The Power of Comparison in Learning and Instruction: Learning Outcomes Supported by Different Types of Comparisons

Comparison is a powerful learning process that has been leveraged to improve learning in a variety of domains. We identify five different types of comparisons that have been used in past research and develop a framework for describing them and the learning outcomes they support. For example, comparing multiple methods for solving the same problem, with a focus on which method is better for solving a particular problem, can improve procedural flexibility. We include a review of our own efforts to design and evaluate educational materials that leverage different types of comparisons to support mathematics learning in classrooms, including our ongoing effort to encourage use of comparison throughout the Algebra I curriculum. In the context of this classroom work, two new comparison types emerged. Overall, we illustrate how cognitive science research helped guide the design of effective educational materials and how educational practice revealed new ideas to test and incorporate into theories of learning.