Abstract
Abstract Analogical reasoning is a fundamental aspect of human cognition: People, even young children, engage spontaneously in analogical reasoning to make sense of unfamiliar situations. However, people often fail to use analogies productively, when the analogies are generated by someone other than themselves (e.g., a teacher). In this chapter I will discuss the challenges of using analogies in mathematics instruction, using as an example the analogy “numbers are points on the line.” This analogy is the product of a long-term comparison between numbers and the Euclidean line, and underlies a common representation of numbers, namely, the number line. Drawing on empirical evidence, I will illustrate the affordances of this analogy along with the challenges that it presents for students. Finally, I will discuss the conditions under which the use of analogies can be fruitful in mathematics instruction, elaborating on the features of successful interventions, particularly on the “bridging analogies” teaching strategy.
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