Society currently finds itself amidst the era of artificial intelligence - an age where the curation and production of knowledge, seemingly regarding anything that can occupy the mind, can be generated at the whim of any user with a computer, internet connection, and access to ChatGPT. Large Language Models (LLM) and Machine Learning (ML) present new capabilities, which can be perceived as daunting and a source for skepticism. The ideas, questions raised, and feelings of uncertainty as a result are not, in a sense, new to us.

Society has continuously contemplated the implementation, utility, and ethical implications of the computer well since the first fully functioning electronic digital computer. ENIAC’s (Electronic Numerical Integrator and Computer) completion in 1945 (Copeland, 2020), and other computers alike, positioned society, education, and governments into vastly unfamiliar territories. And as time has shown, the development of computing technologies (resistors, transistors, integrated circuits, etc.) progressed rather rapidly. By 1991, the release of the “World Wide Web” connected members of society in ways incomprehensible to folks alive even one hundred years ago. Consider the following quotation from Greg Blonder in a 1995 essay for Wired magazine titled “Faded Genes”:

“In 2088, our branch on the tree of life will come crashing down, ending a very modest (if critically acclaimed) run on planet earth…The culprit is the integrated circuit … By 2090, the computer will be twice as smart and twice as insightful as any human being. It will never lose a game of chess, never forget a face, never forget the lessons of history…” (Elon University, n.d.)

Skepticism and even pessimism have persisted across humanity's coevolution with modern technology. However, it isn’t just fear, skepticism, or pessimism that have been expressed by members of society. There has always been an amount of hope, excitement, and potential understanding to be realized. Consider this quotation from Todd Oppenheimer’s publication “The Computer Delusion” to The Atlantic Monthly in 1997:

"Increasingly, the computers of the very near future will be the private property of individuals, and this will gradually return to the individual the power to determine patterns of education. Education will become more of a private act... There will be new opportunities for imagination and originality." (Setzer, 2000)

Modern day technology presents a tremendous amount of power to be harnessed. Information is all around us. Our ability to communicate, share ideas, learn, and construct knowledge is unprecedented. And how we interact with and manage these technologies has been a large concern of educators for the last sixty years.

Particularly, educators in mathematics have wondered how to best implement computing technologies into mathematics curriculum since the production of technologies like ANITA (the first all-electronic desktop calculator) in 1961. Consider the note made by Carles J. Zoet in his 1969 publication “Computers in Mathematics Education”:

“... computers do have a role to play in mathematics education. The nature of that role is uncertain… Perhaps some day that will not be the case but for the present the uncertainty related to the use of computers adds… an intriguing new dimension that has particular significance for mathematics educators.” (Zoet, 1969)

In the present day, mathematics learners and educators, including myself, have so many technological tools available to us to engage in the learning and teaching of mathematics content - all of which range in capability. For example, the HP-28 series of calculators has hosted one of the first Computer Algebra Systems (CAS). In short, Computer Algebra Systems are able to solve and evaluate symbolic equations or expressions, not just numerical ones. Furthermore, there are basic four-function calculators like the Casio SL-450S or the Sharp EL-240SAB that you might find in an office worker’s desk drawer. The TI-84 graphing calculator and TI-30X scientific calculator both can be found widely used across school districts, both of which I personally grew up using. I still use both today and, in particular, students in my Algebra classes use the TI-30X.

Well across the past two decades, teachers and students have run the gamut of dynamic graphing applications like GeoGebra and Desmos - both of which can host lesson activities and are compatible with other educational platforms like Google Classroom. Mathematics research concerns itself quite often with programming applications like MATLAB, Python, Mathematica, etc. Specifically, I teach students the Python and JavaScript languages at the high school level.

To profoundly and also obviously state, the technological landscape we find ourselves in is quite vast and “...pedagogical mediation has undergone a metamorphosis, with technology increasingly playing a role in enhancing learning” (Villan et al., 2023). And now, we find ourselves alongside another commercialized tool - artificial intelligence. Outlets like ChatGPT, Khan Academy’s Khanmigo, or Google’s Gemini were made available to the public only within the last couple years, but are already impacting the educational and corporate worlds.

Thus, like any new technological frontier, such as the era of ENIAC or the release of the TI-84 calculator, understanding the role that artificial intelligence and other technological tools can have in learning mathematics throughout K-12 education is consequently pertinent. In fact, it is necessary. And in particular, it is crucial to explore how artificial intelligence, among its impressive capabilities, can best operate as a tutor, collaborator, lesson planner, or as an assessment tool in education. In this work, I hope to offer insight into pedagogical frameworks that model the educational dynamic between the student, teacher, and artificial intelligence that optimizes student learning and experiences.

This work ultimately considers the following two focus questions:

1. How can artificial intelligence support collaborative learning?
2. How can artificial intelligence leverage productive struggle in learning mathematics?

When we, as educators, consider elements of good teaching and the goals we set for our students in mathematics, the discussion typically revolves around students as “doers” or “explorers” of mathematics. We aim to develop a host of skills within our students, so that they engage in mathematics as “knowledge creators”, not just as “knowledge recipients”. For example, in 9th and 10th grade Geometry, we spend time on geometric constructions and proofs. Students do not just learn about the properties of perpendicular bisectors, but instead how they are constructed and used to prove other theorems or properties, say, in the context of congruence. To that end, we wish to instill creativity, problem solving strategies, the ability to conjecture, to analyze and critique, to construct viable arguments, and so on.

There are countless attributes we work towards fostering in our students. And in doing so, we must always aim to position our students along an appropriate learning path - one that is catered to them. This “path” is often formulated by the teacher through educational practices of differentiation, curriculum development and alignment, scaffolded supports, culturally relevant pedagogy, appropriate level of rigor, implementation of appropriate technologies, and so on. And as there are many answers and approaches to this, I would like to spend time focusing specifically on how AI can play a part in this “path” creation. 

Throughout my experience as a student in mathematics, I found great solace in the ability to graph linear, quadratic, or cubic equations on my TI-84 calculator, for example. In the window view of the graph, the user possesses the ability to zoom in or out, locate local maxima/minima, locate points of intersection, locate intercepts, and so on. The TI-84 served as a tool to manipulate and explore mathematics. In my years as a teacher, I have found great joy in seeing students transform functions in the Desmos Graphing Calculator by manipulating slider values that correspond to the coefficients of the functions. Quickly, students can make conjectures about what a, h, and k do to the graph of a quadratic equation written in vertex form: \(y = a(x-h)^2+k\). These tools empower the learning of mathematics by making the ideas accessible. Artificial Intelligence applications are likely no different. It is just a matter of harnessing their capabilities in the correct manner. 

Thus, we will begin by considering contemporary theories of learning. In particular, the next several sections will focus on notions of Lev Vygostky’s Sociocultural Theory of Learning, Personalized and Adaptive Learning, Ergative and Reflexive Pedagogies (Cope et al. 2015), Bloom's Taxonomy, and notions of productive struggle. These theories, as I will argue, align with and support the use of Artificial Intelligence in the mathematics classroom.

Let us first consider the sociocultural theory of Lev Vygotsky (1934-1978). Vygotsky’s theory has been extremely influential in both cognitive development research and in educational practices for several decades. An integral aspect to his theory is his notion of the Zone of Proximal Development.

As stated by Dr. Saul Mcleod (2024), Vygostky believed cognitive development in areas like speech and reasoning are both influenced by cultural and social factors. In particular, cognitive development is a socially mediated process in which children acquire cultural values, beliefs, and problem solving strategies through collaborative dialogues with more knowledgeable members of society (Mcleod, 2024). To a child, either a parent, teacher, coach, or peer can act as a “more knowledgeable” counterpart - one who provides guidance and modeling of these cognitive skills. Vygostky claims that higher mental abilities in individuals could only develop with the assistance from more advanced members of society. That is, more advanced members of society position learners closer to mastering a particular skill. This, in essence, lays the framework for what is the Zone of Proximal Development (ZPD).

The ZPD is the difference between what a learner can do without help and what they can do with guidance and encouragement from a skilled partner (Mcleod, 2024). In its application, this theory encourages collaborative and cooperative learning between children and teachers. Specifically, Vygotsky defines the ZPD as:

“the distance between the actual developmental level as determined by independent problem solving and the level of potential development as determined through problem-solving under adult guidance, or in collaboration with more capable peers." (Vygotsky, 1978, p. 86).

This can be schematically represented in the following diagram (Figure 1):

Figure 1: Zone of Proximal Development, Source: https://www.simplypsychology.org/vygotsky.html#Zone-of-Proximal-Development

Essentially, there are three tiers: 1) What a student (child) is capable of learning on their own 2) What the student is capable of learning with assistance 3) What the student is incapable of learning even with assistance. The ZPD is exactly where educators should position students. Educators often design lesson activities that bridge previous learning with new learning utilizing proper scaffolds. Scaffolding consists of activities, strategies, and techniques used by the teacher to bridge the gap between a learner’s current abilities and potential development (Mcleod, 2024). It is a dynamic process that changes based on the student’s progress (Mcleod, 2024).

For example, when teaching an Algebra student how to graph a linear equation in slope-intercept form, the teacher might ask first “What is the y-intercept? What is the slope?” The student's response determines the teacher’s next action. If the student cannot appropriately identify either part from the equation, then graphing the equation is no longer the immediate focus of the task. Instead, the teacher should pivot to reviewing how to identify these values from the equation. That is, the structure \(y=mx+b\) is revisited. The teacher is maintaining the student’s position within the ZPD. So, what about AI?

AI technologies like ChatGPT “... [act] not just as a mere virtual assistant but as a technological extension of the human educational mediator, assisting both students and teachers in expanding their horizons.” (Villan et al., 2023, p.67). Current AI technologies seem to operate under the role of “more knowledgeable other” as referred to in Vygotsky’s theory. ChatGPT, for example, can help simplify and explain complex concepts, lay foundations for research, and collaborate as a co-advisor in learning projects (Villan et al., 2023).

Suppose a student was at home working on the mathematics question posed above. A student, if unable to progress towards a solution, might open ChatGPT and enter the prompt “What is slope-intercept form? Provide a simple explanation.” ChatGPT outputs the following (Figure 2):

Figure 2: Prompting ChatGPT, Source: https://chatgpt.com/

Though there was no human teacher involved, a student still engaged in a “somewhat” social interaction with a “more knowledgeable other” to produce knowledge aligned with their placement within the ZPD. With this consideration made, I do recognize that a student's progress within this problem is based on the student’s ability to prompt AI appropriately and to be critical of the output. This is something needed to be addressed later on. But does the use of AI in this way eliminate the role of the teacher? No, not at all. According to Fabiano Villan (2023),

“It is crucial to understand that the advent of ChatGPT does not diminish the central role of the educator. Instead, it serves to enhance and complement teaching, aligning pedagogy with Vygotsky's principles of social and mediated learning. AI serves as a tool for technological mediation, not as a substitute for the teacher. Teachers play a critical role in guiding and interpreting the information provided by ChatGPT, tailoring it to the specific needs of the students. This promotes deeper and more meaningful learning.” (Villan et al., 2023, p. 67)

Moreover, the role that AI technologies play supports positioning students as “doers” or “explorers” of mathematics. Just like the TI-84 or the Desmos Graphing Calculator, AI can streamline the curation of knowledge and support a student towards success within a task. Graphing technologies, CAS, programming languages, and so on, all serve to help students create mathematical objects that they can directly visualize, conceptualize, and manipulate. AI is now just one more tool in the technological arsenal.

Considering the role of AI in this sense, emphasizes Vygotsky's ideas and reinforces the importance of pedagogical support in merging AI with educational practice. By adopting and integrating technology as a collaborator or “more knowledgeable other”, the teacher not only overcomes initial barriers with students but also enhances their own teaching methodology (Villan et al., 2023).

For optimal learning to occur within our students, educators must offer personalized experiences which take into account personal differences. This is what should be provided to learners to ensure that they are within the correct area of ZPD (Ferguson et al., 2022). As educators, we collect a lot of data on students - reflections, surveys, assignment scores, exam scores, standardized testing results, semester transcripts, and so on. From this data, we make well-intentioned decisions about our students' academic journeys. These decisions take the form of course selections or placements, curriculum development, intervention strategies, and so on. Collecting and analyzing data has always been an integral part of education. And with the use of AI, this decision-making can be supported, accelerated, and increasingly personalized.

With this in mind, let us now consider the realm of Personalized Adaptive Learning which first appeared in our educational theories by way of B.F. Skinner’s teaching machine (Peng et al., 2024). Personalized Adaptive Learning consists of two primary elements called Personalized Learning and Adaptive Learning. We will begin first with adaptive learning.

Adaptive learning is technology-based. That is, adaptive learning refers to learning systems that leverage AI algorithms to adapt to an individual learner’s style and progression through content. It is meant to provide real-time feedback and keep the learner positioned in the appropriate zone for mastery - where the content is neither too easy or too difficult (Lorman, n.d.). This seemingly references Vygotsky’s ZPD. And in theory, adaptive learning enables learners to progress at their own pace without any input from teachers (Lorman, n.d.). In other words, adaptive learning refers to the technologies that “...monitor student progress, using data to modify instruction…”(Peng et al., 2024, p.4).

Personalized learning, in contrast, refers to both “... instruction in which the pace of learning and the instructional approach are optimized for the needs of each learner...” and “... promoting students’ individual development, emphasizing that the learning process should adopt appropriate teaching methods, techniques, content, starting points, processes, and evaluation methods to meet the individual characteristics and development potential of students…” (Peng et al., 2024, p.4). It is the pinnacle of differentiated instruction. Each student progresses through learning material designed uniquely for them and are provided the optimal support catered specifically to their understanding, potentials, and capabilities.

Consider the following video (Why AI Won't Replace Teachers, Brown, 2023): 

Personalized learning focuses on learner agency (Spencer, 2023, 2:57). It moves beyond engagement, a focus of adaptive learning, and into empowering students. (Spencer, 2023, 3:02). With the use of AI, students can create their own path of learning. That is, they can operate as knowledge creators where AI supplements and informs this path of knowledge making. Thus, this methodology is still, at its core, human-driven (Spencer, 2023, 3:40). 

Peng et al. (2024) proposes that combining these core elements of both personalized learning and adaptive learning, a framework for personalized adaptive learning can be constructed. That is, personalized adaptive learning consists of: individual characteristics, individual performance, personal development, and adaptive adjustment. This pedagogical framework, for which AI technology use is inseparable, can be shown in the schematic below (Figure 3):

Figure 3: Personalized Adaptive Learning Framework, Peng et al. (2024)

Just recently, the National Council of Teachers of Mathematics (NCTM) published a position on AI in mathematics education. NCTM states:

“Artificial Intelligence (AI)-driven tools can respond to students’ thinking and interests in ways that previous tools could not. By drawing from large language sets, AI has the potential to adjust application-based problems to student interests and identify the sense students have made even in their incorrect answers.” (NCTM, 2024)

Moreover, NCTM believes:

“AI tools can be used to generate multiple explanations for math concepts and formulas aimed at different audiences or levels of expertise. Likewise, they can be used to generate personalized learning experiences that are tailored to a particular audience or level of expertise.” (NCTM, 2024)

Utilizing AI, students can augment intelligence, forming a human-machine partnership that leads to a hyper-personalization of their learning (Engelbrecht et al. 2023). By using AI to make educational decisions, learning can be enhanced and students can then control their own learning pathways. AI can dynamically adjust lessons, provide additional explanations, provide visual aids, or give practice problems tailored to each student’s unique learning style (Engelbrecht et al. 2023). AI has the capability to support students across age groups, academic levels, and socioeconomic backgrounds through this notion of hyper-personalized adaptive learning.

For many years, mathematics educators have contended with the differences and implementations of conveyance technologies and action technologies. Let us focus specifically on mathematical action technologies which are, generally speaking, technologies that can perform mathematical tasks and/or respond to the user’s actions in mathematically defined ways (Cullen et al., 2023).

When I reflect on AI as a mathematical action technology, I consider several modes:

1. AI as a collaborator
2. AI as a tool to personalize learning
3. AI as a tool to extend and create mathematical knowledge

The third point in particular is reminiscent of familiar technologies in mathematics education - GeoGebra or spreadsheets, for example. These mathematical action technologies allow students to engage in mathematical ideas, cycles of proof, the abstraction and encoding of mathematical processes, and so on (Cullen et al., 2023). And by doing so, students participate in the creation and manipulation of knowledge artifacts and representations. Similarly, when students engage with AI tools like ChatGPT, they also create knowledge artifacts and representations through the mode of dialogue. A student can input a prompt or question into the system and ChatGPT will output a response, or knowledge artifact. Students can then refine their prompting and extend their questions, and by doing so, iteratively curate knowledge and, depending on the uniqueness of their prompting, create knowledge - all of which can be stored, like a desktop file, with even a free account using ChatGPT.

This dynamic, where the student and AI interact collaboratively and iteratively, connects nicely to a reflexive and ergative pedagogy. That is, when students use AI, they can engage in “...cycles of interaction with ideas, and objects… “ that are “... work focused – the work of making knowledge…” (Cope et al., 2015). As Cope & Kalantzis (2024) state, a reflexive pedagogy is a varied and open-ended process of knowledge making. It is a dialogue between learners and teachers, peers, parents, experts and critical friends - or in Vygotsky’s terms, a “more knowledgeable other”. To that end, I claim that AI fits into this scheme. AI can position learners into a reflexive pedagogical paradigm - one where students are knowledge creators, activities are meaningful and realistically complex, and the learning environment gives students continuous feedback on their learning (Cope et al., 2024).

Consider the following schematic below (Figure 4):

Figure 4: Machine Mediated Help, Source: https://erichudson.substack.com/p/back-to-school-with-ai-part-4-ai

When we consider AI as a mathematics action technology, we can now formulate the human-machine augmentation of knowledge as the next order in Vygotsky’s ZPD, where AI is a collaborator (or “more knowledgeable other”) within the reflexive paradigm. That is, there are tasks that humans can do independent of technology, and then there are tasks that humans can do with the use of technology. AI, with all considerations made, can position students towards the extension of their mathematical ideas and knowledge making.

Let's consider another video from Sal Khan and his son using OpenAI (GPT-4o math tutoring demo on Khan Academy, Khan Academy, 2024): 

Throughout the duration of the video, an interaction between a student learning geometry and AI can be observed. Together, through a reflexive paradigm and dialogue, the student is held within Vygotsky's ZPD. Knowledge is co-constructed and the feedback provided by the AI is adaptive which informs how the student continues to engage. Thus, the learning progression is also personalized. 

Lastly, let us consider more broad ideas of how AI can be used in pedagogically sound ways. Specifically, I would like to focus attention on Bloom’s Taxonomy and notions of productive struggle. Proposed by Benjamin Bloom in 1956, Bloom's taxonomy refers to six tiers for which teachers can base their construction of learning targets, lessons, and assessments on which are summarized by Jessica Shabatura (2022) as:

1. Remembering: Retrieving, recognizing, and recalling relevant knowledge from long‐term memory.
2. Understanding: Constructing meaning from oral, written, and graphic messages through interpreting, exemplifying, classifying, summarizing, inferring, comparing, and explaining.
3. Applying: Carrying out or using a procedure for executing, or implementing.
4. Analyzing: Breaking material into constituent parts, determining how the parts relate to one another and to an overall structure or purpose through differentiating, organizing, and attributing.
5. Evaluating: Making judgments based on criteria and standards through checking and critiquing.
6. Creating: Putting elements together to form a coherent or functional whole; reorganizing elements into a new pattern or structure through generating, planning, or producing.

Figure 5: Bloom's Taxonomy, Source: https://tips.uark.edu/using-blooms-taxonomy/#gsc.tab=0

Bloom’s taxonomy is hierarchical (Figure 5). In order to achieve a higher level, the prerequisite knowledge and skills must be attained at the lower levels. Eric Hudson (2023) claims that Artificial Intelligence can be used in every function of this taxonomy and provide students the proper guidance to find the correct zone for learning. Hudson (2023) redefines the taxonomy using AI as:

1. Remembering: AI can assist a student in memorizing vocabulary or formulas by learning and presenting the information in a variety of formats.
2. Understanding: AI can assist a student with processing information by organizing or explaining it in different ways.
3. Applying: AI can model a potential way to solve a problem in a way that allows the student to create their own solution and compare it to AI’s.
4. Analyzing: AI can assist students with analysis by reviewing their work and asking follow-up questions.
5. Evaluating: AI can assist students by generating alternative arguments or perspectives for the student to critique.
6. Creating: AI can assist students in creation by offering feedback and elaboration on their new ideas.

As students develop skills and knowledge at every level, they are likely to experience frustration, confusion, mistakes, and so on. Learning is not always an easy and seamless process. In light of this, educators often encourage a notion of productive struggle - where students work through complex problems and overcome their confusion and/or mistakes. As noted by LearnUP Solutions (2024), this is a distinct process from just simply overcoming frustration. Instead, the instructional practice challenges students beyond their current abilities, helping them foster several skills: perseverance, confidence, self-efficacy, and stronger mathematical understanding. It is a practice that instills critical reasoning and knowledge retention. AI can be utilized at every level within Bloom's Taxonomy and increase students' abilities to engage in productive struggle.

As noted by LearnUP Solutions (2024), there are several ways in which AI can assist with this endeavor:

1. Adaptive Learning Systems - analyze students’ responses to problems, track their progress, and adjust the difficulty level of tasks in real time.
2. Intelligent Tutoring Systems - use AI to provide personalized feedback
3. AI-Powered Analytics - collect and analyze data on students’ interactions with learning materials.
4. Virtual Learning Environments and Gamification - motivate students to engage with challenging content and persist through difficulties

These systems and environments can help students sustain productive struggle through mathematics content; however, they only serve to highlight structural and/or environmental uses of AI. At this moment, it is worth referencing a note made earlier in previous sections. When students use AI as a mathematical action technology, they can also endure productive struggle. Consider the “applying” and “creating” tiers to Bloom’s taxonomy. Referencing the linear equations example made earlier, suppose a student successfully identified the slope and y-intercept of the equation \(y = 4x+2\). Suppose also that the student attempted to graph it, but wasn’t confident in their work. The student might prompt ChatGPT’s Wolfram plug-in with “Can you graph an example of slope-intercept form?” To that, ChatGPT returns the following (Figure 6):

Figure 6: Prompting ChatGPT's Wolfram Plug-in, Source: https://chatgpt.com/

The student can now compare their work on the problem to verify its correctness. Productive struggle is maintained and AI is being used in a collaborative, reflexive fashion. As Hudson (2023) notes, learning to use AI is itself a productive struggle. He claims that “Learning how to use AI is challenging… because of the critical thinking involved in analyzing responses, creating prompts, and understanding how to train AI through feedback and dialogue.”

Here is where I should discuss the issue of students using AI as a collaborator (the ideal) compared to using it just to get the answers to complete their learning tasks (the non-ideal). It is true that this is something that needs to be addressed. Moreover, the issue presents a new set of skills needed to be taught well if educators are to truly support AI usage in this manner. My response is simply that teachers should design tasks that allow AI usage to be complex enough that no singular prompt to an AI system could capture the full solution to the task. Thus, students would be forced to engage iteratively and critically. Furthermore, another requirement of using AI successfully is to be critical of the knowledge it shares with you. Students must also be taught to discern the differences between bias, falsehoods, and truth when using AI. So, there is no true abandonment of critical thought processes when we use these tools. Students of mathematics will still have to check the validity of a claim made by AI which is comparable to critiquing the logic and reasoning of their peers.

There are many critics of AI being used in mathematics education for a variety of reasons, one of which is both valid and fundamental to considering AI as a computing tool or action technology. Particularly, AI systems that exist currently, like ChatGPT, are not always correct. As mentioned by John Werner (2024), “...experts note that AI is dysfunctional at math. It tends to produce wrong answers, and can be slow to correct them.” Specifically, AI struggles to produce accurate results in complex areas of mathematics like geometry. AI requires sophisticated reasoning skills like that of humans (Werner, 2024). As Paul T. Von Hippel (2023) claims, ChatGPT cannot provide feedback and answer questions about math in tailored and natural ways. He states,

“Although ChatGPT can talk about math superficially, it doesn’t ‘understand’ math with real depth. It cannot correct mathematical misconceptions, it often introduces misconceptions of its own; and sometimes it makes inexplicable mathematical errors that a basic spreadsheet or hand calculator wouldn’t make” (Hippel, 2023).

AI applications may, as a consequence, inhibit students’ development of computational skills, critical thinking, and communication (Holquist et al. 2024). They may give inaccurate answers and inadvertently reinforce biases or stereotypes in mathematics education (Holquist et al. 2024).

While AI systems are continuously being developed and improved by entities like Wolfram Alpha, Mathway, Symbolab, etc., their current imperfections do present a lot of doubt about their utility in mathematics education. Furthermore, according to Dan Meyer, there is a large disconnect between AI and its use in education. Recently attending the 2024 National Council of Teachers in Mathematics (NCTM) conference, he claimed that roughly 50% of teachers he spoke with never used AI while the other 50% use AI for “quality-of-life improvements” (ex. Parent emails) (Meyer, 2024). He also cited a study conducted by RAND (Figure 7) in which they surveyed American Math Educators:

Figure 7: RAND Survey of American Math Educators, Source: https://danmeyer.substack.com/p/the-ai-disconnect

Figure 7 suggests that during the school year from 2023 to 2024, 82% of educators never used AI tools in mathematics teaching compared to 11% who rarely do. This result definitely spawns doubt about how effective and/or revolutionary AI tools can be in mathematics education. Furthermore, Dan Meyer also conducted an analysis on the 2023 and 2024 annual conference programs of educational entities like National Association of Secondary School Principals (NASSP), NCTM, National Council of Teachers of English (NCTE), National Science Teaching Association (NSTA), and International Society for Technology in Education (ISTE). Meyer categorized their conference program’s content based on a keyword analysis and found a large disconnect in what core content educators are doing compared to what their technology-focused counterparts are doing (Figure 8 & Figure 9).

Figure 8: Conference AI Content (2024), Source: https://danmeyer.substack.com/p/the-ai-disconnect

Figure 9: Conference AI Content (2023 - 2024), Source: https://danmeyer.substack.com/p/the-ai-disconnect

Both figures demonstrate that not much innovation has been made in using AI tools for mathematics education across the past couple years. If there were true innovation with AI technologies, it would be represented at conference programs at a much larger proportion. That is, our educational leadership of core content areas would have more to say about AI in the classroom. As noted in a literary review by Opessemowo et al. (2024) of 10 published journals, none provide a detailed analysis of how AI has been deployed in mathematics education.

So, there is a glaring issue at play here. There are not sufficient studies that I have found that provide tangible analysis as to how AI tools like Wolfram Alpha, Photomath, ChatGPT, Symbolab, and so on, are actually being employed and used to improve the learning of students in a mathematics classroom. It seems as though AI has yet to be incorporated effectively into existing curriculum, where in contrast, tools like the TI-84 graphing calculator and online platforms like Desmos are well-integrated. Thus, my conceptualization of how AI can support productive struggle in learning mathematics, at this moment, meets its end. 

Citing a poll from Education Week, Dan Meyer (2024) doubles down on the notion that AI usage in classrooms has not changed at all between the years 2023 and 2024 by considering another result shown below (Figure 10). 

Figure 10: AI Usage in the Classroom, Education Week, Source: https://danmeyer.substack.com/p/education-week-teacher-ai-use-hasnt

This suggests again that teachers are not finding meaningful ways to integrate the AI technology and pedagogical framing aforementioned in this work. At least, the effectiveness of AI in mathematics education has yet to be reported on across broad scales. Thus, it seems that we, educators, are still within a stage of theorizing, possessed by warranted skepticism. Educators, including myself, are very much on the edge of this "AI in Education" frontier; the so-called “4th Industrial Revolution (4IR)” as Opessemowo et al. (2024) phrases it.

We have now gone down a comprehensive path to pedagogically motivate educators to implement AI into mathematics education. We have made considerations for how AI can be utilized as a collaborator, tutor, an action technology, and so on. It can leverage productive struggle in students, it can be used to research mathematics, it can be used to assess students, maintain detailed analytics, develop personalized curriculum, automate grading procedures, and so on. There are countless potential uses for using AI in the classroom. And the more ideas we try, the more data we have to analyze. The time is now to begin experimenting.

This is my sixth school year as a high school educator in teaching mathematics and computer science. Frankly, within these past few years or so, I have not given much thought towards how I might implement AI into my classroom before this work. Now, more than ever, I feel compelled to implement AI in broader ways - specifically as a mathematical action technology to leverage productive struggle. 

Currently, the school district in which I teach implements a learning platform called ALEKS (Assessment and Learning in Knowledge Spaces) which my Algebra students utilize, though I have little personal experience with it. ALEKS is an artificially intelligent learning and assessment system that adapts content, practice, and tutorials according to skills they need to improve. It epitomizes adaptive learning. 

In the computer science courses I teach, students interact with a web-based Integrated Development Environment (IDE) and curriculum through the platform CodeHS. Within this platform, assignments are graded automatically and I can provide students AI-generated feedback. Some of these capabilities I have explored, but do not utilize all the time.

Beyond ALEKS and programming, I have only ever contemplated the implications of AI in both society and education. I have only personally experimented with AI tools like ChatGPT, Photomath, Wolfram Alpha, and Symbolab. It is becoming increasingly clear to me; however, that these technologies have a stake in mathematics education like every other. I believe now that ChatGPT can be categorized as a mathematics action technology just like Desmos or GeoGebra. 

In any given Algebra lesson, for example, you can expect the use of a TI-30X calculator, chromebooks, Desmos, and google slides. So, why not ChatGPT’s Wolfram Plug-in? Employing the use of ChatGPT is collaborative - it is in the vein of spoken and written language. In many ways, the mathematical objects and knowledge artifacts students might interact with and create become more accessible given the nature of the informal and formal prompting students provide to AI. Additionally, the range of topics and ideas a student might explore becomes broad and readily curated. And despite the use of machinery to achieve this, the learning process is still human-driven. Surely then, there are activities and learning tasks where AI tools can be employed and successfully result in higher order thinking and learning. It is up to educators in mathematics to determine those areas of implementation.