Bloom's 2 sigma problem
Educational phenomenon of greatly improved performance by tutored learners
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Through Tutoring and Standard deviation
The phenomenon's associated problem, as described by Bloom, was to "find methods of group instruction as effective as one-to-one tutoring". The phenomenon has also been used to illustrate that factors outside of a teachers' control influences student education outcomes, motivating research in alternative teaching methods, in some cases reporting larger standard deviation improvements than those predicted by the phenomenon. The phenomenon has also motivated developments in human-computer interaction for education, including cognitive tutors and learning management systems.
Mastery learning
Mastery learning is an educational philosophy first proposed by Bloom in 1968 based on the premise that students must achieve a level of mastery (e.g., 90% on a knowledge test) in prerequisite knowledge before moving forward to learn subsequent information on a topic. Mastery is determined with regular tests, and students who do not yet achieve mastery on the test are given additional educational support before another test. This cycle continues until the learner accomplishes mastery, and they may then move on to the next stage. Failure for a student to achieve mastery is viewed, differently from conventional educational testing, as due to instruction rather than lack of student ability. Another key element of mastery learning is that it requires attention to individual students as opposed to assessing group performance. There is good evidence to suggest the effectiveness of mastery learning for improving student educational outcomes.
Two of the three groups in the original study by Bloom conducted mastery learning, with one control group that did not.
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Correlations
Though Bloom concluded that one-to-one tutoring is "too costly for most societies to bear on a large scale", Bloom conjectured that a combination of two or three altered variables may result in a similar performance improvement. Bloom thus challenged researchers and teachers to "find methods of group instruction as effective as one-to-one tutoring". Bloom's graduate students Joanne Anania and Arthur J. Burke conducted studies of the effect at different grade levels and in different schools, observing students with "great differences in cognitive achievement, attitudes, and academic self-concept".
Bloom classified alterable variables that may have, in combination, a 2 sigma effect as the following "objects of change process":
- Learner
- Instructional material
- Home environment or peer group
- Teacher
Bloom and his graduate students considered and tested various combinations of these variables, focusing only on those variables that individually had a 0.5 or higher effect size. These included:

