In addition to the publications listed below, this project has a number of findings to date. We find that

- cluster analysis leads to groupings of student responses that are aligned with groupings found using more traditional methods, but gives greater insight into the connections between seemingly unrelated groups than the classical analysis methods do.
- reification of ideas (specifically reified mathematical processes acting like objects when talked about as part of larger, more difficult problems) can be described within the resources framework, meaning that we have evidence of knowledge pieces combining and compiling into “primitive” knowledge pieces for students.
- discourse, gesture, and content analysis show evidence of consistent transitions, i.e., that students’ gestures, language, and content understanding shift in unison as students develop new ideas.
- student reasoning about vector physics is context-independent, such that their reasoning about vectors in mathematical situations is only marginally better than their reasoning in physics situations.

PEER REVIEWED JOURNALS

Black, K.E., and Wittmann, M.C. (2009) “Understanding the use of two integration methods on separable first order differential equations,” under review at *Physical Review Special Topics Physics Education Research*. Pre-print available online at http://arxiv.org/abs/0902.0748.

Black, K.E., and Wittmann, M.C. (2009) “Visualizing changes in student responses using consistency plots,” under review at *Physical Review Special Topics Physics Education Research*. Pre-print available online at http://arxiv.org/abs/0812.3136.

Springuel, R.P., Thompson, J.R., and Wittmann, M.C. (2009), “Reevaluating the results of cluster analysis” under review at *Physical Review Special Topics Physics Education Research*.

Springuel, R.P., Thompson, J.R., and Wittmann, M.C. (2009), “How different is ‘not the same’?” under review at *Physical Review Special Topics Physics Education Research*.

McCann, K., and Wittmann, M.C. (2009) “The role of sign in students’ modeling signs of scalar equations,” accepted for publication in *The Physics Teacher*. Expected publish date, Fall, 2009. Pre-print available online at http://arxiv.org/abs/0901.4912..

Sayre, E.C. and Wittmann, M.C. (2008) “The plasticity of intermediate mechanics students’ coordinate system choice,” *Physical Review Special Topics Physics Education Research* 4 020105. Available at http://prst-per.aps.org/abstract/PRSTPER/v4/i2/e020105.

Smith, T.I. and Wittmann, M.C. (2008) “Toward a more effective use of the Force and Motion Conceptual Evaluation,” *Physical Review Special Topics Physics Education Research* 4, 020101. Available at http://prst-per.aps.org/abstract/PRSTPER/v4/i2/e020101.

Wittmann, M.C. and Thompson, J.R. (2007) “Integrated approaches in physics education: A graduate level course in physics, pedagogy, and education research,” accepted for publication in the *American Journal of Physics*. Draft version available online at http://www.arxiv.org/abs/physics/0608240.

Springuel, R.P., Thompson, J.R., and Wittmann, M.C. (2007) “Applying clustering to statistical analysis of student reasoning about two-dimensional kinematics,” *Physical Review Special Topics Physics Education Research* 3, 020107. Available at http://prst-per.aps.org/abstract/PRSTPER/v3/i2/e020107.

Smith, T.I. and Wittmann, M.C. (2007) “Comparing three methods of teaching Newton’s Third Law,” *Physical Review Special Topics Physics Education Research* 3, 020105. Available at http://prst-per.aps.org/abstract/PRSTPER/v3/i2/e020105.

CONFERENCE PROCEEDINGS

Wittmann, M.C. and Black, K.E. (2008) “Describing the Conceptual and Procedural Resources Used in Two Epistemic Games of Integration,” Proceedings of the *2008 International Conference on the Learning Sciences*.

Black, K.E. and Wittmann, M.C. (2007) “Epistemic Games in Integration: Modeling Resource Choice,” in L. Hsu, L. McCullough, P. Heron (Eds.) AIP Conference Proceedings 951 2007 *Physics Education Research Conference Proceedings*, 53–56.

Van Deventer, J. and Wittmann, M.C. (2007) “Comparing Student Use of Mathematical and Physical Vector Representations,” in L. Hsu, L. McCullough, P. Heron (Eds.) AIP Conference Proceedings 951 2007 *Physics Education Research Conference Proceedings*, 208–211.

Sayre, E.C., Wittmann, M.C., and Donovan, J.E. (2007) “Resource Plasticity: Detailing a Common Chain of Reasoning with Damped Harmonic Motion,” in P. Heron, L. McCullough, J. Marx (Eds.) AIP Conference Proceedings 883 2006 *Physics Education Research Conference Proceedings*, 85–88.

Sayre, E.C. and Wittmann, M.C. (2007) “Intermediate mechanics students’ coordinate system choice,” *Conference on Research in Undergraduate Mathematics Education*, from http://cresmet.asu.edu/crume2007/eproc.html.

This project expects to produce open sourced cluster analysis tools for physics education research.