2025 ASEE Annual Conference & Exposition

Mastery Learning and the School Learning Theory of J.B. Carroll

Mastery learning, developed by Bloom (1968), has shown great promise in encouraging (and forcing) students to learn, communicate expectations, and enabling students to truly learn the fundamentals of a subject. In the author's approach to Mastery learning, no partial credit is given on some or all test problems, however, students are able to repeat those problems, possibly with some penalty. Students must demonstrate mastery of basic material by the end of the course to pass. This both forces learning and provides opportunity.

In the School Learning Theory, developed by J.B. Carroll (1963), student aptitude is defined as the time required to learn, rather than the ability to learn. Learning depends on aptitude (time needed to learn), opportunity (time available to learn), ability to understand instruction, quality of instruction, and perseverance (time on task student invests in learning). This approach emphasizes hard work, persistence and flexibility, such as that provided by mastery learning. The amount of learning achieved is dependent on the relationship between the time needed to learn and the time available to learn. Thus a student who fails a test, works hard and learns the material, and successfully tests a week later has both learned, developed persistence, and developed the confidence needed to succeed and be retained in Engineering.

Carroll’s theory suggests that there are ways to provide opportunities for the large number of underprepared students we are seeing, if they invest the time and effort, to succeed in Engineering, and improve retention.

The framework this author has been using is to grade 75% of exam problems on a Mastery basis, give no partial credit for conceptual errors on those problems, allow retakes of those problems only, and require 100% of these mastery problems to be successfully solved to get a ‘C’ in the course. The first retake has no penalty. After that, a 20% penalty is assessed with each retake. The remaining 25% of test questions are more complex and determine grades of A or B. This approach has been used in non-major electrical circuits (generally sophomores) and control systems (generally seniors). A significant increase in class GPA and percentage of students passing has been seen.