When Students Claim AI‑Level Models: Uncovering the Real Gap in Math Modeling Skills

Yesterday I attended a high‑school math modeling competition’s oral defense and noticed a marked improvement over last year: more teams could clearly explain their papers and demonstrate genuine effort.

Nevertheless, several observations raised concerns, prompting this commentary and inviting readers to discuss in the comments.

In a previous contest, a middle‑school team claimed they had built a large predictive model comparable to ChatGPT. Their insistence, despite merely using an API, was puzzling and somewhat insulting.

The judges repeatedly asked, “Did you create this yourself?” and received confident affirmations, yet the work clearly could not have been produced by a few young students alone.

Why do students so firmly defend results that aren’t truly theirs?

Possible reasons include a lack of understanding of how complex models are built, fear of appearing unimpressive, or simply employing rhetorical tactics.

This creates a strong sense of disconnection and inauthenticity , where the students’ abilities seem mismatched with their presented outcomes.

We can envision three pathways to a seemingly good result: (1) curiosity‑driven learning over time, (2) innate talent nurtured early, or (3) external assistance or imposed expert ideas. The first is ideal but time‑consuming; the second is rare; the third, though efficient, is undesirable yet increasingly common.

Some experts suggest incorporating competition results into college entrance assessments—a stance I once fully supported but now view as premature.

Returning to the cultivation of math‑modeling literacy, we must ask what competencies we aim to develop and how to foster them.

I propose two dimensions: model complexity and cognitive depth .

Model complexity refers to the difficulty of the chosen model, ranging from simple linear regression to advanced machine learning. Students must balance problem requirements with their skill level; overly complex models exceed comprehension, while overly simple ones may fail to solve the problem.

Cognitive depth denotes the depth of understanding of the model’s theory and principles, as well as the problem itself. Students need to grasp not only how to use a model but also why it works, enabling effective adjustments and improvements.

Typically, a student starts with low cognitive depth and low model complexity, then gradually deepens understanding before tackling more complex models.

Using high‑complexity models with low cognitive depth is problematic. Students may lack sufficient understanding to explain model workings, leading to unreliable or non‑reproducible results.

Moreover, this reliance on tools hampers independent thinking and problem‑solving skills, fostering a dependence on ready‑made code rather than foundational knowledge.

Finally, superficial success can mask the lack of genuine skill growth, limiting long‑term development and leaving students ill‑prepared for more challenging tasks.

Educators and parents should provide guidance appropriate to a student’s current cognitive depth and model complexity, gradually advancing them toward higher levels.

Mathematical modeling holds a prominent place in modern curricula, yet its current practices demand thoughtful reflection and solutions, lest they become mere “busywork.”

Please share your thoughts and suggestions in the comments so we can collectively improve how we nurture students’ modeling abilities.