A framework for using AI as a tool for enhancing mathematical understanding

The aim of this document is to provide guidelines for the use of artificial intelligence (AI) in mathematics education, ensuring compliance with current rules and regulations while contributing to enhanced mathematical understanding. 

According to one of the Nordic region's most renowned classroom researchers, Professor Kirsti Klette at the University of Oslo, there are four key areas essential for the quality of teaching, and thus for students' learning in the classroom:

1. Clarity of objectives and effective support structures

2. Well-managed classrooms

3. Intellectually stimulating tasks

4. High-quality classroom discussions

(Bjermland, 2022, translated from Norwegian)

To succeed in these four areas highlighted by Klette, teachers need a multifaceted skill set. This includes subject expertise, relational competence, pedagogical and didactic competence, classroom management competence, and developmental competence. Until recently, mastering these areas has been sufficient preparation for the teaching profession.

Hals (2024) argues that the development and accessibility of AI has undergone such a transformative change that it now necessitates entirely new skills for teachers. This is the willingness and ability to explore the opportunities that artificial intelligence (AI) offers in relation to learning. It also includes understanding the limitations and adopting a critical perspective towards all forms of misuse of the technology. AI literacy is a highly complex concept that involves the ability to use, understand, and critically evaluate the application of artificial intelligence.

AI literacy [...] refers to the knowledge and understanding of AI that is necessary for individuals to participate in the broader discourse around AI and make informed decisions about its use and implications [...]. This includes an understanding of the capabilities and limitations of AI, as well as its potential impact on society and the ethical considerations involved in its development and deployment (Southworth et al. (2023).

Some might say that implementing AI in mathematics education falls under the concept of developmental competence, in the same way as learning to adopt other digital tools in teaching. However, artificial intelligence is on the verge of revolutionising the way we acquire new knowledge in ways we have never witnessed before. AI literacy, therefore, deserves its own distinct place within the integrated, comprehensive skill set of an updated and effective teacher.

The use of AI in mathematics education must comply with the EU's General Data Protection Regulation of 2016 (GDPR) and the EU's Artificial Intelligence Act of 2024 (AIA).

The AIA classifies AI systems into three categories based on the risk of adverse consequences for users:

1. High-Risk AI Systems

These systems are subject to strict requirements and obligations due to their potential to cause harm.

2. General-Purpose AI Models (GPAI)

These are AI models that can perform a wide range of tasks and can be integrated into other AI systems.

3. AI Systems That Are Not High-Risk

AI systems that do not meet the criteria for high-risk classification are subject to less stringent requirements.

The AIA imposes different requirements on the various categories of AI systems. Below are some key guidelines derived from the EU documents GDPR and AIA, which are particularly important for the use of AI in education. Each of these points is supported by selected and relevant excerpts from these two EU documents.

• It is crucial that AI technology is implemented in a way that does not create a new barrier between the student and mathematics.

Providers should ensure that all documentation, including the instructions for use, contains meaningful, comprehensive, accessible and understandable information, taking into account the needs and foreseeable knowledge of the target deployers (AIA, article 72).

• A standardised method for risk assessment should be developed before implementing AI tools, focusing on identifying and minimising potential negative impacts on students. Additionally, procedures must be in place to reverse or override decisions made by the AI system.

The assessment should also include the identification of specific risks of harm likely tohave an impact on the fundamental rights of those persons or groups (AIA, article 96).

• The use of AI in education must prioritise students' privacy and data security. Unnecessary personal data about students should not be collected, and data must be processed in compliance with applicable laws and regulations. The processing of sensitive data must not occur. This means that students should only use AI platforms that comply with the GDPR and do not collect or transmit personal information about them.

In order to ensure a consistent level of protection for natural persons throughout the Union and to prevent divergences hampering the free movement of personal data within the internal market, a Regulation is necessary [...] to provide natural persons in all Member States with the same level of legally enforceable rights and obligations and responsibilities for controllers and processors, to ensure consistent monitoring of the processing of personal data (GDPR, Whereas, point 13).

• AI must not be used to evaluate students' performance, assign grades, or diagnose learning difficulties. Evaluation must remain a teacher-led activity based on a holistic assessment of students' work. This is because the GDPR emphasises that individuals should not be subject to decisions based solely on automated processing that have legal or similarly significant effects on them.

The data subject should have the right not to be subject to a decision [...] which produces legal effects concerning him or her or similarly significantly affects him or her [...] Such measure should not concern a child (GDPR, article 71). 

• AI tools used in schools must be designed to be accessible to all students, regardless of their individual needs, and ensure that the technology does not create new inequalities.

The application of universal design principles to all new technologies and services should ensure full and equal access for everyone potentially affected by or using AI technologies, including persons with disabilities (AIA, article 80).

• AI systems used in schools must be designed in a way that allows teachers and students to understand how they work, what they are capable of, and what they are not suitable for. Both teachers and students must evaluate how useful the AI tools are for various purposes.

... AI systems should be designed in a manner to enable deployers to understand how the AI system works, evaluate its functionality, and comprehend its strengths and limitations. [...] Transparency, including the accompanying instructions for use, should assist deployers in the use of the system and support informed decision making by them.

• Chatbots are based on language models, which use advanced statistical methods and probability calculations to predict the most likely next word based on the context. This lies at the core of how such models function. Because language models are probability-based, they can generate responses that appear correct but are actually inaccurate. This is particularly likely in complex or specialised areas such as logic and mathematics, where accurate answers require more than probability-based calculations. Students should be aware of the limitations of AI systems and apply critical thinking to evaluate responses, especially in subjects where precision is essential.

A key characteristic of AI systems is their capability to infer. This capability to infer refers to the process of obtaining the outputs, such as predictions, content, recommendations, or decisions, which can influence physical and virtual environments. The objectives of the AI system may be different from the intended purpose of the AI system in a specific context (AIA, article 12).

Teaching is a highly complex, context-dependent profession that goes far beyond mere content delivery. It involves building relationships, understanding individual student needs, and creating a conducive learning environment.

AI tools should serve as aids for teachers and students, not as replacements for the teacher. It is the teacher who should maintain control over the learning process and use AI as a tool to provide tailored guidance and support to the students.

Teaching is a highly complex, context-dependent profession that goes far beyond mere content delivery. It involves building relationships, understanding individual student needs, and creating a conducive learning environment (Esterman & Jackson, 2024).

Although AI systems cannot replace teachers, they can serve as valuable tools and

support for students. One particularly useful and exciting application of AI in education involves using these tools as endlessly patient and always-available personal tutors. The aim is for students to be guided step by step towards understanding the solution to a mathematical problem, with the help of questions posed by the AI application. In the AIMS project, we have some concrete examples of how this can work in practice. (AIMS stands for Artificial Intelligence as a tool for enhancing Mathematical Skills.)

References

Bjermland, M. (2022). – Lærerne gjør 70 prosent riktig i klasserommet. Artikkel i Forskning.no, 10.01.22. (Teachers do 70 percent right in the classroom. Article in Forskning.no 10.01.22.) Retrieved 09.11.23 from https://forskning.no/partner-pedagogikk-podcast-llaring/laererne-gjor-70-prosent-riktig-i-klasserommet/1957911 

Esterman, M., & Jackson, N. (2024, July/August). Artificial intelligence and teachers: augmentation  not replacement. Blinks Education. Retrieved 13.01.25 from https://www.blinks.education/downloads/Column/2024_08_01_02_guestColumn.pdf 

European Parliament and the Council. (2016). Regulation (EU) 2016/679 of 27 April 2016 on the protection of natural persons with regard to the processing of personal data and on the free movement of such data, and repealing Directive 95/46/EC (General Data Protection Regulation). (OJ L 119, 4.5.2016, pp. 1- 88).

European Parliament and the Council. (2024). Regulation (EU) 2024/1689 of 13 June 2024 laying down harmonised rules on artificial intelligence and amending Regulations (EC) No 300/2008, (EU) No 167/2013, (EU) No 168/2013, (EU) 2018/858, (EU) 2018/1139 and (EU) 2019/2144 and Directives 2014/90/EU, (EU) 2016/797 and (EU) 2020/1828 (Artificial Intelligence Act). (OJ L 2024/1689, 12.7.2024, pp. 1-287).

Hals, S. (2024). Engasjerende matematikk. Sareptas krukke (Engaging mathematics. The Jar of Sarepta). Oslo, CappelenDamm. 

Southworth, J., et al. (2023). Developing a model for AI across the curriculum: Transforming the higher education landscape via innovation in AI literacy. Computers and Education: Artificial Intelligence, 4, 100127. https://doi.org/10.1016/j.caeai.2023.100127