Effects of example variability and prior knowledge in how students learn to solve equations

Abstract

Researchers have consistently demonstrated that multiple examples are better than one example in facilitating learning because the comparison evoked by multiple examples supports learning and transfer. However, research outcomes are unclear regarding the effects of example variability and prior knowledge on learning from comparing multiple examples. In this experimental study, the two critical aspects of problem type and solution method were used to design comparison conditions to teach equation solving. Randomly selected groups of 263 seventh-grade students learned to solve equations by comparing different example pairs. Results showed that students who did not use a shortcut method at pretest benefited least from comparing the two critical aspects first separately and then simultaneously. Students who used a shortcut method at pretest learned equally within conditions. Students may need to separately discern each critical aspect before they benefit from comparing simultaneous variation of these aspects. Examples should be designed according to aspects that are critical for specific students.