I first encountered the “2-sigma problem” through Stripe Cofounder Patrick Collison’s questions.

Is Bloom’s “Two Sigma” phenomenon real? If so, what do we do about it?

Educational psychologist Benjamin Bloom found (PDF) that one-on-one tutoring using Mastery Learning led to a two sigma(!) improvement in student performance. The results were replicated. He asks in his paper that identified the “2 Sigma Problem”: how do we achieve these results in conditions more practical (i.e., more scalable) than one-to-one tutoring?

In a related vein, this large-scale meta-analysis shows large (>0.5 Cohen’s d) effects from direct instruction using mastery learning. “Yet, despite the very large body of research supporting its effectiveness, DI has not been widely embraced or implemented.”

I’d recommend reading Bloom’s original paper from 1984:

👉 The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring. Benjamin Bloom, 1984, PDF

Slideshow and presentation on applying the 2-sigma problem to a software development training program #

I gave a brief presentation on this for the Turing School, back in 2020, making the case for some specific interventions, based on Bloom’s 1984 research.

Here’s the slideshow. I didn’t think to record a video of the actual presentation.

Resources & Sources of Inspiration for Me #

• Patrick Collison: Questions
• On Bloom’s two sigma problem: A systematic review of the effectiveness of mastery learning, tutoring, and direct instruction (Nintil)
• The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring (PDF)
• Bloom’s 2 Sigma Problem (wikipedia)
• Discussion of wikipedia entry for Bloom’s 2 Sigma PRoblem (news.ycombinator.com)