Shaping AI Math How Prompts Influence ChatGPTs Explanations

AI's Evolving Role in Understanding Mathematics

Large Language Models (LLMs) like ChatGPT are rapidly becoming influential tools in mathematics education. Researchers are actively exploring their accuracy in mathematical tasks, problem-solving capabilities, and even their performance in creating proofs. However, a crucial aspect often overlooked is how these AI models represent mathematical content itself. This blog post delves into a recent study that investigates this very question, focusing on ChatGPT's "perspectives" on mathematics.

Unpacking ChatGPTs Mathematical Viewpoints

The study introduces an approach based on "belief systems about mathematics" to understand how ChatGPT frames mathematical ideas. It distinguishes four primary perspectives:

• Formal-Abstract: This view emphasizes rigorous definitions, logical structures, and the axiomatic nature of mathematics.
• Empirical-Concrete: This perspective treats mathematical concepts as tangible, observable, or related to real-world objects and experiences.
• Application: This viewpoint focuses on how mathematics is used to solve problems in various fields and practical situations.
• Toolbox: This perspective sees mathematics primarily as a collection of tools, formulas, and procedures to be used for specific tasks.

How the Study Was Conducted

Researchers performed a qualitative content analysis on 450 responses generated by ChatGPT. These responses were prompted with questions about three core mathematical concepts:

• Real numbers
• Straight lines
• Probability

The qualitative findings were then quantitatively evaluated using chi-square tests to identify statistically significant patterns in ChatGPT's responses.

Key Findings What ChatGPT Emphasizes

The results revealed some fascinating tendencies in ChatGPT's explanations:

• Dominance of the Concrete: The empirical-concrete perspective appeared much more frequently than the other viewpoints. This means ChatGPT often defaults to explaining math in tangible or experiential terms.
• Rarity of the Formal: In stark contrast, the formal-abstract perspective was found very rarely. This suggests that AI might not inherently prioritize rigorous, abstract definitions unless specifically guided.
• Concept-Specific Differences: The way ChatGPT presented concepts also varied. For example, "straight lines" were significantly more often defined using an empirical-concrete lens and less often from a formal-abstract viewpoint compared to "real numbers" or "probability."

The Critical Impact of Prompts

One of the most significant findings is the influence of prompting. The study showed that:

The use of appropriate prompts can significantly increase or decrease the occurrence of perspectives.

This highlights that users can actively shape the nature of ChatGPT's mathematical explanations by carefully crafting their questions or instructions. If a more formal explanation is needed, the prompt must guide the AI in that direction.

Implications for Learners and Educators

These findings have important implications for anyone using AI in mathematics education. Understanding ChatGPT's default tendencies and the power of prompts can help educators and students leverage these tools more effectively, ensuring a more balanced and comprehensive understanding of mathematical concepts.

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This research summary is based on the article "ChatGPT's Perspectives on Real Numbers, Straight Lines and Probability -A Quantitative Study on the Influence of Prompting" by Frederik Dilling, University of Siegen, Germany, provisionally accepted for publication in Front. Educ. Sec. STEM Education, Volume 10 - 2025.

The original research is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). Its use, distribution, or reproduction in other forums is permitted provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution, or reproduction is permitted which does not comply with these terms.