Richard Skemp, author of The Psychology of Learning Mathematics, says that gradually equipping students with the analytical skills to address mathematical situations without their aid is one of three tasks for mathematics teachers. This ability involves a different skill set than understanding the mathematics for solutions. The self-talk required to explore a non-routine situation to determine how to get started mimics questions the teacher uses to guide students through assisted learning. Discovery is the creative process of modifying existing schemas to accommodate the new situation. Whereas problem-solving is considered by students as narrowing to an answer, investigation and discovery are expansive to new learning.


Crawford, R.A. Jr. (2021) A web-based resource of ideas and problems for addressing non-routine problem solving at the secondary mathematics level.

Davies, C. (1855). Arithmetic, designed for Academies and Schools; uniting The Reasoning of the French with the Practical Methods of the English System. New York: A. S. Barnes & Co.

Meiring, S.P. (unpublished manuscript) ThinkAbout It: A Resource Guide for Secondary Mαth Teachers and Students.

Pólya, G.A. (1973) How to Solve It (2nd edition). Princeton: Princeton University.

Skemp, R.R (1987) The Psychology of Learning Mathematics. 2nd Edition. London: Penguin Books.

Sternberg, R.J. ed. (1994) Thinking and Problem Solving. San Diego, California: Academic Press.




How to Cite

Meiring, S. P. (2022). Investigation and Discovery. Ohio Journal of School Mathematics, 92(1), 50–56. Retrieved from