Personalization and the 2 Sigma Problem


Thirty years ago this month, Benjamin Bloom posed a challenge to the learning sciences community: How could we replicate the effectiveness of one-to-one or small-group tutoring in a more cost-effective, scalable way (Bloom, “The 2 Sigma Problem”)? In Bloom’s study, students who learned a topic through tutoring, combined with regular formative assessment and corrective instruction, performed two standard deviations (2 sigma) better than students who received conventional classroom instruction. In other words, the average tutored student performed better than 98 percent of the students in the traditional classroom. What was the difference? Personalization. Personalization is defined as differentiating instruction and providing regular corrective feedback based on the needs of each student. This included personalizing both path and pace–identifying and addressing missing prerequisite knowledge, and spending more time where necessary to ensure students achieved mastery of topics before moving on.

In a more recent study, Roland Fryer at Harvard’s EdLabs evaluated the impact on student achievement of five instructional practices implemented in Houston ISD’s Apollo 20 program, including high-dosage tutoring. Secondary students who received math tutoring outperformed their peers in the treatment schools who did not receive tutoring by 0.4 sigma, or 200 percent (32).
Of course, the “problem” in the 2 Sigma Problem is that individual or small-group tutoring is “too costly for most societies to bear on a large scale.” (The Apollo 20 program is reported to cost $29 million annually for nine schools.) The challenge, then, as Bloom framed it, is this: Can researchers and teachers devise teaching-learning conditions that will enable the majority of students under group instruction to attain levels of achievement that (at present) can be reached only under good tutoring conditions?

From the Tutor to the Class

Essentially, Bloom asks, what are the key factors at play in tutoring that could be scaled into more cost-effective classroom teaching models? Bloom identified several, the most important of which was mastery learning. In mastery learning, the teacher reteaches topics that the majority of students don’t master, small groups peer-tutor one another on challenging topics, and students individually review materials they’ve missed. In short, the class adjusts its pace and path to ensure foundational topics are mastered before moving on. The results? Mastery learning classroom practices produced a 1 sigma gain in student achievement in Bloom’s studies; in other words, the average student in a mastery learning environment performed better than 84 percent of the students in a conventional instructional environment. Not satisfied with 1 sigma, Bloom’s researchers identified and tested other group instructional strategies that might reproduce at scale the key elements of personal tutoring. Researchers coached teachers to implement the following practices and measured their impacts on student achievement:

• Identify and address gaps in prerequisite knowledge before starting instruction (a foundation for mastery learning).
• Actively engage more students in the learning process (increase participation, ownership).
• Attempt to find something positive in students’ responses (positive reinforcement).
• Use regular checks for understanding to determine students’ understanding/mastery (formative assessment).
• Provide additional clarification and illustration as needed (corrective feedback).

When combined with a commitment to mastery learning (adjusting pace and path to students’ mastery), these group instructional practices produced a 1.7 sigma gain in student achievement; in other words, the average student learning through these classroom instructional strategies performed better than 96 percent of the students in a conventional instructional environment–and that’s without tutoring. What Bloom understood is that learning is a cooperative task between teacher and students, one that is most effective when an expert teacher is differentiating instruction and providing regular corrective feedback based on the needs of each student. Recognizing that one-to-one tutoring was too expensive to scale, he encouraged teachers to adopt personalization strategies in the classroom, taking advantage of the social learning resources (like small groups and peer tutoring) that are available. These strategies improve students’ positive academic self-concept, increase their interest in the subject, and spark a greater desire to learn, thus making students better partners in their own learning (Bloom 7).

Personalization for Whom?

Bloom’s perspective unwinds a recent debate on personalization that has focused primarily on the tension between teacher-directed and student-centered learning: Reflecting a teacher-centric view, Benjamin Riley claims in “Don’t Personalize Learning” that students don’t have the requisite knowledge schemas to effectively direct their own learning (path). We know from the literature on expertise that experts have well-organized knowledge of the concepts and inquiry procedures that define their domains, and they use these to process and contextualize new information. Novices don’t have these organizational knowledge schemas and so are not as fast or flexible in processing new information (Bransford 31-50). Advocates of personalization are not suggesting, however, as Riley claims, that students should be allowed simply to “pick what to study next.” Again, it’s a cooperative task: “If teaching is conceived as constructing a bridge between the subject matter and the student, learner-centered teachers keep a constant eye on both ends of the bridge” (Bransford 136). Effective teachers not only have deep knowledge of these domain-specific organizational structures, they know how to make them comprehensible to others and to scaffold students’ development of them (Shulman 1986). Riley further argues that students generally won’t push themselves to learn without external oversight (managing their own pace). Advocates of student-centered learning models believe that children are natural, self-directed problem solvers, as evidenced by their desire and ability to discern language associations and structures and develop the ability to communicate as infants and toddlers. They eagerly learn narrative structures to help process their experience of the world, and they develop concepts of space, time, and physical causality. They do this largely on their own initiative, with little incentive other than the natural desire to know, define, and master their world.

Of course, research shows that intrinsic motivation lessens as students move from elementary to middle to high school as their interest and curiosity in learning lessens. Educators must take up the challenge to keep this natural desire to learn healthy and active as they guide students increasingly into the formal structures of academic learning. They can do this by keeping learning relevant, connected to prior knowledge, and aligned with student interests and goals. “When curiosity, independence, and exploration result with experiences of mastery and meet the approval and encouragement of parents or teachers, children experience pleasure, feel competent and in control of their environment, and have stronger intrinsic motivation for the domain or activity (Harter, 1992).
Rereading Bloom’s article on personalization 30 years after its publication suggests that today’s inquiries into personalized, student-centered, and blended learning models would benefit from knowing his research into effective teaching and learning practice. Personalization is a cooperative task between teachers and students–adopting teacher-centric practices that adapt instruction to ensure mastery and student-centric practices that tap student interest, build academic self-concept and autonomy, and spark the desire to learn are both necessary–and proven to be effective.

Whether he’s familiar with the 2 sigma problem or not, Alex Hernandez in “Personalize Learning, Please” recommends this cooperative approach when he observes that schools that move to student-centered models create supports so students succeed. These include increased coaching, goal-setting, feedback on progress, tiered supports, peer tutoring, and small group instruction so that a greater percentage of students can effectively manage their learning.

Sounds like a mastery learning classroom to me.


(This post first appeared August 10, 2014 on

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