Procedural resources and resource graphs: extending the resources framework to model epistemic actions in mathematical problem solving¶

Theory · All theories
Evidence · 1 claim (1 for) · 1 study (1 qualitative), q2 · 0 of 1 report an effect size · 1 claim rests on one study

Description¶

Within the Knowledge-in-Pieces resources framework, a resource is "an idea or a tool that one uses in problem solving" with no inherent correctness. The authors extend resource graphs, previously used for conceptual and epistemological resources, to include procedural resources representing epistemic actions such as "Find Value", "Choose Limits", and "Extract Boundary Condition". These procedural resources require certain conceptual resources to be used appropriately, and resource graphs visualize the pathways students take through epistemic games.

Design Implications¶

Context¶

Requirements¶

• Procedural resources are inferred from transcript data since researchers cannot observe student thinking directly; identification of small-scale epistemic games ideally requires several observations of the same student.

Constraints¶

• The article notes a complete identification of a small-scale epistemic game must involve several observations of the same student, which is often impractical, so games are speculated about from single observations; absence of links in a resource graph indicates only that resources were not observed as connected in that context.

Target Learners¶

• intermediate mechanics (second-year physics) undergraduates

Target Learning Objectives¶

• applying mathematical reasoning (separation of variables, integration, boundary conditions) to physics problems

Claims¶

• Students Choose Unphysical Limits Ignoring Functional Relationship Across Equal Sign [+M]

Related Theories¶

• Two facets of the 'Making Meaning of Mathematics' epistemic game: Finding a Family of Functions and Fitting the Physical Situation
• Epistemic Games

Examples¶

• Represent two correct mathematical procedures in terms of shared resources to clarify student thinking and address failures to connect ideas

Key Sources¶

• Black, K.E. and Wittmann, M.C. (2009). Understanding the use of two integration methods on separable first order differential equations. https://perlnet.umaine.edu/imt/