Bloom's 2 sigma problem refers to the educational phenomenon that the average student
tutored one-to-one using
mastery learning
Mastery learning is an instructional strategy and educational philosophy that emphasizes the importance of students achieving a high level of competence (e.g., 90% accuracy) in prerequisite knowledge before moving on to new material. This approac ...
techniques performed two
standard deviation
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
s better than students educated in a
classroom
A classroom, schoolroom or lecture room is a learning space in which both children and adults learn. Classrooms are found in educational institutions of all kinds, ranging from preschools to universities, and may also be found in other place ...
environment. It was originally observed by
educational psychologist
An educational psychologist is a psychologist whose differentiating functions may include diagnostic and psycho-educational assessment, psychological counseling in educational communities ( students, teachers, parents, and academic authorit ...
Benjamin Bloom
Benjamin Samuel Bloom (February 21, 1913 – September 13, 1999) was an American educational psychology, educational psychologist and Didactic method, didactician who made contributions to the classification of educational objectives and to ...
and reported in 1984 in the journal ''
Educational Researcher
''Educational Researcher'' is a peer-reviewed academic journal that covers the field of education. The editors-in-chief are Thurston Domina (University of North Carolina, Chapel Hill), Andrew McEachin ( NWEA), Dana Thompson Dorsey (University of So ...
''.
Bloom's paper analyzed the dissertation results of University of Chicago PhD students Joanne Anania and Joseph Arthur Burke. As quoted by Bloom: "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.
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 method
A teaching method is a set of principles and methods used by teachers to enable student learning. These strategies are determined partly by the subject matter to be taught, partly by the relative expertise of the learners, and partly by constrai ...
s, 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
The philosophy of education is the branch of applied philosophy that investigates the nature of education as well as its aims and problems. It also examines the concepts and presuppositions of education theories. It is an interdisciplinary fiel ...
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
In the design of experiments, hypotheses are applied to experimental units in a treatment group.
In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one tr ...
that did not.
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
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the ...
. These included:
References
Further reading
*
* {{cite thesis , last1=Burke , first1=Arthur Joseph , date=August 1983 , title=Students' potential for learning contrasted under tutorial and group approaches to instruction , id={{ProQuest, 252076952 , oclc=1194704545
External links
Bloom's 2 Sigma and Vockell's -2 SigmaThe 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring (original paper)
Educational psychology
1984 introductions