Emily H. van Zee Corinne Manogue National Science Foundation DUE , DUE , DUE , Oregon State University Department of Physics Department of Science and Mathematics College of Science Compare and Contrast Wrap-Up Discussion #1 Typical Beginning of Class Sessions Students pick up small whiteboards as they enter & sit at tables in small groups Instructor - Uses props to visually represent concept or process -Welcomes student questions and comments - Asks small whiteboard questions Pedagogical Strategies Video record class sessions Discuss priorities with instructor Transcribe high priority segment Watch video of segment together Record video interpretation session Type instructor’s comments into transcript Ask questions to prompt reflection as needed Preparation Articulate reasons for selection Summarize physics context Long version: - Provide “blow-by-blow” account - Interweave instructor comments Short version: - Narrow long version to high priority topics with enough context to be comprehensible Construction Small Group Collaborations Compare and Contrast Wrap-Up Discussion #2 Issues. Looking for Patterns Resources on Wiki A wiki documents our reforms for ourselves and others through links on the National Science Digital library. Information includes instructor’s guides for individual activities, rational and tips for different strategies, links to classroom video, and detailed narratives of specific examples. Geometric Interpretation of Transforming Vectors Documenting and Interpreting Ways to Engage Students in ‘Thinking Like a Physicist’ What does it mean to engage students in ‘thinking like a physicist’? How can instructors learn how to do this? How can instructors who are attempting to do this share their successes and challenges with others? Narrative Interpretations Provide Examples of Discussions Document - What was said by students and instructor -How instructor thinks about Structuring discussions Interpreting what students say Forming questions and comments in response Small group activity: Use given matrix to transform common set of given vectors; Represent transformed vectors graphically Wrap-up Discussion: Students examine similarities and differences in what the different groups did and found Small groups work together on large whiteboards at their tables and/or whiteboards on the walls Instructor & TA move from group to group - Assist as needed - Monitor and shape progress - Become aware of successes and challenges Wrap-Up Discussions Instructor guides students in thinking together about challenging aspects of the topic they have just explored through the small group activity Main idea emerges from the wrap-up discussion rather than the activity itself Students experience what it is like to deduce a result from looking at many examples – the experience that many professional theoreticians have Students discuss the determinant and what it means geometrically Students come to realize that an eigenvector is a vector whose direction is not changed when multiplied by a vector Algebraic Interpretation of Transforming Vectors Small group activity: Solve for eigen- vectors and eigenvalues of particular matrices Wrap-up Discussion: Students examine similarities and differences in what the different groups did and found Students gain a deeper understanding of the relations between geometric and algebraic representations of eigenvectors Students experience nuances in solving set of linear algebra problems, particularly those involving degeneracy Prompting Expectations I: What do you expect to happen along the z axis?” S: “Nothing.” I: “Nothing, you expect the z axis to be unchanged” (S: (eigenvector) I: therefore you expect it to be an eigenvector, yes!”