Problem Solving in Realistic, Arithmetic/algebraic and Geometric Context

Abstract

In the last decades, voluminous research has been dedicated to the modeling process and students’ understanding of word problems (verbally set problems with realistic context). These problems were considered as a natural framework for the development of the meaning of mathematical relations and for linking mathematical knowledge and everyday situations. In this study we examine three different contexts of verbally set problems: realistic, arithmetic/algebraic and geometric. The research sample consists of 62 fourth-grade elementary school students (10 – 11 years old). The results show that there is a significant relationship between students’ achievement in problem solving in the three different contexts as well as a relationship between the choices of strategies in different contexts. It is shown that students solve problems without the use of visual-schematic representations. Surprisingly, not even in geometric context did student use visual representations. Therefore, a joint activity of students and teachers in constructing visual-schematic representations should be an important aspect not only of solving problems with realistic context, but also of solving geometry problems and problems posed in the mathematical language.