Even after many decades of productive research, problem solving instruction is still considered inefective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the frst view argue that insight is the consequence of ...

Mathematical techniques in proof writing can be narrowed down to specific proof styles. Simply put, proofs can be direct or indirect- the latter using the Law of the Excluded Middle from logic as well as the axiom of Choice, to prove existence of mathematical objects. However, the thinking skills involved in writing indirect proofs are prone to errors, especially from novice proof writers such as ...

Inquiry-based mathematics education (IBME) is an increasingly important ingredient of the mathematics education in the Nordic countries. The central principle of IBME is that the students are to work in ways similar to how professional mathematicians work. In this qualitative case study, we investigate whether mathematical pathologies induce students to work like mathematicians, and thus if ...

This study investigates high achieving students’ mathematical reasoning when given an unfamiliar trigonometric equation. The findings indicate that the students’ way of thinking is strongly linked with imitative reasoning and only when they received some form of guidance, were they able to display flexible and creative mathematical reasoning.