Comparison of Two Teaching Techniques in Elementary School Mathematics. Final Report.

Three studies attempted to assess the relative effects of two methods of instruction: (1) teaching by a carefully structured sequence of questions (intermediate guidance) and (2) teaching by stating each concept with illustrations and then having the students practice the behavior embodied in these concepts (maximal guidance). One of the studies used fourth grade subjects and a programed presentation of addition and multiplication of integers; the second used sixth grade subjects and a programed presentation of modulus seven arithmetic; the third used eighth grade subjects and a programed presentation of selected topics from vector arithmetic. Within each of three ability subgroups, the subjects were randomly assigned to one of the two treatments. The results of the studies indicated that (1) the high ability subgroup had mean scores significantly greater than those for the middle ability subgroups which in turn had mean scores significantly higher than those of the low ability subgroups, and (2) the significant differences pertaining to treatment effects favored the maximal guidance treatment. It was concluded, therefore, that when mathematics instruction is provided by means of a linear program, a relatively high level of guidance should be provided. (RP)