Taking reflective teaching to the next level

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?

• 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?

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?

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?

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?

Amplitude of force harmonic oscillator: Why?

Why this reorganization?

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

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

Changing formchanging 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.”

Compound symbolic form

Shifts emphasis from forces (physics) to variables (math)

“Just math”

Amplitude of force harmonic oscillator: Why was it said?

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

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?

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

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

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

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