Tracing proof schemes: some patterns and newperspectives

Abstract

The aim of this paper is to review some studies conducted withdifferentlearning areas in which the schemes of different participants emerge. Alsoit is about to show how mathematical proofs are handled in these studiesby considering Harel and Sowder's classification of proof schemes withspecific examples. As a result, it was seen that the examined studies wereaddressed in the learning areas of Analysis, Geometry, Algebra, LinearAlgebra, Elementary Number Theory, Probability, Combinatorics, andMIX. Students in early grades tend more towards external and empirical proof schemes. On the other hand, the characteristics of theproof schemes become more sophisticated as the participants' profiles changeto pre-service teachers or as they become more specializinginmathematics. Some results are as follows: the academic achievementlevels, genders, and grade levels of the participants in the studiesexamined in this paper have indicated that they have similar traces withthe schemes they use. In addition, it has been determined that newperspectives such as examining Harel and Sowder's classificationwithnew lenses, revealing the overlooked roles of some dynamics inproof, orimproving the framework provide an important research area intermsof revealing students' potentials.