The Importance of Prior Knowledge When Comparing Examples: Influences on Conceptual and Procedural Knowledge of Equation Solving

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing different solution methods to the same problem, comparing different problem types solved with the same solution method, or studying the examples sequentially. Unlike in past studies, many students did not begin the study with equation-solving skills, and prior knowledge of algebraic methods was an important predictor of learning. Students who did not attempt algebraic methods at pretest benefited most from studying examples sequentially or comparing problem types, rather than from comparing solution methods. Students who attempted algebraic methods at pretest learned more from comparing solution methods. Students may need sufficient prior knowledge in a domain before they benefit from comparing alternative solution methods. These findings are in line with findings on the expertise-reversal effect.