Beyond formal preferences: the influence of mathematical thinking styles on problem solving processes in systems of linear equations

Abstract

There is limited research examining how mathematical thinking styles influence students’ problem solving processes, particularly in nonroutine tasks involving systems of linear equations. This study analyzed which mathematical thinking styles are identified in students and how these styles influence their problem solving strategies. The research followed an interpretive qualitative design. Data were collected from 16 undergraduate students in a Mathematics and Computer Science Pedagogy program at a Chilean university who completed a problem solving task on systems of linear equations. Students’ task developments were examined through content analysis. Results revealed analytical, integrated, and visual preferences, with no significant predominance among them. These tendencies shaped students’ strategies, promoting nontraditional approaches beyond those typically taught in linear algebra courses. The study highlights the importance of recognizing and valuing the diversity of mathematical thinking styles as a didactic resource for addressing nonroutine mathematical tasks in the classroom.