Students’ reported justifications for their representational choices in linear function problems: an interview study

Abstract

Thirty-six secondary school students aged 14–16 were interviewed while they chose between a table, a graph or a formula to solve three linear function problems. The justifications for their choices were classified as (1) task-related if they explicitly mentioned the to-be-solved problem, (2) subject-related if students mentioned their own characteristics as representational users, (3) context-related if contextual features surrounding the choice were mentioned and (4) representation-related if formal characteristics of the representations were pointed out. Justifications were mostly task- and subject-related, although contextual and representational features also played an important role. Some students (reportedly) tried to reconcile different (task-, subject-, context- and representation-related) factors before selecting a representation, which was interpreted as an attempt to use their meta-representational competence to make appropriate representational choices. The influence of the didactical contract and the experimental contract on students’ representational choices, as well as the tensions between them, are also discussed.

Keywords:

• external representations
• mathematics
• problem solving
• choice/no-choice

Acknowledgements

This research was partially supported by the grant GOA 2006/01 “Developing adaptive expertise in mathematics education” from the Research Fund K.U. Leuven, Belgium, and the grant G063709N “Representational adaptivity in mathematical thinking and learning: analysis and improvement” from the Fund for Scientific Research Flanders.