Benjamin Bloom is well known for the cognitive taxonomy of educational objectives (1956) and for the idea of mastery learning (1968). It is mastery learning that this blog will be about, for somewhat to my surprise mastery learning is kind of a model of fair schooling. Benjamin Bloom wrote a book (1976) on the role of differences between children and their achievements, more particularly about instructional design that will enable all students to reach the same high goals. And yes, that is an important aspect of fair schooling. It so happens that Bloom’s preface describes the issues very well. I will quote a large part of it.
- When I first entered the field of educational research and measurement, the prevailing construct was:
1. There are good learners and there are poor learners
This was considered to be a relatively permanent attribute of the individual. It was also the prevailing view that individuals possessed it in different amounts and that a quantitative index of it could be made by the use of an appropriate intelligence, aptitude, or achievement test. Furthermore, it was believed that good learners could learn the more complex and abstract ideas, while poor learners could learn only the simplest and most concrete ideas. School systems throughout the world have been organized on the basis of this construct and selection systems, and even the curriculum has been built on the basis of it.
During the early 1960s, some of us became interested in the Carroll Model of School Learning pdf, which was built on the construct:
2. There are faster learners and there are slower learners
While we were not entirely clear whether or not rate of learning was a permanent trait of individuals, we dedicated ourselves to finding ways by which the slower learners could be given the extra time and help they needed to attain some criterion of achievement. In this research, in both educational laboratories as well as classrooms in different nations, it has become evident that a large proportion of slower learners may learn as well as faster learners. When the slower learners do succeed in attaining the same criterion of achievement as the faster learners, they appear to be able to learn equally complex and abstract ideas, they can apply these ideas to new problems, and they can retain the ideas equally well—in spite of the fact that they learned with more time and help than was given to others. Furthermore, their interests and attitudes toward the school subjects in which they attain the achievement criterion are as positive as those those of the faster learners.
During the past decade, my students and I have done research which has led us to the view that:
3. Most students become very similar with regard to learning ability, rate of learning, and motivation for further learning—when provided with favorable learning conditions
This research questions the first two constructs, especially about the permanence of good-poor learning ability or fast-slow learning characteristics. However, the research does demonstrate that when students are provided with unfavorable learning conditions, they become even more dissimilar with regard to learning ability, rate of learning, and motivation for further learning. It is this research which underlies the theory of school learning developed in this book. It is this research which we believe has profound consequences for the prevailing views about human nature, human characteristics, and school learning. [p. ix-x]
At Bloom 1. The prevailing idea, of contemporary educationalists as well as those of the past centuries, is that education has to deal with the differing yet immutable capabilities of students/pupils by adapting the instruction to those differences. In that sense education traditionally has always differentiated instruction according to perceived differences in capabilities that are considered as once and for all given. In consequence, education will enlarge already existing differences between students. On a societal scale the implication is that education will reproduce class differences (Pierre Bourdieu, 1977).
At Bloom 2. Having read that section it might not have occurred to you that John Carroll’s model was what triggered Bloom to develop this idea of mastery learning. The crucial aspect of Carroll’s model is that it uses the concept of time on task to define aptitude. Carroll:
- Aptitude is the name given to the variable or variables that determine the amount of time a student needs to learn a given task, unit of instruction, or curriculum to an acceptable criterion of mastery under optimal conditions of instruction and student motivation. High aptitude is indicated when a student needs a relatively small amount of time to learn; low aptitude is indicated when a student needs much more than average time to learn. Opportunity to learn is defined as the amount of time allowed for learning, for example by a school schedule or program. Frequently, opportunity to learn is less than that required in view of the student’s aptitude. [Carroll, 1989, p. 26]
That last sentence is a crucial observation. Its meaning depends on the interpretation of what an aptitude is: a more or less stable personal characteristic of the student, or aptness for the tasks at hand. After 25 years Carroll sticks to the stable personal characteristic. Bloom struggled with that model, and came to another view, as expressed in his third bullet above.
At Bloom 3. Bloom’s view might be read as a characteristic of fair schooling, in sharp contrast to conventional schooling that tends to enlarge differences. Let me repeat it:
- 3. Most students become very similar with regard to learning ability, rate of learning, and motivation for further learning—when provided with favorable learning conditions
The point might be this: the general aptitude of psychology (e.g. Carroll) does not cover what happens when students develop expertise or talent (Bloom p. 209-211). The question then becomes: is education meant to develop general aptitudes, or specific ones that we call expertise or talents? The answer to that question has large consequences for the design of instruction, as Bloom says. Expertise is an important subject that I will attend to in future blogs, for an introduction see Ericsson (2018) pdf. General aptitude is just another term for what generally is called intelligence, another subject that will take up many future blogs.
From the summary of the first chapter.
- The central thesis of this book is that variations in learning and the level of learning of students are determined by the students’ learning history and the quality of instruction they receive [my emphasis, b.w.]. Appropriate modifications related to the history of the learners and the quality of instruction can sharply reduce the variation of students and greatly increase their level of learning and their effectiveness in learning in terms of time and effort expended. Where conditions for learning in the home and school approach some ideal, we believe hat individual differences in learning should approach a vanishing point.
( . . . )
However, the main import of the entire book is that human nature is not the barrier to educational and cultural development that philosophers, politicians, social scientists, and educators have frequently alleged. The characteristics f the students and of the instruction dealt with in this book are claimed to be alterable, and if this is so, changes in the school environment can relatively quickly (in a single decade) make great changes in the learning of students. ( . . . )
Societies in the past have relied largely on prediction and selection of talent as the means for securing a small group of well-educated persons. Modern societies stress the development of a very large number of well-educated persons and attempt to produce this by legal and social pressures which require individuals to attend school for a minimum of 10 to 12 years.
A society which places such great value on education and schooling that it requires the individual to attend school for long periods of time must find the means to make education attractive and meaningful to the individual learner. Modern societies no longer can content themselves with the selection of talent; they must find the means for developing talent. [p. 16-17]
In the last sentence Bloom proposes to disregard individual differences that will initially exist, and to go for quality instruction for all of the pupils, regardless of their initial capabilities. It is absolutely possible to do so in grade 1, except for those pupils that will be better off in special education. A minor problem will be that some pupils already know some basics of reading, writing and counting, while others don’t. Essentially, cognitive school stuff is new for all pupils; teaching it without making learning dependent on (differences in) capabilities we tend to call intelligence should level the learning field for all pupils, and should itself result in a level learning field the next day (week, year) regarding newly acquired knowledge.
Sounds mysterious? Let me explain it differently. A simple model for differences in achievement is that they are a function of (differences in) capabilities (including prior knowledge), aspiration level, and time on task (a prominent item in Carroll’s model). A short paper on that heuristic model: Tromp and Wilbrink 1977 here.
The constructs in the diamond figure: top: exogenous variables like capability and prior knowledge; left: aspiration level; bottom: time on task; right: achievement. The idea of Bloom’s mastery learning then is: (1) initially capabilities may outweigh prior knowledge; (2) very soon prior knowledge will be all important; (3) mastery learning will secure prior knowledge to be the same for all pupils; (4) therefore teaching and learning in following periods (days, weeks) will be smooth for all pupils.
Is this day dreaming educational ideology, or is it possible to implement it? A kind of existence proof was published by Bloom in 1984 (a and b, here and here). Bloom reports on experiments comparing conventional teaching mastery teaching, and tutoring. The tutoring part is a kind of benchmark for what pupils in the best of circumstances can achieve. And that is a lot: their mean achievement is two standard deviations better than that of the pupils in the conventional condition. The famous ‘2 sigma’ experiment. Bloom claims that mastery teaching (direct instruction coupled with mastery criteria) approaches the high results of individual tutoring. I will not dwell on the details of these studies now, nor on the question of their replicability. For now it suffices that the 1984 studies show mastery learning probably to be possible in principle.
Benjamin S. Bloom (1964). Stability and change in human characteristics. New York: Wiley. lccc 64-17133
- My annotation: A theory of fair schooling is in dire need of a general theory of assessment in education. The latter theory does not yet exist, which is a bloody shame on the educational research community. Such a theory will of necessity revolve around personal differences: e.g., what they might be, how they are perceived, how education handles them or should handle them. Bloom’s book might be regarded as a camel nose: is such a theory possible at all? Yes, it definitely is. The problem being that such a general theory will be strongly inter-disciplinary. In one way or another it will have to be integrated with the kind of social systems theory developed by James Coleman (1989): education is a complex game between different stakeholders.
- Benjamin S. Bloom (1966). Stability and Change in Human Characteristics: Implications for School Reorganization. Educational Administration Quarterly, 2, 35-49. abstract
- Avshalom Caspi, Brent W. Roberts & Rebecca L. Shiner (2005). Personality development: Stability and change. Annual Review of Psychology, 56, 453-484. researchnet
- R. Chris Fraley & Brent W. Roberts (2005). Patterns of Continuity: A Dynamic Model for Conceptualizing the Stability of Individual Differences in Psychological Constructs Across the Life Course. Psychological Review, 112, 60-74. adademia.edu
Benjamin S. Bloom (1976). Human characteristics and school learning. McGraw-Hill.#mastery
- Dr. Bloom contends that much of individual differences in school learning may be regarded as man-made and accidental rather than fixed in the individual at the time of conception. tweeted
- The main thesis of this book is that individual differences in learning is an observable phenomenon which can be predicted, explained, and altered in a great variety of ways. In contrast, individual differences in learners is a more esoteric notion. It frequently obscures our efforts to deal directly with educational problems in that it searches for explanations in the person of the learner rather than in the interaction between individuals and the educational and social environments in which they have been placed. [p. 8]
Benjamin S. Bloom (May 1984a). The search for methods of group instruction as effective as one-to-one tutoring. Educational Leadership, 4-17. pdf #2sigma
Benjamin S. Bloom (June 1984b). The 2 Sigma Problem: The Search for Methods of Group Instruction as Effective as One-to-One Tutoring. Educational Researcher, 13 #6, 4-16. pdf
Pierre Bourdieu (1977). Cultural reproduction and social reproduction pp 487-510 (pdf scan) in Jerome Karabel and A. H. Halsey (Eds.) (1977). Power and ideology in education. New York: Oxford University Press. isbn 0195021398 info pdf scan [alternative: Pierre Bourdieu, excerpt from ‘Cultural reproduction and social reproduction’ from Richard Brown (Ed.): Knowledge, education, and cultural change. pdf]
John B. Carroll (1989). The Carroll Model: A 25-Year Retrospective and Prospective View. Educational Researcher, 18, 26-31. pdf
- The following admonition by Carroll is not exactly (exactly not) what Bloom is proposing in his mastery approach. Carroll: The model’s emphasis on aptitude as a determinant of time needed for learning suggests that increased efforts be placed on predicting student and instruction to those potentialities and designing instruction appropriate to those potentialities, if ideals of equal opportunity to learn are to be achieved within a diversity of educational objectives. [p. 26]
- What, then, is Carroll’s take on Bloom’s mastery approach? Carroll believes in once and for all given differences in capabilities that education should honor by differentiating instruction. Remark how Carroll uses some straw man arguments here. Carrol: How can appeal to the model of school learning be made to improve education? Part of my answer relies on a fundamental tenet of my philosophy of education, that we should seek mainly to achieve equality of opportunity for all students, not necessarily equality of attainment. In this respect, the model of school learning differs from Bloom’s mastery learning concept, which seems to be focused on achieving equality of attainment. In view of the model’s emphasis on the role of individual differences in aptitudes and in students’ ability to understand instruction, I doubt that true equality of attainment can ever be realized, even if this were desirable (a point that is at least debatable). Emphasizing equality of opportunity means not only providing appropriate opportunities to learn (appropriate, not necessarily equal for all students), but also pushing all students’ potentialities as far as possible toward their upper limits. Assessing students’ potentialities (which differ markedly) implies that every available means, including carefully devised psychological and educational tests, for work-sample learning tests, and many other ways of acquiring information about students, should be used to estimate, at least provisionally, what each student’s potentialities may be, and their nature. Given those potentialities and with a view to the realities of time available, educational programs should be devised and selected to permit students to travel as far as possible toward realizing their capabilities for learning. There should also be continual reassessment of potentialities, with corresponding adjustments in educational programs. [p. 30]
K. Anders Ericsson (2018). An Introduction to the Second Edition of The Cambridge Handbook of Expertise and Expert Performance: Its Development, Organization, and Content. In K. Anders Ericsson, Robert R. Hoffman, Aaron Kozbelt, A. Mark Williams (Eds.) (2018). The Cambridge Handbook of Expertise and Expert Performance, 3–20. doi:10.1017/9781316480748.001 pdf sci-hub
Thomas R. Guskey (2010). Lessons of Mastery Learning. Interventions That Work, 68 #2, 52-57. pdf
- Bloom believed that nearly all students, when provided with the more favorable learning conditions of mastery learning, could truly master academic content (Bloom, 1976; Guskey, 1997a). A large body of research has borne him out: When compared with students in traditionally taught classes, students in well-implemented mastery learning classes consistently reach higher levels of achievement and develop greater confidence in their ability to learn and in themselves as learners (Anderson, 1994; Guskey & Pigott, 1988; Kulik, Kulik, & Bangert-Drowns, 1990).
Kenneth R. Koedinger, Paulo F. Carvalho, Ran Liu, and Elizabeth A. McLaughlin (2023). An astonishing regularity in student learning rate. PNAS https://www.pnas.org/doi/abs/10.1073/pnas.2221311120
Dick Tromp & Ben Wilbrink (1977). Het meten van studietijd. [Measuring time on task] Congresboek OnderwijsResearchDagen. webpage
next blog might be one on Francis Galton, man of genius from the 19th century.
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