Exploring pre-service mathematics teachers’ thinking for solving linear programming word problems

Solving word problems in linear programming presents significant challenges, not only for secondary school students but also for pre-service mathematics teachers. This study aims to investigate the cognitive processes of pre-service mathematics teachers in solving word problems related to linear programming. To achieve this objective, a comprehensive review of mathematics textbooks designed for pre-service teachers and secondary school students, as well as the corresponding curriculum, was conducted to identify an appropriate learning sequence for this topic. Subsequently, key problems were selected to facilitate learning, and predictions regarding the cognitive processes involved in solving these problems were formulated based on Newman’s error analysis framework. Following this preparatory phase, an individual written assessment was administered to 27 pre-service mathematics teachers to examine their problem-solving approaches in linear programming word problems. The findings of this study include the identification of essential word problems in linear programming and a comparative analysis between the predicted and actual problem-solving processes exhibited by the participants. In conclusion, this study highlights the potential of cognitive process predictions in anticipating learning difficulties and informing instructional strategies. These insights can be leveraged to provide targeted support for pre-service teachers facing challenges in problem-solving and to develop pedagogical interventions aimed at enhancing their problem-solving skills.