Why I’m So Against Discovery Learning

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Learning by trying to discover solution principles on your own might feel big-brain until you remember how many generations of actual geniuses it took to carry the torch from algebra to calculus. Today, working with explicit guidance, that takes just 5 years of standard schooling, and with properly individualized / optimized instruction, it can be done in a little over a year.

Based on my read of thousands of research papers, my experience working hands-on with 300+ students over the course of a decade, and my experience self-studying:

• discovery learning does not seem to be supported in the research,
• I have not seen it help any students I worked with (and in fact quite a few students I tutored needed tutoring mainly because they weren't getting enough explicit practice in the classroom),
• and it did not work nearly as well for me personally as compared to working through a structured curriculum.

The closest I’ve seen discovery learning come to working was with a student who is actually a somewhat of a math prodigy, the brightest student I’ve ever worked with – which is saying a lot, since I spent 5 years focusing on radically accelerated students studying high school and college math far above their grade level (e.g. AP Calculus BC in 8th grade). This kid is well above 99.9th percentile math talent.

Back when he was learning algebra, I was often able to dangle a problem a couple steps ahead of him and he could figure it out on the fly. But it couldn’t be too far ahead. It would have to be perfectly calibrated to the edge of his generalization ability, which was far relative to other students but not far in an absolute sense.

As a concrete example, he couldn’t come up with factoring as an approach for solving quadratics, but after learning how to multiply binomials he was able to solve quadratics by completing the square with just a few hints, and he was able to get from completing the square to the quadratic formula all on his own.

We got through all of high school math in this way. And then this less-guided approach fell apart during calculus, where I had to leverage full explicit guidance to keep him making progress.

Anyway, I’ve seen this stuff play out the same way in front of me, hands on, hundreds of times, across students of all ages, all personalities, learning all levels of math. And the mountain of research into the cognitive science of learning seems to convey the same principles.

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