My Education Research Obsession: Bloom's 2-Sigma Problem

Benjamin Bloom is best known for his taxonomy, but I think his most interesting work pivoted around the 2-Sigma Problem.

The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring

I have read this paper at least once a year for the past 12 years.

Bloom found that students who received 1-1 tutoring performed 2 standard deviations (2 sigmas) better than the control group, but he realized that 1-1 tutoring is financially infeasible, so he looked for a combination of scalable strategies that could help teachers with normal class sizes get to the same level of student learning as 1-on-1 tutoring.

Here are a couple things that bug me about how and why people cite or revisit Bloom's paper:

A: Mastery Learning isn't totally free form!

Many people use Bloom's paper to justify ideas for mastery learning that are quite different from what Bloom used. For some, "mastery learning" and "competency-based learning" are synonymous. The idea is that students should move at their own pace based on their ability to demonstrate mastery of the content. Bloom's idea of mastery learning was different. Here is a diagram from Thomas R. Guskey's Closing Achievement Gaps: Revisiting Benjamin S. Bloom’s “Learning for Mastery.”

Bloom's model assumed that all students were studying the same unit (maybe 2-weeks long?) at the same time. The different pathways through the unit were informed by Formative Assessment A. Students who didn't initially master the content would get more instruction on the basic content, while those who did master the unit's content after one attempt at instruction which would get enrichment. Notice that all students would move on to the next unit at the same time.

B: It's not just about Mastery Learning!

Mastery learning showed 1 sigma effect, but was not the whole story. The greatest impact (1.6 sigma) came when he coupled mastery learning with "enhanced prerequisites." Essentially, they figured out what specific skill gaps students had relative to the content they were about to learn and remediated those gaps before having students dive into mastery learning with the on-level content. It's important to note how targeted the enhanced prerequisite instruction was. This wasn't about remediating all of pre-algebra before taking algebra. It was about bridging specific foundational skill gaps that were critical to the content to come.

When I go on about student readiness or using formative assessment to inform instruction while keeping an entire class on the same unit of instruction, I'm basing my ideas on Bloom. I'll save my rants about formative assessment death spirals and catching kids up for another day.