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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. doi: 10.3102/0013189X013006004

Salient quotes from the paper:

I believe an important task of research and instruction is to seek ways of accomplishing this under more practical and realistic conditions than the one-to-one tutoring, which is too costly for most societies to bear on a large scale. This is the “2 sigma” problem. 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? (p.4-5)

If the research on the 2 sigma problem yields practiced methods (methods that the average teacher or school faculty can learn in a brief period of time and use with little more cost or time than conventional instruction), it would be an educational contribution of the greatest magnitude. (p. 5)

When we compare student learning under conventional instruction and tutoring we note that approximately 20% of the students under conventional instruction do about as well as the tutored students. (See Figure 1). That is, tutoring probably would not enable these top students to do any better than they already do under conventional instruction. In contrast, about 80% of the students do relatively poorly under conventional instruction as compared with what they might do under tutoring. We have pondered these facts and believe that this in part results from the unequal treatment of students within most classrooms… The studies find that typically teachers give students in
the top third of the class the greatest attention and students in the bottom third of the class receive the least attention and support. (p. 11)

In some of our research on the 2 sigma problem, we have viewed the task of teaching as providing for more equal treatment of students. (p. 11)

We believe that this research makes it clear that teachers in both the Nordin and Tenenbaum studies could (at least temporarily) change their teaching methods to provide more equal treatment of the students in their classes. When this more equal treatment is provided and supplemented with the ML feedback and corrective procedures, the average student approaches the level of learning found under tutoring methods of instruction. (p 13)

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