This chapter establishes a fundamental methodological distinction between first-order and second-order approaches to studying creative problem solving. Second-order procedures, which dominate cognitive psychology, deliberately isolate mental processes from material engagement by presenting problems as static displays and prohibiting interaction with physical objects. This methodological choice reflects ontological commitments that locate creativity within individual minds, enabling only cognitive explanations while obscuring the material work of problem solving. First-order procedures, by contrast, allow and encourage participants to manipulate problem elements and construct solution prototypes, making visible the iterative dialog between problem solvers and the objects they create. Using matchstick arithmetic problems as illustrations, the chapter demonstrates how restructuring occurs through physical transformation of solution models or prototypes rather than exclusively through mental operations. This distinction reveals that methodological choices fundamentally shape what kinds of explanations become possible, with profound implications for understanding where and how creative ideas emerge.