ABSTRACT

An experiment was carried out to determine the effect of several elements of mastery learning on student achievement in an undergraduate course on curriculum development and instruction, which is a less sequential course than the type of courses used in prior studies. Learning in a less sequential course can be facilitated by previous learning, but the lack of prerequisites does not obstruct learning. Students were randomly assigned to three groups: conventional teaching methods; enhancing cognitive entry behavior plus conventional teaching methods; and feedback/corrective procedures, enhancing cognitive entry behaviors, and conventional teaching methods. The combination of feedback/corrective procedures and initial enhancement of cognitive prerequisites was significantly more effective than using only enhancement of cognitive prerequisites, which in turn was significantly more effective than using conventional methods. The results indicate that using a combination of alterable variables effectively in the teaching-learning process may solve the “two sigma problem” in less sequential subject series and at the university level.

Bloom’s (1976) model of mastery learning explains variation in school learning in terms of three alterable variables. The first is the student’s cognitive entry behaviors, that is, the prerequisite learning needed for a particular set of learning tasks. According to Bloom, this variable may explain 50% of the variation in school learning. The second variable is affective entry characteristics that influence the student’s motivation to learn the new learning tasks: 25% of variation in school learning may be explained by this variable. The third variable is quality of instruction, which involves the use of cues, participation” of students in instruction, reinforcement, and feedback/correctives. This also may explain 25% of the variation in school learning. When students’ entry characteristics and quality of instruction are favorable, ail the learning outcomes should be at a high level and there should be little variation in measures of learning outcomes.

Research has shown that the average achievement of students who learn under one-to-one tutoring or under one tutor for two or three students simultaneously is two sigmas above the average achievement of students who learn under conventional group methods (typically in a class with 30 students and with tests given periodically only to determine students marks and one sigma above the average of students who learn under mastery learning with feedback/corrective- procedures and are given formative tests ‘”or feedback and corrective work, followed by parallel formative tests to determine the extent to which die students have mastered ;he subject (Anania. 1981: Burke. 1983). In the last decade. Bloom (1994) and his colleagues have been trying to solve what they call the “two sigma problem.” That is they have been seeking more practical conditions than one-to-one tutoring co help students achieve two sigmas higher than students who receive conventional instruction.

Leyton (1983) suggested chat one approach to the “two sigma problem”‘ would be to use mastery learning during an advanced course in a sequence in addition to enhancing students initial cognitive entry prerequisites at the beginning of the course. He conducted an experimental test of this method in algebra and French at the high school level. Two classes were helped to relearn the specific prerequisites they lacked. Their achievement was compared with two classes for whom this was not done. The classes that had been retaught the initial prerequisites were approximately 0.7 sigma higher than the other two classes on the first formative test given at the end of a 2-week period of learning tasks in the advanced course. One of these enhanced classes then continued with conventional methods, as the control group, but the other class was also provided with feed-back/corrective procedures over a series of learning tasks. After a 10- v, 12-week period of instruction, this experimental group approximately 1.6 sigmas above the control group or he summative examination.. The average effect or ink enhancement of prerequisites alone was about and the average effect of mastery learning alone was sigma. It appears that the separate effects of initial enhancement and master were additive.

In a similar study (Sayan 1986) of teaching English as a second language at a private high school, the average effect of initial enhancement of prerequisites alone was about 0.73 sigma and the average effect of mastery learning one was 1.76 sigmas. The average effect of combining the two variables was 2.76 sigmas.

This solution to [he two sigma problem” is likely to be explicable to sequential courses, that is. where learning each course/task is a prerequisite for success in the next course/task in the series. When alterable variables of mastery learning and entry characteristics are used with such courses and tasks, student achievement can reach mastery level, and variation in achievement can decrease (Block. 1971; Block & Bums; 1976; Bloom, 1976: Clark. Giskey, & Beninga. 1983: Guskey & Monsaas. 1979: Ozcelik. 1974).

Although much research has been carried out on sequential subjects, there has been no study of the relevance of mastery teaming for less sequential subjects, that is. where the learning of previous content is not required but previous learning facilitates the learning of subsequent content in the series. For example, learning in one course in a less sequential series can facilitate learning in the next course but lack of learning in the first course does not obstruct learning in the later course, as it would in a sequential series. In sequential series, certain behavioral objectives cannot be achieved or learned unless the student has mastered previous learning, In the study described here, we investigated [he effects of enhanced cognitive entry behavior in combination with feedback corrective procedures on overall learning, as well as on learning at the levels of knowledge, comprehension, and application, in a less sequential subject at the university level.

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