MaiTH tutor
An AI math tutor to cultivate intrinsic motivation and student-directed exploratory learning in advanced mathematics.
Bair + Penny Hays
Problem Space
American students are struggling in math. Researchers measured “sharp, steep declines” in competency scores between 2019 and 2023 (Carr, 2024). The Trends in International Mathematics and Science Study (TIMSS) recorded a loss of 18 points by 4th graders and 27 points by 8th graders — the largest drop since the U.S. joined the study in 1995 (Schwartz, 2024). These losses may be partially attributable to education disruptions during the COVID-19 pandemic, but declines were seen prior to the pandemic (Schwartz, 2024), and other studies show a mixed picture and minimal recovery post-pandemic (NAEP, 2024).
This is occurring in a context wherein students broadly report disinterest in academic mathematics. 49% of middle and high school respondents to American Youth Panel surveys (a nationally representative group of ~2,000 youth ages 12–21 who regularly complete surveys via email and text message about attitudes, behaviors, school experiences, and other issues affecting their lives) reported losing interest in math about half or more of the time, and 75% reported losing interest for at least some class time (Schwartz et al., 2025). This loss of interest is consistent across genders and racial and ethnic groups (Schwartz et al., 2025).
- “The students who are the most likely to maintain interest in math are the same ones who comprehend math, feel supported in math, are confident in their ability to do well in math, enjoy math, believe in the need to learn math, and see themselves as a math person.” (Schwartz et al., 2025, p. 1)
- “The students who are the most prone to disengage in math lessons want fewer online activities and more real-world applications in their math classes.” (Schwartz et al., 2025, p. 1)
- “Thirty percent of middle and high school students said that they have never considered themselves a ‘math person.’ Those who did identify as math people developed this view during elementary school, suggesting that elementary school math teachers have a large role in cultivating positive math attitudes.” (Schwartz et al., 2025, press release)
It’s notable that students who report considering themselves a “math person” locate the genesis of this feeling in elementary school. It may be, as Schwartz et al. assert, that elementary school math teachers play a key role. But we’d like to broaden the view of potential influencing factors. We wonder if key experiences during this window - having or not having a certain positive or negative experience, whether a teacher is involved or not, whether the experience is intentional or not - may significantly impact a students’ developing self-concept. In fact, while self-concept is relevent to all learning, it’s interesting to see the enhanced importance it seems to have in math learning.
At the other end of the spectrum of students’ experiences with math is math anxiety, which is increasing worldwide (Schwartz, 2024).
Definition, symptoms, and impacts of math anxiety are detailed in the following quotes:
“Mathematics anxiety is a negative emotional reaction towards mathematics that can be described as ‘feelings of tension, apprehension, or fear that interfere with mathematical performance’ (Richardson & Suinn, 1972, p. 551). The consistency of the individual effects of mathematics anxiety across countries (Lau et al., 2022) is concordant with the idea that mathematics anxiety is a ‘global phenomenon’ (Foley et al., 2017, p. 52) and highlights the universality of the adverse effects of mathematics anxiety which can manifest in various ways including feelings of tension, apprehension or even fear. These negative emotional responses can occur in both academic and non-academic situations (Ashcraft, 2002), and have been shown to cause emotional, psychological and even physical pain (Lyons & Beilock, 2012). A further consequence of mathematics anxiety would be the development of negative attitudes and limiting beliefs about the subject which can lead to apathy, defined as a motivation and a lack of interest, and the manifestation of further stronger negative emotions towards the subject like ‘I hate mathematics and I would rather die’ (Brown et al., 2008, p. 6) than study mathematics which, in Itter and Meyers, 2017) words, ‘reflects a repeated symptom of “dis-ease”’ (p. 124).” (Smith, Fotou, & Sharpe, 2025, p. 1-2)
“Mathematics anxiety is therefore significantly associated with mathematics avoidance behaviours and a wide spectrum of self-motivation measures (Hembree, 1990). For example, self-efficacy and self-concept are two widely used self-motivation measures which are both negatively associated with mathematics anxiety (Ahmed et al., 2012; Li et al., 2021). The relationship between mathematics anxiety and mathematics ability has been studied since the 1950s, with numerous meta-analyses showing a negative association between mathematics anxiety and mathematics ability in all levels of education (e.g. Barroso et al., 2021; Hembree, 1990; Ma, 1999; Namkung et al., 2019).” (Smith, Fotou, & Sharpe, 2025, p. 1-2)
There is also evidence that students worldwide broadly report disliking academic math and failing to see its relevance (Many potential sources! We need more time to verify this and identify high quality sources). Research by educational psychologist John P. Smith III substantiates this assessment, finding that “mathematical reasoning in workplaces differs markedly from the algorithms taught in school.” (Need to find citation! This quote is used all over the place but no one cites it!).
Overall, this situation constitutes a “Wicked Problem” (Rittel & Webber, 1973).
Solutions to Wicked Problems are never truly “right” or “wrong.” The goal is to contribute to making a massive, complex, multifaceted situation better. So what contribution might we make?
If we were to make a word cloud around the concept of mathematics in education today, “performance” and “achievement” would figure prominently. Performance and achievement are valued from an academic point of view as indicators of content mastery and transferability.
But are they relevant to learning? Are there other ways to cultivate, describe, or measure engagement and learning in mathematics? Can mathematics practice have other goals, and rewards, besides academic performance and achievement?
Problem Statement
K–12 mathematics is largely taught via direct instruction, offered to students with little to no rationale, and focused on external and extrinsic motivators, metrics, and indicators (grades, scores, etc.). Students are under- or unmotivated. At the same time, fear of failure is so high that it leads to significant incidence of clinical anxiety.
Proposed Solution
Develop a one-on-one AI-assisted learner-directed learning application that supports intrinsic motivation, exploratory learning and productive failure in interaction with advanced mathematics. This will require an AI that views mathematics holistically, rather than a large set of logical procedures and algorithms.
Rationale
When new technologies emerge, the first phase of integration tends to consist of grafting old methods onto the new medium. If these old methods are as we say in our problem statement, this grafting can further bake in existing inequities and inefficiencies. It takes time, effort and creativity to leverage the affordances of the new technology to amplify and ultimately transform pedagogy to realize its benefits (see PICRAT Matrix).
In this context, we propose to explore how new, novel affordances of AI-assisted learning might transform the student experience of mathematics learning. This is an early-stage attempt to explore the novel affordances of this new technology and how they intersect with what is currently known about effective cognitive, affective and motivational design for learning. As such, we will ultimately narrow our problem space, problem definition and target learner in order to keep focus on exploring novel ways to cultivate, capture and sustain a motivating, rewarding experience of mathematics learning that responds to the frustrations of today’s students.
We’re interested in exploring an alternative form of mathematics engagement that begins to address and respond to shortcomings of current pedagogical methods in academic mathematics instruction. It’s not our intention to topple or replace current K-12 pedagogy and assessment, nor to join the overcrowded ranks of ed tech aimed at supplementing, boosting or remediating performance and achievement in K-12 mathematics. We believe that mathematics exploration can be intrinsically motivating and rewarding. Our hypothesis is that many kinds of students can benefit from self-directed “productive play” with advanced mathematics. In fact, we believe they deserve to experience and engage with these higher levels, as these levels are often gatekept from the average student in honors, AP or other other advanced courses. Thus, we plan to research, ideate, design and implement an AI-based learning application based on:
Intrinsic Motivation in Mathematics Learning
We’ll consider how our design might support the intrinsically motivating satisfactions defined by Self Determination Theory: competence, autonomy, and relatedness (Deci & Ryan, 1985, 2000, 2017). We’ll search out additional concepts and theories that explain what fuels intrinsic motivation and how it can be cultivated and maintained - in general, in a variety of specific contexts, and in mathematics learning in particular. And we’ll explore how sound, color, and other affective design features can stoke intrinsic motivation. If our learner never asks ‘why am I learning this?’ we will have done our job!
Mathematics learning without direct instruction
Most academic math learning occurs via direct instruction in a compulsory context - students are told or shown what to do and how to do it, no real reason given. Exploratory learning, by contrast, is a bottom-up learner-driven approach. Learners engage with a problem in an active, hands-on way, asking questions and experimenting to find answers and gradually build strategic problem-solving toolkits. It encourages curiosity, investigation, and discovery, and fosters critical thinking, creativity, and adaptability. Exploratory learning in mathematics is often encouraged at the earliest levels, as youngsters work with manipulables in a largely self-directed way. But soon, the focus shifts to performance, achievement and progression. We aim to reintroduce authentic exploration and discovery, and will research ways our AI agent can foster the self-reflexive skills learners need for effective exploratory learning at high levels.
The power of productive failure
Failure activates the amygdala, a tiny structure deep in the brain that plays a key role in emotion processing, memory formation and social interaction. It evolved to assess potential threats and, in response, release neurotransmitters that compel us to mitigate that threat (fight, flight, freeze) and help us learn to avoid future threats. So, failure activates brain processes that can actually enhance learning. In fact, failure and disequilibrium are broadly understood to be vital to math learning (CITE!). But important conditions must be met to ensure this activation remains positive and productive. This activated state can be informed and reinforced by multiple factors present during and experience. And if arousal gets too high it can be extremely negative, damaging and debilitating over the long term. We will unpack this phenomenon in greater depth and detail, with citations, and explore ways to use our learner’s interaction with AI to establish and maintain this “goldilocks” state of positive, productive failure.
Exposure to mathematics outside traditional K-12 scope and sequence
In schools today, learners just starting out in a given domain are encouraged to engage with, appreciate, and be inspired by work that comes from its highest levels. Students learning the basics of jazz performance are encouraged to listen deeply to the greats. First graders study the work and motivations of a master like Matisse or Basquiat, then create their own art in the master’s style. Language arts students perform Shakespeare, sometimes reset into a context relevant to their day-to-day lives. All learning involves levels - of complexity and sophistication, of experience and mastery. But it seems intrinsically understood that learners benefit from direct access to higher levels of practice (relates to Vygotsky’s model of language development?). Engaging with high-level work allows a novice to appreciate the beauty of a practice, perceive products beyond their current skill level, witness a goal state of virtuosity, be inspired to pursue greater skill and understanding, and gain insight into their own current practice. Even if they never achieve mastery level their engagement will have been meaningful, will have broadened their experience and knowledge, and will inform who they are as a person and what they bring to the world.
Mathematics would seem to be the only domain where this is not so. Essentially, students are prevented from engaging with advanced mathematics until they demonstrate sufficient mastery of “foundational” or “lower level” concepts and competencies. There are reasons for this. Mathematics learning may be unique in the way that it builds upon itself, often requiring a lot of procedural knowledge to fully comprehend complex math. There is valid concern that students can’t grasp higher-level work without solid grounding, and that overwhelm can lead to negative outcomes in academic mathematics. But we wonder if this “shut out” phenomenon blocks students’ view of the beauty and relevance of mathematics, and reinforces negative self-image that is shown to, on its own, negatively impact mathematics performance (many different citations that get at this in different ways - we need to winnow out some specific ones). We also wonder if a frame that foregrounds performance and achievement unintentionally privileges certain learners and disadvantages others in a way that starkly, perhaps incorrectly, narrows our concept of who has mathematics capacity.
Target Learners
Group 1 (primary): Advanced HS math students (age 14-18) who want to self-teach advanced mathematics concepts
Group 2: High-school aged students with the intellectual capacity to engage with advanced math who don’t have access to advanced mathematics classes:
- Have not demonstrated sufficient mastery of lower-level work to progress to advanced-level work. NOTE: These learners may actually struggle with academic mathematics and may not see themselves as target users
- Other reasons: homeschooled individuals, incarcerated individuals, etc.
Group 3 (outliers):
- Older learners interested in exploring advanced math they’ve never been exposed to
- Younger learners with particular interest and motivation to explore advanced math
The Role of AI
The role of AI in our project centers around two main questions…
What’s going in? What information is AI collecting about our learner (what learner variables)? How is it collecting them (how are variables operationalized)? And what is the AI doing with this information (what model of the learner is it creating to inform future action-steps)?
What’s coming out? How is AI interacting with our learner? How are these interactions informed by the information that has gone in? AI personalization as it exists today can unintentionally blunt affective experiences in the “activated/unpleasant” valence of Russel’s Circumplex Model (Russell, 1980) that can be productive and may, in fact, be necessary for effective learning. So it’s important to note that intentional non-action by the AI is potentially as important as action. As such, we will research and explore ways to avoid overintervention and overmodification, and preserve and support productive failure and positive dysregulation.
![Russel’s Circumplex Model of Affect (Russell, 1980)] (https://raw.githubusercontent.com/peh9341/images-xdai/refs/heads/main/Russel%20circumplex.png)
Imagined Use Case
The learner logs into the MaiTH and begins doodling on the whiteboard or maybe they have a specific question for MaiTH. MaiTH and the learner then co-design a specific learning goal (that stays flexible) throughout the session. MaiTH then selects a teaching method based on the learning goal and other variables, such as background knowledge (we can expand on the number of variables it responds to throughout the process of design). This could be DI, like when the learning goal involves some sort of very basic algorithmic process (holdable in working memory), or pure exploratory learning when the learning goal is about sparking initial interest in a broad topic area OR exploratory learning with productive failure if the learning goal does have an identifiable mathematical problem to be solved.
Footnote for Brief 1
Bair contributed the original idea, and is contributing all mathematics, pedagogical, and teaching-experience knowledge. Penny is contributing writing skills and real-world anecdotal experience as a parent of a learning disabled student. Penny & Bair are discussing everything regularly and building a detailed contextual picture of the multifaceted “Wicked Problem” problem space - in person, via Slack, and on our shared work documents. Penny wrote the initial brief. Bair is contributing feedback, insights, key revisions, and is ideating and defining our Imagined Use Case - what we will actually build.
References
Schwartz, S., (2024, December 4). ‘Sharp, Steep Declines’: U.S. Students Are Falling Behind in Math and Science. Education Week. https://www.edweek.org/leadership/sharp-steep-declines-u-s-students-are-falling-behind-in-math-and-science/2024/12
NAEP. 2024. NAEP Mathematics Assessment, aka “Nation’s Report Card”, a Congressionally Mandated National Assessment Program. Institute of Education Sciences. https://www.nationsreportcard.gov/reports/mathematics/2024/g4_8/?grade=8
Schwartz, H., Bozick, R., Diliberti, M. K., Ohls, S. (2025, June 17). Students Lose Interest in Math: Findings from the American Youth Panel. Rand Corporation. Funded by the Gates Foundation. https://www.rand.org/pubs/research_reports/RRA3988-1.html
Schwartz, S., (2024, November 25). Which Nation’s Students Are Defying the Math Anxiety Trend?. Education Week. https://www.edweek.org/teaching-learning/which-nations-students-are-defying-the-math-anxiety-trend/2024/11#:~:text=By%20Sarah%20Schwartz%20%E2%80%94%20November%2025,Canada%20who%20studies%20mathematical%20thinking.
Smith, J., Fotou, N., & Sharpe, R. (2025). Changes in mathematics anxiety and mathematics confidence. International Journal of Mathematical Education in Science and Technology, 1–19. https://doi.org/10.1080/0020739X.2025.2475928 https://www.tandfonline.com/doi/full/10.1080/0020739X.2025.2475928#d1e127
Rittel, H., & Webber, M., (1973) COMPLETE THIS CITATION of “Wicked Problem”
Kimmons, R., Draper, D., & Backman, J. (2022). PICRAT: The PICRAT Technology Integration Model. EdTechnica: The Open Encyclopedia of Educational Technology. https://doi.org/10.59668/371.5895; https://edtechbooks.org/encyclopedia/picrat
Ryan, R. M., & Deci, E. L. (2017). Self-Determination Theory: Basic Psychological Needs in Motivation, Development, and Wellness. New York: Guilford Press. SCIRP Open Access More recent and comprehensive book that provides a thorough and updated account of the theory’s concepts, research, and applications.
Russell, J. A. (1980). A circumplex model of affect. Journal of Personality and Social Psychology, 39(6), 1161–1178. https://doi.org/10.1037/h0077714