Control Paths and Covariation of Variables as an Expression of Cognitive Change in Problem-Solving

This research characterizes the paths and trajectories that 136 university subjects follow when solving a physical-mathematical problem of proportionality, posed through interactive software, with the aim of analyzing intra and intersubject variability regarding the type of variable control and covariation used. Five types of variable control (a: No Control, b: Simple Control of two attempts, c: Simple Control greater than two attempts, d: Control with Alternation, and e: Controlled Change) and four of covariation (f: No covariation, g: Increasing Covariation, h: Decreasing Covariation, and i: Mixed Covariation) were evidenced. The microgenetic method with qualitative and quantitative measures was used. The various paths and trajectories attest to the cognitive change in problem-solving. It is concluded that there is significant variability in the procedures used by the population, as well as significant differences regarding trajectories with consolidated control or covariation, compared to those that did not have them, also between those that presented paths with intermittence and without intermittence.