Cognitive Processes and Mental Models in Mathematics Teaching Using Artificial Intelligence

Abstract

In the context of increasing digitisation of education, this study examines the level of digital competence of recent high school graduates in the use of generative language models and equation editing tools in mathematics teaching. The research aimed to verify how effectively students can work with artificial intelligence tools in creating and solving word problems, primarily through systems of linear equations, and to identify the mental models they apply in doing so. The research was conducted on a sample of 25 first-year students from the Faculty of Education. The methodology employed a combination of quantitative and qualitative approaches, with the key analytical unit being the so-called semantic-logical structure (S-L structure), which enabled the monitoring of the transformation of scientific content (A), the teaching task (B), and the student's mental schema (C). The results showed that students' digital skills are predominantly at the basic level – only 28% of participants were able to adjust the prompt and use AI effectively and critically. Most were satisfied with the output generated without more profound reflection. Using the equation editor was a completely new experience for more than half of them. The data also shows that while students can handle basic technical tasks, they often lack knowledge of more advanced tools, confidence, and tend to be satisfied with the first result without conducting a thorough check. On the other hand, it was confirmed that students who reflected on their mistakes and actively adjusted prompts were able to gradually improve their outcomes, which suggests that these skills can be developed in a targeted manner. The study highlights the need for the systematic development of digital literacy, problem-solving skills, and reflective thinking in future teachers. The S-L structure has proven to be an effective tool for monitoring cognitive processes in digitally oriented teaching and learning. Practical strategies include prompt engineering workshops, guided reflection, and subject-specific AI training to improve learning outcomes and e-learning quality.