Transcript workshops:talks:invitedtalkwiki

Paradigms in Physics:
Facilitating Cognitive Development in
Upper Division Courses
Elizabeth Gire
Oregon State University
This material is based upon work supported by the National Science
Foundation under DUE Grant No. 0618877.
Included in this talk:
 A bit about who I am
 My Paradigms Experience
 How do Paradigms address
issues of cognitive and
professional development?
 Final Thoughts
A Little Bit About Me
Labs for Life
Scientists
Physics 2A –
Mechanics for
Engineers
Physics 205 – Mechanics &
Thermo for Life Scientists
Paradigms in Physics
My Paradigms Experience
 Co-taught the six “core” Paradigms:
• Symmetries & Idealizations
• Spins
• Static Vector Fields
• Waves
• Oscillations
• Central Forces
 Taught Classical Mechanics Capstone
If only I knew…
Pedagogical Content
Knowledge (PCK)
 What are the students going to
be like when they arrive?
 What should I watch out for?
What do I want them to be
like when they leave?
 What can be reasonably
expected?
What are they like at
the beginning?
What do I want them to
be like when they leave?
Some knowledge about many
physics ideas
Deep knowledge about some
physics ideas, some knowledge
about lots of physics ideas
Representational literacy
Representational fluency
Used to working with multiple
variables
Proficiency with working
symbolically (what’s a variable,
what’s a constant, what’s a
parameter, notational flexibility)
Algebra skills, some calculus
skills (derivatives, simple
integration)
Vector calculus, linear algebra,
differential equations, some
complex analysis skills
Know that physics consists of
laws (formulas) that are the
basis for solving problems
Some appreciation of the
hierarchy of physics ideas
(what’s more fundamental)
What are they like at
the beginning?
Have some experience with
executing short laboratory
experiments
How to collect and record data
Experience with multistep
problems
Have learned how to deal with
scientific numbers (calculator
agility)
Know about and have some
comfort with units
Judging the reasonableness of an
answer
What do I want them to
be like when they leave?
Laboratory skills – how to get
good data (how do you know it’s
good?), deciding how to handle
different types of data, data
presentation, how to discuss data,
designing an experiment)
Building and handling larger
cognitive chunks
Sophisticated monitoring
(metacognitive) skills in problem
solving (dimensional analysis,
considering limiting cases,
reasonableness, consistency)
Continually refining
monitoring skills…
 How do I know when I really understand
something?
 How can I evaluate whether or not
something is “true physics”?
 Generating questions for furthering
understanding
Paradigms - Essence
Themes throughout the core
Paradigms (1997)
Multiple Pedagogical
Strategies
 Energy
 Lecture
 Discrete & Continuous
Representations
 Small white boards
(individuals)
 Normal Modes & Complete
Sets of States
 Kinesthetic Activities
 Expectation Values &
Probability
 Maple Worksheets
 Small Groups
 Resonance
 Computer Simulations
 Symmetry
 Integrated Labs
 Homework
How does the pedagogy
support development?
 Lecture
 Illustrates professional thinking
 Small White Boards
 Integrated Labs
 Professional discourse about
theory/data
 Multiple Representations
 How do you know if your data is
good?
 Integrating/extending what’s already
known (building larger chunks)
 Very strong connection between
theory development and experiment
 Small Group
 Coaching new ways of thinking
 Representational fluency
 Monitoring understanding
 Kinesthetic Activities
 Representational fluency
 Maple Worksheets
 Mathematical complexity
 Representational fluency
Series Expansions & Vector Spaces
Symmetries & Static Vector Fields
 Power Series Expansions
Oscillations
 Fourier Series
 Calculating Coefficients (Lecture,
SGA)
 Orthogonal Functions/Normalization
(Lecture & SGA)
 Plotting Expansions (Maple)
 Calculating Coefficients (Lecture,
SGA)
 Applications (SGA)
 Electrostatic Potential Due to a pair of
charges
 V, E B A due to a charged ring
(spinning)
Spins & 1-D Waves
 2-D Vector space model of SternGerlach experiments (Lab, Lecture,
SWB)
 Fourier Series (Lecture)
 Quantum Wavefunctions (Lecture,
SGA)
 Plotting Expansions (Maple)
 Applications
 Driving an LRC circuit with a pulse
(Lab)
Central Forces
 Eigenstates of a particle confined to a
ring: eim
(Lecture, Maple, SGA)
 Eigenstates of a particle confined to
spherical surface: spherical
harmonics, associated Legendre
functions (Lecture, Maple)
 Eigenstates of the hydrogen atom:
Laguerre Polynomials (Lecture,
Maple)
Professional Expectations
 Deciding what the relevant physics is
 Examining assumptions
 Building understanding from incomplete
knowledge base
 Evaluating others’ statements
Some of my thesis results…
Physics majors overall
sophistication didn’t
change during first three
years of study
100
90
Average % Favorable
 Used CLASS to
measure overall
sophistication in
undergraduate’s views
about physics
80
70
60
50
40
30
20
10
0
Eng.
Year 1
Year 2
Year 3
Measuring sophistication?
Conclusions
 Multiple pedagogical approaches foster
sophisticated ways of thinking about physics.
 Classroom expectations aligned with
professional norms aid in building
sophistication.
 For student buy-in, these goals/lessons need
to be made explicit.
A little advertising…
 Paradigms materials can be found:
www.physics.oregonstate.edu/portfolioswiki