Prospects and Perils of Artificial Intelligence in Mathematics Learning in the Digital Era

• In Event: Emerging technologies in mathematics education

Proposal

Introduction

Traditionally, mathematical proof is introduced to students in middle and high school geometry and to a lower degree in algebra. In mathematics education, the meaning of proof has been constantly developing, and there are different understandings of this concept. Griffiths (2000) defined the concept of proof as “a formal and logical line of reasoning that begins with a set of axioms and moves through logical steps to a conclusion” (p. 2). Conversely, and mainly in education, proof has been seen from a broader perspective. This leads to considering other functions and structures of proof rather than only viewing it as a process of validating a binary (either true or false) statement. Scholars consider proof in school mathematics as a process of explaining, showing, and justifying the relative trueness of a mathematical idea. They consider proof as a social discourse between community members about the validity of a statement. Once this validity is approved by the community, the given discourse becomes proof for the statement. Thus, mathematical proof is a social act.

In a mathematics classroom community, students, along with their teacher and in interaction with their curriculum, shape the community that holds the traditional responsibility of evaluating mathematical proofs. In such a classroom, students—traditionally unable to tap into ready-made information resources such as Artificial Intelligence (AI) and various online resources —are challenged by their community to develop their mathematical cognitive structures by engaging in problem-solving tasks. They are also expected to satisfy certain criteria for proving mathematical statements (clarity, rationality, justificatory, etc.). Nowadays, however, benefiting from new-era technologies, the walls of traditional mathematical communities fall in the blink of an eye. Students could suddenly—and generally under no supervision from a more competent person—find themselves in other online learning communities, sometimes the right and helpful ones, sometimes not.

On the one hand, the traditional role of teachers has been challenged. Students can freely benefit from their virtual presence in these new communities and explore new ideas. On the other hand, the role of new agents in supporting mathematics learning is emerging. Are these new agents, such as AI, supportive and competent enough to scaffold student learning in mathematics? Are these supports productive? Using a qualitative analysis methodology, this paper explores how one of the most used AI resources, ChatGPT, as a new emerging agent in the education community might play a role in mathematical proof education.

Methodology

In our endeavor to respond to these questions, we used a qualitative approach to explore, analyze, and interpret how AI might influence geometry education. We selected ten different geometry problems involving mathematical proving from recent mathematics textbooks being used in the 7th and 8th grades in Quebec schools, Canada, and carefully prompted ChatGPT to answer these questions. Our aim was to let this program explicitly know that we want to solve each problem so that the answer could be used as a mathematical proof for a hypothetical middle-grade classroom. We mainly drew on commonly used criteria of mathematical proving developed by Balacheff (1988) to evaluate the ChatGPT responses. These criteria focus on clarity, validity, justificatory reasoning, etc.

The salient concepts in the responses were identified through coding and thematic analysis. Then, patterns of similarities and differences were analyzed. The analysis of AI responses revealed several interesting findings. AI has become very intelligent. It unbelievably understood and interpreted all of the problems, although we used a variety of different problems based on our selection criteria. Additionally, the ChatGPT 4O version analyzed and interpreted pictures really well. We uploaded some pictures taken from the textbooks, and it perfectly detected all the necessary elements related to the questions. However, several grave shortcomings were noticed: (a) Students' success in working with AI hugely depends on their reading skills; (b) AI does not involve productive interaction with learners; (c) Although the answers were mathematically valid and justified, this AI tool did not consider students’ age, the existing level of understanding, and their ability to comprehend the suggested proofs. (d) AI fails to provide visual support to students. These problems and the answers will be discussed in detail during the presentation.

Conclusion and Implications

In sum, we argue that ChatGPT is increasingly becoming a smart tool that could potentially play a useful role in mathematics learning. However, from a pedagogical perspective, this tool has a long way to go to become competent and capable enough to meet the unique needs of students and to scaffold their understanding adequately. The fast-developing AI tools have strong implications for mathematics teachers. Nowadays teachers need to get prepared to appropriately react to students’ emerging needs as they consult and draw on AI tools and resources while learning mathematics.

We are realizing an expansion in the meaning of the mathematical community. New technologies are rapidly and extensively connecting people from different mathematical communities together. This would unavoidably influence the social aspect of mathematical proving. The criteria for a proof are not being solely determined by the teacher and other student of the local classroom.
New agents, such as software developers, programmers, and other contributors in AI companies, are now playing a role in this game. It is important to become aware of the pedagogical potential of AI programs and tools in terms of enhancing mathematics teaching and learning. At the same time, it is imperative to critically examine the risks involved in using these tools in the current digital era to appropriately and timely deal with such emerging issues in mathematics education.



References:
Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, Vol. 18, no 2, 147-176.
Griffiths, P. A. (2000). Mathematics at the turn of the millennium. American Mathematical Monthly, 107, 1-14.

Authors

• Ali Motlagh

• Anila Asghar, McGill University