About Us


John Carroll

Mastery Learning

Robert Gagné

Fred Keller




This page seeks to explain why this site is as it is.

The 1960s saw great changes in social outlook.  Not only were people looking for greater freedom in their adult life, but also in how education was provided - the mood of "liberal education" was in vogue.  The publication of Taxonomy of Educational Objectives (Bloom 1956) set things in motion by considering the needs of the learner as opposed those of the teacher.

This trend was reversed in the more pragmatic 1970s.  The emphasis shifted back towards teacher controlled education and anything that smacked of liberal education was dismissed.  Many of the ideas were consigned to the educational wilderness.  The number of articles citing the ground breaking How Children Fail (Holt 1966) had plateaued by the early 1970s and then started to decline as we moved into the 1980s.

However, several educational babies may have been thrown out with the liberal education dishwater.   The Keller Plan (also known as the Personalised System of Instruction) (Keller 1968) survived in pockets, but has never become mainstream.  The Keller Plan required the curriculum to be broken in small piece which were taught and assessed in sequence.  Paper-based materials were used to teach and the student had to pass a test on each topic at 80% or above before moving on.  This encouraged to topic to be understood before moving on to the next task.

The 1960s

A Model of School Learning (1963)

John B Carroll wrote what he thought was a throw-away paper (Carroll 1963) on allowing students to progress at their own pace rather than that of the teacher.  The paper put forward the argument that there were five factors which determined whether a student acquired a new concept:-

  1. Aptitude for learning this task
  2. Ability to understand instruction
  3. Quality of instruction
  4. Time allowed for learning (opportunity)
  5. Time the learner is willing to spend in learning (perseverance)

Those teaching cannot affect the first two items on the list above.  The third item, quality of instruction, is the same for all those in a class.  Therefore the determinants of learning become the final two items, which Carroll expressed as:-

Degree of learning = f((time actually spent learning)/(time needed to learn))

This implies that students will only learn a portion of any syllabus and that this quantity of learning could be increased by allowing students to travel at their own pace.

Mastery Learning (1968)

Benjamin Bloom read the paper by Carroll took the idea further (Bloom 1968).  He argued that if ability is normally distributed then standard teaching methods would ensure that the results of assessment would also be normally distributed.  However, his research implied that most students (he claimed 95%) could understand a topic if allowed sufficient time.  He estimated that the ratio of the difference in time needed to master a topic between the most able and least able was approximately 1:6, i.e. for every hour needed by the most able, the least able would need six hours.  His studies showed that this ratio decreased as students got used to the process and suggested that the ratio might decrease to 1:3 in the longer term.

The paper also argued that student understanding (and therefore performance) could be enhanced if students had to master a task before moving on the next one on a course.  Bloom called this system mastery learning.

Personalised System of Instruction (1968)

At the same time as Bloom was working on mastery learning, Fred Keller and his colleagues at the University of Brazil devised a system of teaching based on the work of B.F. Skinner.