Transforming formal knowledge to language and graphs to promote mathematics learning: A repeated-measures mixed design quasi-experiment

Abstract

The transition from school to university mathematics presents a significant challenge for students, as both the demands on mathematical reasoning and the level of abstraction increase. This often makes it difficult for learners to construct the mental models necessary for understanding mathematical content and meeting academic requirements. Research has shown that incorporating a second level of content representation—particularly graphical representations—can help students develop more viable mental models. This longitudinal quasi-experimental study aims to enhance mathematical learning in higher education by supporting students' mental modeling. We use a new approach called natural-language conceptual Graph (NaGra), which translates mathematical formalism into natural language. Using computer-linguistic software, we then generate knowledge maps from these texts, providing two distinct types of additional representations to complement traditional instruction. In a 6-point repeated-measures control-group design, 139 math undergraduates received either (a) a natural language text, (b) a knowledge map, (c) both the natural language text and the knowledge map, or (d) the traditional instruction based solely on mathematical formalism. Results from non-parametric longitudinal analyses indicate that students in the experimental conditions consistently outperformed those in the control group over time in mathematical performance. However, students did not perceive the added value of these representations. These findings suggest that the NaGra method can contribute to students’ understanding of STEM subjects (science, technology, engineering, and mathematics), where first-year students often struggle to adapt to abstract formal content.