Bloom's 2 Sigma Problem
Encyclopedia
Bloom's 2 sigma problem refers to an educational phenomenon observed by educational psychologist
Benjamin Bloom
and initially reported in 1984 in the journal "Educational Researcher". Bloom found that the average student tutored one-to-one using mastery learning
techniques performed two standard deviation
s better than students who learn via conventional instructional methods--that is, "the average tutored student was above 98% of the students in the control class" . Additionally, the variation of the students' achievement changed: "about 90% of the tutored students ... attained the level of summative achievement reached by only the highest 20%" of the control class. Bloom's graduate students J. Anania and A. J. Burke conducted studies of this 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":
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:
Educational psychologist
An educational psychologist is a psychologist with a Master’s degree in Educational psychology An educational psychologist (many countries use this term to signify those who provide services to students, their teachers, and families while other countries use this term to signify academic training...
Benjamin Bloom
Benjamin Bloom
Benjamin Samuel Bloom was an American educational psychologist who made contributions to the classification of educational objectives and to the theory of mastery-learning...
and initially reported in 1984 in the journal "Educational Researcher". Bloom found that the average student tutored one-to-one using mastery learning
Mastery learning
In Mastery learning, "the students are helped to master each learning unit before proceeding to a more advanced learning task" in contrast to "conventional instruction"....
techniques performed two standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
s better than students who learn via conventional instructional methods--that is, "the average tutored student was above 98% of the students in the control class" . Additionally, the variation of the students' achievement changed: "about 90% of the tutored students ... attained the level of summative achievement reached by only the highest 20%" of the control class. Bloom's graduate students J. Anania and A. J. Burke conducted studies of this effect at different grade levels and in different schools, observing students with "great differences in cognitive achievement, attitudes, and academic self-concept" .
Objects of Change Process
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 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
Effect size
In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population, or a sample-based estimate of that quantity...
. These included:
| Object of change process | Alterable variable | Effect size !! Percentile equivalent | |
|---|---|---|---|
| Teacher | Tutorial instruction | 2.00 | 98 |
| Teacher | Reinforcement | 1.2 | |
| Learner | Feedback-corrective (Mastery Learning) | 1.00 | 84 |
| Teacher | Cues and explanations | 1.00 | |
| Teacher, Learner | Student classroom participation | 1.00 | |
| Learner | Student time on task | 1.00 | |
| Learner | Improved reading/study skills | 1.00 | |
| Home environment / peer group | Cooperative learning | 0.80 | 79 |
| Teacher | Homework (graded) | 0.80 | |
| Teacher | Classroom morale | 0.60 | 73 |
| Learner | Initial cognitive prerequisites | 0.60 | |
| Home environment / peer group | Home environment intervention | 0.50 | 69 |
Implications
Considering the significant outcomes of these studies on student performance, educational researchers can make a number of implications and conjectures for follow-up studies. Among them:- Labeling students as low achievers is less relevant, since altering one or two variables can have significant positive effects on the average learner.
- Technology may simulate tutoring affects without the high cost of providing a live tutor for each student.
- Social aspects present in one-to-one tutoring may imply a larger role for consideration of sociality in (or the social nature of) learning.