1. Taking reflective teaching to the next level

2. Why Reflective Teaching? DBER reveals student misconceptions, develops curricular materials to address them adopting research-based instructional strategies (RBIS) doesn’t solve problem disparity in faculty implementations of RBIS pedagogical content knowledge is critical how do faculty develop PCK?

3. reflecting on teaching is fun encourages discussions between faculty, spreads ideas across disciplines doesn’t require additional effort (travel, time) Think of the last time you talked with a colleague about class/teaching. What did you talk about? Why Reflective Teaching?

4. Deeper reflective teaching Faculty often discuss student understanding of ideas, what they know, where they struggle – develop strong insight into common difficulties and strategies to address them Deeper questions focus on teaching practice: why do we do what we do?

5. Reflective Teaching: An Example from physics Why do physicists present derivations? – what mathematical moves are contained in derivations? – what are motivations/meanings behind thesm? – do they tell us anything new about how we do/understand physics? – do they reveal anything new about what we want students to learn?

6. Buried in here are the continuity equation and the conservation of momentum, and teasing out where they are cancels many terms, so it's worth the math. Conservation of Energy in Fluid Mechanics Why?

7. Amplitude of force harmonic oscillator: Why? Why this reorganization?

8. forces can be summed into an important net force force in opposite direction of displacement damping force opposes motion Net force produces a proportional acceleration Physics embedded in math

9. Symbolic Forms (Sherin, 2001, SVF & Lindine 2013, Redish & Kuo 2014 )

10. Changing form changing frame The change form from one that emphasizes forces to one emphasizing the relationship between variables changes the frame --- surrounding communicative context - -- of the classroom from “physics” to “math.”

11. Compound symbolic form Shifts emphasis from forces (physics) to variables (math) “Just math” Amplitude of force harmonic oscillator: Why was it said?

12. Lessons Rearranging equations changes meaning, symbolic forms (existing literature) Multiple reasons faculty manipulate equations – shift emphasis from concept to process – “Just math” --- working toward a hoped-for resolution – Changing meaning can emphasize critical concepts, deconstruct complicated ideas into smaller “chunks.” These can all occur in a single “simple” derivation

13. Disciplinary differences Derivations are common in physics. What techniques are common in other disciplines? What are the “typical” explanations for why these practices are used? Are there deeper reasons?

14. Conservation of Energy in Fluid Mechanics Buried in here are the continuity equation and the conservation of momentum, and teasing out where they are cancels many terms, so it's worth the math. Expand – Cancel/Apply- Contract

15. Expand-Cancel/Apply- Contract: Why Physics (science) values simplicity because simplest form can reveal new relationships Derivation conveys cultural value (“hidden curriculum”) Demonstrates mechanism for achieving simplicity Change in thermal energy friction-like rubbing

16. Reflective teaching It’s fun (and sometimes worthwhile) to ask deep questions about our teaching practice No question should be off-limits can be bridge to DBER

17. What have I learned? Higher-level motivation connected to “first principles” – equations “hidden” in equations New language to try out next time I teach: – motivate with “expand/apply/contract” – “add-to-zero” form for continuity equation can look for other instances of expand/apply/contract