Learning beyond Accuracy: Evidence for Worked Examples as a Support for Students' Proportional Reasoning Gains

A series of studies examined the cognitive underpinnings of worked examples as a tool for introducing multiple solution strategies for the same concept, here proportional reasoning, and for supporting complex higher order thinking. Worked examples were also tested as a tool to protect against temporarily strained cognitive resources (i.e., high pressure contexts), and resultant student solutions were explored in detail to understand affordances and limits in problem solving based on worked examples. Specifically, across this dissertation latent class analysis was used to assess learning beyond problem accuracy; qualitative frequency codes provided quantitative data about emergent patterns in students' problem-solving including their selection of approach (type of proportional or non-proportional solution strategy), setup, procedures, and final solution accuracy. In Study 1, I examined students' learning of novel solution strategies when provided with instructional packets that included i) fully worked examples or ii) partially worked examples, compared to learning gains in a control condition: iii) problems only. Study 2 built on Study 1 by examining the potential benefits of incorporating worked examples during classroom instruction. Study 3 further built on Studies 1 and 2 by imposing pressure as a means to reduce students' cognitive capacity, thereby allowing us to evaluate whether visual support with worked examples could increase instances of higher order thinking and improve longer-term problem-solving outcomes. Together, findings from these experiments indicate that fully worked examples are a highly implementable, malleable tool, which provide the necessary scaffolding for students to fundamentally change their thinking and promote novel and more sophisticated problem-solving approaches with success. Further, worked examples may buffer against the detriments caused by pressure or lower availability of cognitive functioning resources.