Thoughts on the NCTM Position Statement on Artificial Intelligence and Mathematics Teaching
The National Council of Teachers of Mathematics (NCTM) has recently unveiled their Position Statement on Artificial Intelligence and Mathematics Teaching. This document, which focuses on the use of Generative AI (GenAI) is commendable in several areas, but it also is in need of critical enhancements.
Starting with the commendations:
The NCTM contextualizes AI within the broader history of technological advancements in mathematics education, and underscores the persistent need for equitable access to such technologies.
The statement acknowledges the limitations of GenAI, such as biases and hallucinations, without dismissing GenAI’s potential value in educational settings.
It invites educators to reconsider traditional teaching and assessment; for instance moving from students applying predetermined procedures to solve problems, to students investigating the potential correctness of multiple solutions.
It emphasizes the importance of Pedagogical Content Knowledge (PCK) and Mathematical Knowledge for Teaching (MKT), and highlights the indispensable role of skilled educators, noting that using AI in the classroom “makes the need for experienced math educators more critical—not less.”
The document recognizes the potential of GenAI to assist teachers, and stresses the importance of educator involvement in the development and evaluation of AI tools in education.
However, there are several areas where the position statement falls short.
A notable omission is the lack of discussion regarding collaborative learning or group work. Effective mathematics education requires not only individual cognition, but also social interactions, where collaborative problem-solving and peer discussions are key to the learning experience. This is well known by the NCTM, whose own Guiding Principles for School Mathematics states:
“An excellent mathematics program requires effective teaching that engages students in meaningful learning through individual and collaborative experiences that promote their ability to make sense of mathematical ideas and reason mathematically.” [emphasis added]
Although the use of GenAI in education is currently focused on personalization, the NCTM should not be complicit in promoting the assumption that this is the only, or even most important, use of GenAI in the future. As I’ve said in a prior post, the evolving capabilities of GenAI present opportunities for fostering productive group interactions–but for this to happen all of us, especially organizations such as the NCTM, should be pushing to drive change in that direction.
Another concern is that the NCTM accepts, rather than challenges, the assumption that the use of GenAI can “provide engaging, personally relevant problems and questions for every student,” helping to implement “a critical component of culturally relevant instruction.” Much has been written about the implicit biases in GenAI, and there is no reason to think that these biases magically disappear when asking a GenAI tool to generate “personally relevant problems” based on a student’s background. Instead, the generated problems may inadvertently reinforce stereotypes, particularly affecting marginalized and minoritized students. A more critical stance on the potential pitfalls of personalized problem generation and a call to action for developers to prioritize inclusivity in their AI models would strengthen the statement.
This is not to say that biases are ignored, as shown in this excerpt:
“AI tools are only as good as the training input they receive, and conscious or unconscious bias may influence the choice of that training data. This increases the need to teach students to solve problems themselves in order to identify potential bias in the output.“
While the acknowledgement of bias, and the importance of teaching students about the bias inherent in GenAI output, are vitally important, this statement misses the mark. It is not clear that the best way for students to recognize bias in GenAI is to solve problems themselves: as I discuss above, the bias may be in the very construction of the problem! It is also not clear that the onus of detecting bias should be primarily on the students – this seems akin to saying that we should expect errors in math textbooks, and it is up to students to detect such errors.
Wrapping up, the NCTM's Position Statement serves as an important step towards a more nuanced and comprehensive approach to leveraging AI in mathematics teaching and learning. However, it is imperative that these discussions continue to evolve, at the least by incorporating a broader understanding of collaborative learning and a more critical examination how to reduce bias and achieve the goals of culturally relevant and sustaining education through the use of GenAI.
