The 2-Sigma Problem

Introduction featured image

Bloom's 2-Sigma Problem

Richard Bloom was an American educational psychologist who published a landmark paper in 1984 called The 2 Sigma Problem. Bloom compared three different methods of instruction: the traditional classroom approach; teaching students individually with 1:1 tutors; and group instruction with a mastery-based learning approach. And what he discovered influenced educational research for decades!

Bloom found that under mastery learning, students on average achieve 1 standard deviation (1 sigma or 1σ) higher on examinations than their peers who are taught conventionally. On a percentile basis, this means that 84% of students achieve higher scores when taught under mastery learning!

When mastery learning is combined with tutoring, however, the results are truly astonishing. Bloom observed that tutoring and mastery learning combined produces achievement levels 2 standard deviations (2σ) higher. This means that the average student tutored with mastery learning techniques achieves higher test scores than 98% of students who learn in conventional classes.

Figure 1 shows the impacts of mastery learning (1σ) and tutoring plus mastery learning (2σ) compared to conventional class teaching (mean of a normal distribution).

Adapted from “The 2-Sigma Problem: The Search for Methods of Group Instruction As Effective as One-to-One Tutoring,” by B. Bloom, 1984, Educational Researcher, Volume 13 (6), pg 5.

How effective is tutoring?

Bloom asserted that tutoring with a mastery learning approach has a 2σ impact on student achievement. But what effect does tutoring have by itself?

Research has shown that tutoring is powerful.

For instance, in a meta-analysis evaluating the effect of 1:1 tutoring in 52 different studies, a research team from Dartmouth College and the University of Michigan showed that the test scores of tutored students improved in 45 out of those studies (Cohen, Kulik, and Kulik, 1982). Tutoring led to an average 0.4 standard deviation improvement in test scores. Other studies by Elbaum et al. (2000), Nickow, Oreopoulos, and Quan (2020), and Slavin et al. (2011) found similar things - 1:1 tutoring significantly improves student test scores, with average improvements of around 0.4 standard deviations.

Though a 0.4 standard deviation improvement is a sizable improvement, you may be wondering why it’s not as big as the 1 standard deviation predicted by Bloom’s 2-sigma paper. We should note that these meta-analyses include some studies where parents or volunteers served as tutors, rather than teachers or teaching assistants (paraprofessionals). Tutoring by parents or volunteers is known to produce smaller impacts (Nickow, Oreopoulos, and Quan, (2020). Bloom’s research (relying on Anania and Burke’s studies) used 1:1 tutoring with education majors, however, so the typically larger tutoring impacts from for paraprofessionals and 1:1 tutoring are more relevant comparisons.

Secondly, the vast majority of studies on tutoring after since Bloom’s paper have focused on tutoring as a supplemental activity. On the other hand, Anania (1981) and Burke (1983)’s research was based on the complete replacement of group instruction with tutoring- just like at!