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?
Why Reflective Teaching?
• 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?
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?
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. Why?
Amplitude of force harmonic
oscillator: Why?
Why this reorganization?
Physics embedded in math
force in opposite
direction of
displacement
damping force
opposes motion
mx +cx
= -kx+ -kxcx=+F(t)
F(t)
Net force
produces a
proportional
acceleration
forces can be
summed into an
important net force
Symbolic Forms (Sherin, 2001, SVF &
Lindine 2013, Redish & Kuo 2014 )
Changing form
changing frame
The change form from one that emphasizes forces
mx = -kx - cx + F(t)
to one emphasizing the relationship between variables
mx +cx + kx = F(t)
changes the frame --- surrounding communicative context -- of the classroom from “physics” to “math.”
Amplitude of force harmonic
oscillator: Why was it said?
Shifts emphasis from
forces (physics) to
variables (math)
“Just math”
Compound
symbolic form
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
Expand
– Cancel/ApplyContract
conservation
of momentum,
and teasing
out where they
are cancels many terms, so it's worth the math.
Expand-Cancel/ApplyContract: Why
• Physics (science) values simplicity because
simplest form can reveal new relationships
Change in thermal energy
friction-like rubbing
• Derivation conveys cultural value (“hidden
curriculum”)
• Demonstrates mechanism for achieving simplicity
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