Using Pictures as Cultural Means in Finding Similarities between Solutions to Algebraic Tasks

Abstract

Solving textual algebraic tasks requires finding important mathematical variables in the text and turning them into equations. Many students, following their teacher’s advice or at their own initiative, use pictures as a means of better understanding the mathematical structure of the task. In this study we explored which features of pictures were the most essential to the students in finding the appropriate solution based on their experience. We created a set of pictures that differed in parameters of analogy and completeness of relationships between elements. The subjects were asked to evaluate the usefulness of the solution to the initial task (represented by the picture) for solving the target task. As it was revealed, in their evaluations the subjects were more likely to focus on the completeness of the depicted relationships rather than on the analogy of the picture. This tendency was also more evident in experienced subjects as compared to inexpe- rienced ones. The outcomes of our study are interpreted in terms of the development of cultural means in the transition from everyday concepts to scientific concepts in the process of learning.

Keywords

• algebraic tasks
• solution
• representation
• symbolization