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The Way We Learn · Episode 7 of 8 · 21 min

The Two-Sigma Problem

In 1984 Benjamin Bloom reported that one-to-one tutoring beat the classroom by two standard deviations, and called it a problem because no one could afford it. The episode separates legend from evidence, from mastery learning and computer tutors to the more sober real-world gain of about a third of a standard deviation.

Who's who

  • Benjamin S. Bloom+1 more episodeUniversity of Chicago educational psychologist; author of The 2 Sigma Problem
  • Fred S. KellerBehavioral psychologist who devised the Personalized System of Instruction
  • John B. CarrollPsychologist whose 1963 model recast aptitude as time needed to learn
  • Kurt VanLehnLearning scientist whose 2011 review found human tutoring near 0.79 sigma
  • Philip OreopoulosCo-author of the 2020 tutoring meta-analysis finding about 0.37 sigma
  • Andre NickowCo-author of the 2020 tutoring meta-analysis
  • John R. AndersonCarnegie Mellon scientist whose ACT-R theory powered Cognitive Tutors
  • Piotr WoźniakPolish researcher who formalized spaced-repetition algorithms

Timeline

  1. 1963Carroll publishes A Model of School Learning, recasting aptitude as time-on-task
  2. 1968Bloom's Learning for Mastery and Keller's Personalized System of Instruction appear
  3. 1984Bloom publishes The 2 Sigma Problem in Educational Researcher
  4. 1987Woźniak's SM-2 spaced-repetition algorithm dates from this year
  5. 2011VanLehn's review finds human tutoring about 0.79 sigma and intelligent tutoring systems about 0.76
  6. 2020Meta-analysis of randomized tutoring trials pools to about 0.37 sigma

Still debated

The real size of the tutoring effect, and how much of Bloom's gain came from the tutor versus bundled feedback and retesting, are argued. No rigorous study has replicated two sigma, and whether tutoring survives scaling and funding cuts remains open.

tutoringmastery learningbenjamin bloomeducation researchintelligent tutoring systemsspaced repetition
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