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

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

Labs for Life Scientists Physics 2A – Mechanics for Engineers A Little Bit About Me Physics 205 – Mechanics & Thermo for Life Scientists Paradigms in Physics

My Paradigms Experience  Co-taught the six “core” Paradigms: Symmetries & IdealizationsSymmetries & Idealizations Static Vector FieldsStatic Vector Fields OscillationsOscillations  Taught Classical Mechanics Capstone Spins Waves Central Forces

If only I knew… Pedagogical Content Knowledge (PCK) What are the students going to be like when they arrive? What are the students going to be like when they arrive? What should I watch out for? What should I watch out for? What do I want them to be like when they leave? What can be reasonably expected? What can be reasonably expected?

What are they like at the beginning? Some knowledge about many physics ideas Deep knowledge about some physics ideas, some knowledge about lots of physics ideas What do I want them to be like when they leave? Used to working with multiple variables Algebra skills, some calculus skills (derivatives, simple integration) Know that physics consists of laws (formulas) that are the basis for solving problems Representational fluency Proficiency with working symbolically (what’s a variable, what’s a constant, what’s a parameter, notational flexibility) Vector calculus, linear algebra, differential equations, some complex analysis skills Some appreciation of the hierarchy of physics ideas (what’s more fundamental) Representational literacy

What are they like at the beginning? Have some experience with executing short laboratory experiments How to collect and record data 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) What do I want them to be like when they leave? Have learned how to deal with scientific numbers (calculator agility) Know about and have some comfort with units Judging the reasonableness of an answer Building and handling larger cognitive chunks Sophisticated monitoring (metacognitive) skills in problem solving (dimensional analysis, considering limiting cases, reasonableness, consistency) Experience with multistep problems

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) Energy Energy Discrete & Continuous Representations Discrete & Continuous Representations Normal Modes & Complete Sets of States Normal Modes & Complete Sets of States Expectation Values & Probability Expectation Values & Probability Resonance Resonance Symmetry Symmetry Multiple Pedagogical Strategies Lecture Small white boards (individuals) Kinesthetic Activities Small Groups Maple Worksheets Computer Simulations Integrated Labs Homework

How does the pedagogy support development?  Lecture Illustrates professional thinking Illustrates professional thinking  Small White Boards Multiple Representations Multiple Representations Integrating/extending what’s already known (building larger chunks) Integrating/extending what’s already known (building larger chunks)  Small Group Coaching new ways of thinking Coaching new ways of thinking Representational fluency Representational fluency Monitoring understanding Monitoring understanding  Integrated Labs Professional discourse about theory/data How do you know if your data is good? Very strong connection between theory development and experiment  Kinesthetic Activities Representational fluency  Maple Worksheets Mathematical complexity Representational fluency

Series Expansions & Vector Spaces Symmetries & Static Vector Fields  Power Series Expansions Calculating Coefficients (Lecture, SGA) Calculating Coefficients (Lecture, SGA) Plotting Expansions (Maple) Plotting Expansions (Maple) Applications (SGA) Applications (SGA) Electrostatic Potential Due to a pair of charges Electrostatic Potential Due to a pair of charges V, due to a charged ring (spinning) V, due to a charged ring (spinning)Oscillations  Fourier Series Orthogonal Functions/Normalization (Lecture & SGA) Calculating Coefficients (Lecture, SGA) Plotting Expansions (Maple) Applications Driving an LRC circuit with a pulse (Lab) Spins & 1-D Waves  2-D Vector space model of Stern- Gerlach experiments (Lab, Lecture, SWB)  Fourier Series (Lecture)  Quantum Wavefunctions (Lecture, SGA) Central Forces  Eigenstates of a particle confined to a ring: (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…  Used CLASS to measure overall sophistication in undergraduate’s views about physics  Physics majors overall sophistication didn’t change during first three years of study

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.

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