An explorative study of search of model space in problem-solving

Abstract

Building on dual-space theories, the three-space theory of problem solving suggests to add search of a model space in addition to search of experiment and hypothesis space. This study aimed at exploring the three postulated spaces, especially model space, by means of verbal protocols. Participants (n=32) were asked to think aloud while working with a computer based learning program. With this program they could learn about torques in physics using interactive graphics in which experiments with levers and forces could be conducted. Their knowledge about torques was tested before and after working with the program. Verbal protocols were analyzed with regard to the amount of search of the three spaces and regarding the quality of the participants' models for torques. The three postulated spaces could be reliably identified in the protocols. For validity, the model quality score was related to performance and predicted final knowledge beyond prior knowledge. Our results add to the validity of model space and allow us to derive more specific hypotheses from the three-space theory.

The importance of understanding: Model space moderates goal specificity effects

“…To implement variation in model quality, participants worked with two different versions of the computer simulation. Based on Kistner et al (2014), we knew that a good model of torques in the context of similar simulations is conceptualizing torque as the area of the parallelogram spanned by force and lever arm (illustrating this was the aim of the original programme). Thus, in the good-model condition this parallelogram was depicted in the simulation as a red area (printed in grey here), which adjusted when variables were manipulated (see Figure 1b).…”

“…To test our interaction hypothesis, we conducted two experiments using different tasks in which it was possible to manipulate model quality: a task on learning about torques used by Kistner, Burns, Vollmeyer, and Kortenkamp (2014), and the water tank task from Burns and Vollmeyer (2002). By using two different tasks, we can see whether our hypothesis holds in general and we can clarify what we mean by model space.…”

“…Knowledge tests. A prior knowledge test similar to the one in Kistner et al (2014) was used. This contained four items addressing factual knowledge about torques (Cronbach's α = .63).…”