Learning a mathematical concept from comparing examples: the importance of variation and prior knowledge

Abstract

In experiment 1, novice fourth-grade students (N=92) who compared multiple examples that separately varied each critical aspect and then simultaneously varied all critical aspects developed better conceptual knowledge about the altitude of a triangle than students who compared multiple examples that did not separately vary each critical aspect but simultaneously varied all critical aspects. In experiment 2, this pattern was the same for fourth-grade students (N=90) but not for sixth-grade students (N=94) who had greater prior knowledge about the concept. Aspects that are critical for learning should be varied first separately and then simultaneously, and students with different levels of prior knowledge may perceive different aspects as critical for their learning and thus benefit differently from the identical instruction.