Contextualizing Learning with AI

As math educators in the IB Diploma Programme, we often face a familiar hurdle: the "Abstraction Gap." For years, functions were taught from a purely conceptual starting point - memorizing domains, ranges, and the generic "parent shapes" of graphs.

This year, I decided to flip the script. Instead of starting with the concept and searching for a context, we started with the Winter Olympics and allowed the math to emerge from the movement.

The Pedagogy: Contextual Grounding

Our approach followed a specific learning design sequence inspired by Laurillard’s Conversational Framework (as highlighted in the Jisc report on Curriculum and Learning Design). We moved through:

1. Acquisition & Inquiry: We watched explainer videos of Olympic events (Ski Jumping, Curling, Biathlon).

2. Discussion: Students created mind maps of the forces and variables at play.

3. Practice: Grounding the variables—velocity vs. time, altitude vs. temperature, heart rate vs. recovery time.

By starting here, "Domain and Range" stopped being abstract constraints and became physical boundaries. In curling, a domain restriction isn't just a math rule; it’s the moment the stone stops moving.

Analytical Thinking and "Model Validity"

We then used a series of AI generated models to investigate functions through a Winter Olympics lens. A key focus of this project was fostering critical thinking. Drawing from recent discussions on AI and information literacy (Hilles, 2025), we treated mathematical models like any other "generated" content: something to be interrogated, not just accepted.

In our function set, we didn't just ask students to solve for x. We asked them to challenge the model's validity. For example:

• The Biathlon Logarithmic Model: Mathematically, a log function decreases forever. Analytically, students realized that if a biathlete waited 60 minutes, the model would predict a heart rate that is biologically impossible.

• The Bobsleigh Rational Model: Understanding the vertical asymptote v = 2 became a lesson in physics—below a certain velocity, friction wins, and the sled stops.

Designing for Inquiry

Using a Learning Design lens (MacNeill & Beetham, 2022), this project shifted the student's role from a "passive consumer" of formulas to an "active investigator" of data. The final task—a Cubic Regression on the TI-Nspire—required students to take messy GPS coordinates from a cross-country course and find the "line of best fit."

This mimics the actual work of sports scientists and aligns with the AISL Internal Assessment (IA) requirements, providing a scaffolding bridge between classroom exercises and independent research.

Tech Integration: The GDC as a Tool for Discovery

We leveraged the TI-Nspire as a laboratory. By using the Lists & Spreadsheet app to perform regressions and the Graph app to visualize asymptotes, students could see the "math in motion."

The Takeaway for Teachers: Contextual learning allows for a Learning Design that prioritizes analytical thinking. When we ground functions in the real world, we give students the tools to not only solve equations but to question the world those equations attempt to model.

References:

• Hilles, S. (2025). ARTificial Intelligence: opportunities for art librarians to engage students' critical thinking. ARLIS.

• MacNeill, S., & Beetham, H. (2022). Approaches to curriculum and learning design across UK higher education. Jisc Report.

• Laurillard, D. (2012). Teaching as a Design Science: Building Pedagogical Patterns for Learning and Technology.