Probabilistic modeling and AI in upper secondary mathematics
Probabilistic modeling and AI in upper secondary mathematics
- An SRP experiment
IND's Studenterserie nr. 126, 2025, Speciale i Matematik
Victor Lynge Nielsen
Vejleder: Carl Winsløw
Abstract:
This thesis considers whether students are able to approach a model for the calculation of insurance premiums when encouraged to use ChatGPT or other Large Language Models (LLMs), since the use of such tools instantly solves tasks on probability, which are already part of the mathematics syllabus in Danish upper secondary school. Concretely, a Study and Research Path (SRP) is developedon this model and experimented in a third-year class of Danish upper secondary school.
Q&A diagrams are developed both in the a priori and a posteriori analysis of the SRP design. A priori it is assumed that students find the most significant factors which insurance companies consider when calculating premiums for car insurance. Additionally, it is assumed that the students find formulas for the calculation, which they can connect to theory from the syllabus of upper secondary school mathematics, and that they can calculate the estimates for the expected loss for a given insurance portfolio as well as for smaller groups of policyholders within the portfolio.
A posteriori we find, that students find the most significant factors to consider in premium calculation, but that ChatGPT gives them formulas containing subtle misconceptions. Using these less-than-correct formulas students find estimates for the insurance company’s expected loss both for the entire portfolio and for smaller groups within it. This way we see, that LLMs were helpful in the experiment as a sort of instrumented technology but were less effective when used as instrumented theory. We find that ChatGPT shows especially high potential in explaining the use of mathematics software and consider whether some teaching on prompt design should be recommended for this use specifically. Finally, it is found that students adapt well to SRP-based teaching when it is combined with the use of ChatGPT.
Find the Appendix here.