The benefit of combining teacher-direction with contrasted presentation of algebra principles

Teacher-directed and self-directed learning have been compared across various contexts. Depending on the settings and the presentation of material, mixed benefits are found; the specific circumstances under which either condition is advantageous are unclear. We combined and reanalyzed data from two experimental studies investigating the effects of contrasted versus sequential presentation of materials on learning the principles of algebraic addition and multiplication in sixth-grade classrooms. In both studies, students were presented the same structured materials that differed only in whether the principles were explained by the teacher (n = 154) or inferred by the students (n = 91). We found short- and medium-term advantages of combining teacher-direction with contrasted presentation of algebra principles. An examination of aptitude-treatment interactions shows that particularly students with lower reasoning abilities benefited from teacher-direction in the demanding contrasted condition. Based on these findings, we discuss the particular circumstances under which teacher-directed instruction reveals its advantages.