Syllabus Lesson 16 of 141 · Rules of the duel
Rules of the duel

The compare step

Why it matters Struggling with a problem before being taught is not wasted time, but only if you then compare your attempt with better ones. This course is built on that.

A large review of 53 studies found that trying a problem before instruction beats being taught first, with a moderate effect, and a stronger one when the attempt is followed by comparing solutions (Sinha and Kapur 2021). Researchers call it productive failure.

How to read the compare panel

When you pass a problem, a panel opens under it with the sealed AI answers and an expert's route. Spend two minutes on it. Ask three questions:

  • Which fact in the problem did the winning route use, and the sealed ones ignore?
  • Did my route find that fact, or did I pass another way? Is mine better or worse, and for whom?
  • What is the principle, in my own words?

Recap Attempt, then compare, then name the principle. Skipping the compare step throws away most of the learning.

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