My Teaching Philosophy

I recognize that effective teaching operates at distinct levels of sophistication, and after watching AI transform how students interact with mathematics, I'm convinced we need to fundamentally rethink what we're trying to accomplish.

Level 1 is getting students to actually understand what they're supposed to do. This sounds basic, but most instructors never reach this baseline. Students need to grasp procedures and follow algorithmic steps without getting lost. But here's the thing: when my students can pull up ChatGPT and get step-by-step solutions, pure procedural instruction becomes pointless. If I'm only teaching them to execute algorithms that machines perform faster and more accurately, I'm preparing them for a world that disappeared last year.

Level 2 is helping students see what's actually happening beneath the formulas. This is where math stops being about following rules and starts being about making sense. Students develop intuition—they can look at problems and have a gut feeling about which approach might work. AI makes this level more important and more achievable simultaneously. As machines handle calculations, human value shifts toward pattern recognition and strategic thinking—exactly what Level 2 develops. Plus, AI can serve as that infinitely patient tutor, letting students explore concepts without time pressure.

Level 3 is where I'm still figuring things out: seamlessly connecting intuition back to rigorous content. Students should move fluidly between understanding what's happening and executing technical details. AI creates both urgency and opportunity here—when students can outsource calculations, remaining human value lies in knowing which calculations to perform and why. This makes the bridge between intuition and formalism absolutely critical.

The reality is that AI makes incomplete teaching genuinely dangerous. Students who only get Level 1 become obsolete when AI performs those procedures. Students getting intuition without technical grounding can't verify ideas rigorously. Students experiencing the first two levels but never seeing how they connect treat mathematics like separate worlds rather than understanding how rigor serves insight.

My current challenge is building bridges while integrating AI thoughtfully. This means sequencing explanations so formal definitions feel like natural extensions of intuitive ideas, and showing students how to use AI as a learning amplifier rather than a shortcut—leveraging these tools to build deeper understanding rather than avoid thinking.

Because reaching Level 3 consistently isn't just a pedagogical goal anymore—it's essential preparation for a world where humans and AI collaborate on mathematical problems.