A Brief History of Mastery Learning

Mastery learning is a strategy in which students demonstrate proficiency on prerequisites before advancing. While even loose approximations of mastery learning have been shown to produce massive gains in student learning, mastery learning faces limited adoption due to clashing with traditional teaching methods and placing increased demands on educators. True mastery learning at a fully granular level requires fully individualized instruction and is only attainable through one-on-one tutoring.

This post is part of the book The Math Academy Way (Working Draft, Jan 2024). Suggested citation: Skycak, J., advised by Roberts, J. (2024). A Brief History of Mastery Learning. In The Math Academy Way (Working Draft, Jan 2024). https://justinmath.com/a-brief-history-of-mastery-learning/

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Mastery learning, proposed by famed psychologist Benjamin Bloom in 1968, is a learning technique in which students must demonstrate proficiency on prerequisite topics before moving on to more advanced topics.

Mastery learning is closely related to Vygotsky’s Zone of Proximal Development, which refers to the range of tasks that a student is able to perform while supported, but cannot do on their own. Students maximize their learning when they are completing tasks within this range.

True mastery learning at a fully granular level requires fully individualized instruction. Unfortunately, in the absence of proper technology, it is infeasible for a single teacher, who can only teach one topic at a time, to manually support true mastery learning across a class full of students who all have different learning profiles. As researchers have discovered, knowledge profiles vary immensely even across students in the same grade (Pedersen, et al., 2023):

“our results suggest that nearly 38% and 49% of students in grade four and eight classrooms may either struggle to understand ‘grade-level’ content or have already mastered the content, respectively.”

There are methods by which a single teacher can loosely approximate mastery learning, such as Bloom’s Learning For Mastery (LFM) strategy and Keller’s Personalized System of Instruction (PSI). As Kulik, Kulik, & Bangert-Drowns (1990) summarize:

“In both LFM and PSI courses, material to be learned is divided into short units, and students take formative tests on each unit of material (Bloom, 1968; Keller, 1968)… Lessons in LFM courses are teacher presented, and students move through these courses at a uniform, teacher-controlled pace. Lessons in PSI courses are presented largely through written materials, and students move through these lessons at their own rates.”

However, as Bloom (1984) discovered when characterizing the two-sigma problem, a single teacher practicing mastery learning with 30 students could only produce a one-sigma effect size as compared to the two-sigma effect size of individual tutoring. And while numerous studies reproduced the finding that even loose approximations of mastery learning (managed manually by a single teacher) produce substantial learning gains, most studies were unable to reproduce gains as strong as one sigma (the average effect size was about 0.5 standard deviations) (Kulik, Kulik, & Bangert-Drowns, 1990):

“The data show that mastery learning programs have positive effects on student achievement. On the average, such programs raise final examination scores by about 0.5 standard deviations, or from the 50th to the 70th percentile, in colleges, high schools, and the upper grades of elementary schools. Although PSI and LFM strategies differ on several points and the two teaching methods have been studied in distinct ways, studies of PSI and LFM report similar results. PSI raised examination scores by an average of 0.48 standard deviations; LFM raised examination scores by an average of 0.59 standard deviations.”

Unfortunately, despite producing well-documented learning gains in classrooms, even loose approximations of mastery learning were not widely adopted as they faced opposition for deviating from traditional convention and requiring more effort from teachers and administrators (Sherman, 1992). (It’s true that a minority of teachers now attempt some degree of differentiated instruction, but this is not the same as true mastery learning, which holds all students to the same standard and is completely individualized.)

As lamented by John Gilmour Sherman (1992), who was a co-creator, researcher, and practitioner of Keller’s Personalized System of Instruction (PSI):

*“Some PSI courses have been prohibited in spite of their success. I know of several colleagues who were given ‘cease and desist’ orders. Some are names prominent in the literature, their courses effective, according to objective data.

I experienced this also. Avoiding a frontal attack, the chairman of the Psychology Department at Georgetown declared by fiat that something on the order of 50% of class time must be devoted to lecturing. By reducing the possibility of self-pacing to zero, this effectively eliminated PSI courses.

He issued this order on the grounds that in the context of lecturing ‘it is the dash of intellects in the classroom that informs the student.’ No data were presented on this point! The spectacle of purporting to defend scholarship while deciding the merits of instructional methods by assertion is silly.

The troubling aspect of all these cases was that data played no part in the decisions. It is disturbing when one has to wonder whether research on the education process makes any difference.”*

As Buskist, Cush, & DeGrandpre (1991) elaborate, mastery learning methods like PSI were shot down because they threatened the traditional educational establishment:

*“The first and most important task of any institution is self-preservation. Once in place, its primary goal must be to hold its ground or, if possible, advance. If this goal is not met, then its demise is eminent. PSI poses certain implications that threaten the preservation of the educational establishment and its guardians (department heads, deans, and academic vice-presidents). According to Keller,

‘Suppose that a system such as PSI were to be given official approval for adoption throughout the educational scale from top to bottom… With every student given individual treatment, when would formal education start?… What would happen to the classroom hour, the college quarter, the semester, or the academic year?… Who would win the scholarships and prizes? Who would make Phi Beta Kappa? Who would be the class valedictorian?… What changes would be made in the payment of tuition when the period of course attendance varied? How would a course of study be defined?’

In other words, the major impediment to educational reform is the educational system itself. That is perhaps why all major efforts at educational reform in this century have been directed at renovating curricula and not at changing how teachers teach (see, e.g., Skinner, 1984; McGovern, 1990).

Revamping curricula requires no revamping of the educational establishment. The curriculum changes, but that is all. Courses are still taught by lecture within a term’s time. Grade distributions still approximate the normal curve and students enroll in upper division courses without first mastering more fundamental material. Students still take about four years, give or take a term, to finish what higher education demands of them.

The Keller Plan runs contrary to this strategy. It is a bold attempt to change how we teach, despite what we teach. In an entirely PSI-based college, students might finish in two years, maybe sooner, and learn a good deal more. Imagine what would happen if the entire educational system were PSI-based: huge numbers of people, most still in the throes of puberty, might be graduating from college-an unsettling thought for many educators. Indeed, PSI represents a threat to the educational system and its guardians.

PSI simply does not fit well into our modern educational system. The longstanding tradition of teaching by lecture has accumulated inertia that has proven difficult to dislodge. In the interests of self-preservation, the educational establishment has backed reforms favoring what teachers teach instead of how teachers teach.”*

References

Bloom, B. S. (1968). Learning for Mastery. Instruction and Curriculum. Regional Education Laboratory for the Carolinas and Virginia, Topical Papers and Reprints, Number 1. Evaluation comment, 1 (2), n2.

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.

Buskist, W., Cush, D., & DeGrandpre, R. J. (1991). The life and times of PSI. Journal of Behavioral Education, 1, 215-234.

Kulik, C. L. C., Kulik, J. A., & Bangert-Drowns, R. L. (1990). Effectiveness of mastery learning programs: A meta-analysis. Review of educational research, 60 (2), 265-299.

Pedersen, B., Makel, M. C., Rambo-Hernandez, K. E., Peters, S. J., & Plucker, J. (2023). Most mathematics classrooms contain wide-ranging achievement levels. Gifted Child Quarterly, 67 (3), 220-234.

Sherman, J. G. (1992). Reflections on PSI: Good news and bad. Journal of Applied Behavior Analysis, 25 (1), 59.

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