## ANALOGICALLY COMPARING PROBLEMS

In order to teach students how to solve problems, instructors most often demonstrate how to solve a problem using procedures and equations and then ask learners to apply that method to solve a new transfer problem. Transferring learning how to solve a problem from a single example to a new problem requires that learners induce a schema for that kind of problem from that single example and then apply that schema to a new, contextually varied problem (see Chapter 15 for more detail on problem schemas and Chapter 9 for more detail on worked examples). This single-example approach to teaching problem solving usually results in students imitating the process for solving the problem while ignoring the structural characteristics of the problem. As a result, when asked what kind of problem they are solving or transferring the solution methods varied problems, student fail. They fail for three reasons:

1. over-reliance on a single form of problem representation; 2. student conceptions of problems are based on surface level

characteristics of the problem; 3. over-reliance on a single example or analogue. Over-reliance on a

single example also results in failure to understand basic concepts during instruction as well.