Using diagrams as tools for the solution of non-routine mathematical problems

Using diagrams as tools for the solution of non-routine mathematical problems[/size]

Marilena Pantziara & Athanasios Gagatsis & Iliada Elia
Published online: 10 February 2009
# Springer Science + Business Media B.V. 2009

Abstract :

[left][left]The Mathematics education community has long recognized the importance of diagrams in the solution of
mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems’ structure and information.
(Novick & Hurley, 2001; Diezmann, 2005).
Novick and Hurley were the first to introduce three well-defined types of diagrams, that is, network, hierarchy, and matrix, which represent different problematic situations. In the present study, we investigated the effects of these types of diagrams in non-routine mathematical problem solving by contrasting students’ abilities to solve problems with and without the presence of diagrams. Structural equation modeling affirmed the existence of two first-order factors indicating the differential effects of the problems’ representation, i.e., text with diagrams and without diagrams, and a second-order factor
representing general non-routine problem solving ability in mathematics. Implicative analysis showed the influence of the presence of diagrams in the problems’ hierarchical ordering. Furthermore, results provided support for other studies (e.g. Diezman & English, 2001) which documented some students’ difficulties to use diagrams efficiently for the solution of problems.
We discuss the findings and provide suggestions for the efficient use of diagrams in the problem solving situation.[/left[/left]][left]