## Research Projects - Reasoning Resources in Math and Physics

*Creation, Coordination, and Activation of Resources for Learning Undergraduate Physics*

PIs: Wittmann, Thompson

Sponsored in part by NSF grants REC-0633951

- Project summary (hosted by ARC)
- Publications on Resources, Coordination Classes, epistemic games, and cluster analysis, and the interplay of mathematics and physics
- Theses and Dissertations: Eleanor C. Sayre
- Contact Michael C. Wittmann by email for more information

The time is ripe for better integration of theories of learning and applications to pedagogical development throughout the undergraduate science curriculum. Studying learning in physics will help researchers understand what triggers and connects elements of student reasoning when intuitions and everyday thinking interact with appropriate verbal, graphical, and mathematical formalism. Using a coordination class framework to analyze student reasoning in terms of resources used in reasoning, investigators seek a deeper understanding of resource creation, coordination, and activation. Results will affect how developers create, modify, and implement curricular materials to match student needs. Instruction in intermediate mechanics and mathematical methods are the primary research area, but a general education non-majors course in “Intuitive Quantum Physics” and introductory physics courses will also be studied.

Three research questions drive this work:

- By what processes do ideas reify into coherent resources useful across contexts and domains, specifically outside the context in which they were first learned?
- How do disparate ideas, e.g., mathematical resources in physics, coordinate to form resource networks, and how context and domain specific are these networks?
- What activations trigger individual resources or coordinated networks, and which aspects of an activation are most important in the triggering and readout process?

Research tools include individual, clinical, task-based interviews; small-group mini-interviews which are repeated with cohorts of students on a weekly basis; statistical analysis of large data sets from written survey questions; and observation of videos from classroom and out-of-class help sessions. The purpose of the data gathering and analysis process is to follow the development of students as they are introduced to, struggle with, and refine skills in mathematical, representational, and physical reasoning.

*Intellectual merit*: Researchers will extend the theoretical framework of coordination classes to include mesoscopic scales that exist between the individual resource and the large-scale, concept-like coordination class. These coordinated sets are an appropriate model for describing learning in a single class during a single semester (or two). Connections will be made between the common physics education models of learning and models of reasoning more common to mathematics education research, such as process/object and RBC (recognize, build with, and construct) models. Topics to study in resource creation include how students develop new resources as their skills in mathematics reify into quickly applied actions and processes. Topics to study in resource coordination include how students pull together mathematical and physical reasoning and how students learn to use fundamental ideas of calculus and vectors. Topics to study in resource activation include how students interpret small representational and graphical cues. Content areas of interest include mathematical reasoning, representations of motion in two dimensions, and ways of representing differential equations.

*Broader impact*: Exploring student reasoning in new content areas on new tasks will extend the field of physics education research, while descriptions of reasoning will provide a deeper foundation for understanding learning. Connections between mathematics and physics education research theoretical frameworks will impact both research fields. Graduate students working on the project will have a rich background in theoretical and experimental education research. Work will be carried out with all physics majors and with a majority of students in the introductory physics sequences. Results will help curriculum developers better match to student needs in advanced physics courses and also introductory physics courses in which mathematical and physical reasoning are necessary. Results will be included in a graduate level course on integrated approaches in physics education (research methods, results, and research-based instructional tools) which is taught to future and in-service high school teachers.