An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge

摘要

The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear. Aims. We tested the impact of conceptual instruction preceding or following mathematics problem solving to determine when conceptual instruction should or should not be delayed. We also examined the learning processes supported to inform theories of learning more broadly. Sample. We worked with 122 second- and third-grade children. Method. In a randomized experiment, children received instruction on the concept of math equivalence either before or after being asked to solve and explain challenging equivalence problems with feedback. Results. Providing conceptual instruction first resulted in greater procedural knowledge and conceptual knowledge of equation structures than delaying instruction until after problem solving. Prior conceptual instruction enhanced problem solving by increasing the quality of explanations and attempted procedures. Conclusions. Providing conceptual instruction prior to problem solving was the more effective sequencing of activities than the reverse. We compare these results with previous, contrasting findings to outline a potential framework for understanding when instruction should or should not be delayed.