Achievement, Understanding, and Transfer In a Learning Hierarchy

A set of skills is defined in the trigonometry of the right triangle and a learning hierarchy is validated. Examples of lateral and vertical transfer are identified within the hierarchy. Two instructional treatments identified as “achievement only” and “achievement with understanding” are used in two experiments with 90 eighth-grade students and 87 ninth-grade students in their ordinary mathematics classes. The achievement with understanding treatment is better for the development of lateral transfer for most students, and of vertical transfer for the more mathematically able students, whereas the differences between the treatment groups on tests of achievement and retention of taught skills are not significant. A small amount of additional instruction on vertical transfer items produces much better performance under both treatments.