A problem-solving process using the Theory of Didactical Situations: 500 lockers problem

Abstract

The main focus of this study was to examine the mathematical thinking skills of the undergraduates in an adidactical situation. Didactical Situations Theory was adopted to explain and determine the complexity of students’ mathematical thinking. The current case study was conducted with 16 volunteers, pre-service primary school teachers of mathematics and a task called “500 lockers” was used to challenge their reasoning process. The data obtained through observation and student works were analyzed deductively and according to the five stages of adidactical learning described by Brousseau (2002). One of the main results of the study is that the designed learning environment with the given problem context provoked participants to make conjectures and provided them with an opportunity to defend their own hypotheses. Consequently, the implementation of the problem resulted in invaluable reflections enhancing participants’ mathematical thinking.

Keywords

• Didactical situations
• adidactical learning setting
• problem solving
• 500 lockers problem