“Students’ Potential for Learning Contrasted Under Tutorial and Group Approaches to Instruction”, Arthur Joseph Burke1983-08 (psychology)⁠:

[a source for Bloom’s 2 sigma problem (Bloom1984)] One reason for chronically low achievement is that, under conventional instruction, the teacher’s time and attention are so divided among a group of students that the specific needs of each student can not be met. Under these conditions, students’ learning is so full of errors that their achievement is far below their potential.

Our thesis was that students’ potential for learning will be developed to very high levels when instruction is fully adapted to each student’s specific needs. To explore this idea, we contrasted students’ cognitive and affective learning under tutoring, Mastery Learning, and conventional group instruction.

~260 4^th and fifth graders participated in the 3 replications of this study. In each replication, students were randomly assigned to learn probability under one of the 3 instructional arrangements. Tutors were undergraduate education students in pre-professional training. The Mastery and the conventional conditions were managed by the students’ regular mathematics teachers.

Students’ cognitive and affective characteristics were very similar at the beginning of instruction. By the end of 3 weeks, dramatic differences had emerged. The final achievement of the average tutored student was at a level above ~95% of the control students. The final achievement of the average Mastery student was at a level above ~85% of the control students. In addition, the high levels of final achievement were retained at high levels under tutoring and Mastery Learning. These differences held for both lower and higher mental processes, as defined by the Taxonomy of Educational Objectives. What is especially noteworthy, under tutoring and Mastery Learning low aptitude students achieved at higher levels than students of high aptitude who received conventional instruction.

These findings have many implications for schooling. Perhaps the most important implication is that the student’s potential for learning can not be accurately predicted from the student’s home environment, from tests of the student’s aptitude, or even from the student’s prior achievement under conventional instruction. The student’s full potential for learning can properly be estimated only when the student is learning under the most effective instructional conditions that can be devised.