ChatGPT's perspectives on real numbers, straight lines, and probability—A quantitative study on the influence of prompting - Dilling, Frederik (Frontiers in Education, 2025)
Large language models like ChatGPT are currently a hot topic in mathematics education research. Various analyses are available on the correctness of mathematical responses and on performance in problem solving or proving contexts. However, the adequate representation of mathematical content in the responses has not yet been sufficiently considered in research. This article addresses this desideratum using the approach of belief systems about mathematics. For this purpose, four perspectives on mathematics are distinguished—the formal-abstract, the empirical-concrete, the application and the toolbox perspective. A qualitative content analysis of 450 ChatGPT responses to the mathematical concepts of real numbers, straight lines and probability and the subsequent quantitative evaluation with chi-square tests showed that the empirical-concrete perspective occurs much more frequently than the other perspectives and the formal-abstract perspective is found very rarely in comparison. The use of appropriate prompts can significantly increase or decrease the occurrence of perspectives. There are also significant differences between the mathematical concepts. The concept of a straight line is significantly more often defined in terms of the empirical-concrete and less often in terms of the formal-abstract perspective compared to the other concepts.