UC Irvine

Comparing different student solutions to a single instructional problem is a key recommended pedagogical tool in mathematics and for inducing conceptual change. However, these instructional comparisons can overload children’s cognitive resources, and may be more demanding for some children than others. In my dissertation, I examine the relations between individual differences in children’s cognitive resources and their thinking and learning from instructional comparisons. Individual differences in children’s resource capacities provide a useful lens for understanding the contributions of cognitive mechanisms in learning from comparisons. Manipulating the kinds of instructional representations and sequence of presentations provide further insights on how to best manage students’ limited processing resources. The dissertation has three main chapters. The first discusses a novel methodology for deriving causal relationships through stimuli in which the complexity of everyday classrooms is held constant. The second describes Experiment 1, which tested the role of visual representations when learning from comparing three solution strategies (one incorrect and two correct). In this experiment, fifth graders watched a mathematics video-lesson on ratio edited to either: a) present solutions only orally; b) present only the most recent solution visually; and c) present all solutions visually. Visual representations served as a double-edged sword, where simultaneous presentations led to durable, conceptual understanding, whereas presenting solutions sequentially as in condition b) led to the poorest learning outcomes possibly reflecting limitations in cognitive resources. This result is further examined in the third chapter, which reports on Experiment 2. This experiment replicates only condition b) of Experiment 1, where solutions strategies were presented sequentially, but with a larger sample of fifth graders who were also administered four cognitive measures. The results of Experiment 2 reflect a positive relationship between children’s learning and their cognitive control capacities. Finally, the theoretical and practice relevant implications of these results and future directions are discussed.