Benjamin Bloom found that tutoring and mastery learning were incredibly powerful ways to teach and learn. In the decades since, teachers and researchers alike have asked how those techniques can be used in a group setting. In fact, I conducted some research and wrote an article about it 13 years ago (Searching for the two sigma advantage: Evaluating algebra intelligent tutors). Here, we’ll review practical implications of the quest for what he called the “2 sigma problem.”
“The tutoring process demonstrates that most of the students do have the potential to reach this high level of learning…Can researchers and teachers devise teaching-learning conditions that will enable the majority of students under group instruction to attain levels of achievement that can at present be reached only under good tutoring conditions?”
The Big Ideas
- One-to-One Tutoring: Bloom showed that an average tutored student outperformed 98 percent of peers in a standard classroom, an effect two standard deviations (“2 sigma”) above the mean.
- Mastery Learning Matters: When students had to reach 90 percent on formative checks before moving on, the average gain was a full standard deviation. Bloom labeled the cycle of test/feedback/corrective work the “feedback-corrective process.”
- Alterable vs. Static Variables: Bloom sorted influences we can change (quality of teaching, time on task, and formative assessment) away from factors we largely can’t, like socio-economic status. He urged the stacking of the changeable elements for the biggest bang for our effort .
- Synergy Beats Silver Bullets: The magic isn’t one strategy; it’s combining high-leverage practices so that 1 + 1 > 2. Mastery learning plus strong cues, active participation, and immediate feedback begins to close the tutoring gap.
Key Terms
- Standard Deviation (σ). A measure of spread; two σ means a result so big it leaves 95 percent of students behind.
- Effect Size (d). How much a strategy moves learning; Bloom flagged d = 0.4 as the “hinge point” for worthwhile change.
- Mastery Learning. Teach/quick check/relearn if under 90 percent/parallel reassessment. Think of it as academic weight-training: getting the reps in until the muscles fire smoothly.
What This Means for Everyday Teaching
- Quick Checks, Quick Fixes. After modeling how to identify central ideas (like asking sixth grade students to “determine a central idea of a text and how it is conveyed through particular details” ) give a two-item exit slip. Anyone scoring below 90 percent meets in a five-minute mini-lesson while others start an application task.
- Randomized Response. Bloom noticed teachers rely on the same hand-raisers; instead, use cold-call sticks so feedback reflects the whole class and every student has the expectation to think about every question.
- Knowledge Organizers Up Front. Instead of passing out a summary sheet only for review, hand it out before the unit to prime schemata. This is exactly what Advance Organizers were meant to do .
- Parental Pincer Move. Invite families to engage in “show-me-what-you-learned” conversations at home; Bloom’s research found this home-school double-team especially potent.
Standards Examples
- 4th Grade Reading: While tackling historical fiction, students must “describe in depth a character…drawing on specific details” . Use mastery quizzing: identify three character-trait quotes; reteach with sentence stems for any student scoring under 90 percent.
- 7th Grade Writing: During argument units, the standard asks for claims supported by “logical reasoning and relevant evidence” . Integrate peer feedback checklists that mirror the mastery criteria claim clarity, evidence relevance, counterclaim.
- 9th Grade Science: Students must “evaluate whether reasoning is valid and evidence sufficient” . Turn labs into mastery cycles: interpret data/formative quiz/immediate/corrective mini-lab for misconceptions.
Bloom’s Holy Grail still gleams on the horizon. We’re closer each time we tighten feedback loops and insist on true mastery before moving ahead.
The Challenge
This week, choose one upcoming lesson and add a single mastery-learning loop mini-assessment, immediate corrective, rapid retest. Track the results and share them with a colleague.
Bloom, B. S. (1984). The 2 sigma problem: The search for methods of group instruction as effective as one-to-one tutoring. Educational Researcher, 13(6), 4-16.
For more information on this concept, read How Learning Happens: Seminal Works in Educational Psychology and What They Mean in Practice (https://a.co/d/a0tZSMR) This post is a summary of concepts from How Learning Happens.
School Intellect 