Active Learning in Upper-Division Physics

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1 Active Learning in Upper-Division Physics lessons from the Paradigms David Roundy Oregon State University DUE National Science Foundation DUE

2 Teaching upper-division physics well departmental culture what students learn depends on what students do math in physics courses is not like math in math courses faculty need to agree on what is taught connecting math with the real world integration as summation measurable partial derivatives 2 / 33

3 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses faculty need to agree on what is taught connecting math with the real world integration as summation measurable partial derivatives 2 / 33

4 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses intentional and planned just-in-time teaching of math faculty need to agree on what is taught connecting math with the real world integration as summation measurable partial derivatives 2 / 33

5 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses intentional and planned just-in-time teaching of math faculty need to agree on what is taught faculty need to discuss what is taught!!! connecting math with the real world integration as summation measurable partial derivatives 2 / 33

6 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses intentional and planned just-in-time teaching of math faculty need to agree on what is taught faculty need to discuss what is taught!!! connecting math with the real world integration as summation computational lab and integrated lab activities measurable partial derivatives 2 / 33

7 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses intentional and planned just-in-time teaching of math faculty need to agree on what is taught faculty need to discuss what is taught!!! connecting math with the real world integration as summation computational lab and integrated lab activities measurable partial derivatives in-class activities and experiments in thermal physics 2 / 33

8 Organization of curriculum 16 years ago, we began a major reform of our upper-division physics curriculum. 25 incoming majors (class size students) 91% of incoming majors continue to second quarter 68% of incoming majors obtain a degree in Physics Junior-year Paradigms intensive 7-hour-a-week 3-week-long courses (2 credits) forces us to talk with each other forces students to talk with each other Senior-year Capstones more conventional 3-credit courses 3 / 33

9 Paradigms in Physics Computational Lab and Electrostatics Energy and Entropy Conclusion Classroom norms Breaking boundaries Kinesthetic activities Group work Integrated labs Group presentations Small whiteboards 4 / 33

10 Passing it on monthly meetings of upper-division group regular peer teaching observation Paradigms in Physics wiki page documents what we do in each course documents why we do what we do (e.g. stand on table) shared problem sets 5 / 33

Computational lab parallel to traditional courses A computational lab for traditional courses reinforce learning in traditional courses save time by not having to introduce the physics students have

11 Computational lab parallel to traditional courses A computational lab for traditional courses reinforce learning in traditional courses save time by not having to introduce the physics students have a very busy schedule: just one credit All work is done in the lab Today all physicists need to program Struggling students make little progress outside of class These are the students who need a computational course 6 / 33

power comparable to Matlab used by professional

12 Python and matplotlib Reasoning free software, readily available to students ease of use and power comparable to Matlab used by professional scientists tutorials and help readily available on web 7 / 33

13 Teaching programming to physics students No templates needed students write their programs from scratch they google for help Pair programming students work in pairs: a driver and a navigator swap roles every 30 minutes or so show and tell when projects are done 8 / 33

14 Electrostatics The first two Paradigms cover electrostatics and magnetostatics. Learning goals shared with the Paradigms how to compute distances curvilinear coordinates plotting with slices and lines through V ( r) integration as chopping and adding (how to set up integrals) taking advantage of symmetry Learning goals specific to computing plotting writing functions and using loops 9 / 33

15 Electrostatics (student work) Day 1: 4 point charges Potential (V) Distance (m) how to compute distances how to plot 10 / 33

16 Electrostatics (student work) Day 2: 4 point charges 2.0 v(x,y,.1) Y (m) X (m) plotting with slices 11 / 33

17 Electrostatics (student work) Day 3: Square of charge 10 Simplest default with labels chopping and adding googling for help 12 / 33

18 Electrostatics (student work) Day 4: Square of charge (with varying density on left) V y Sig = f, y= Sig = f, Potential x y V visualizing in multiple dimensions Sig = 1, y= Sig = 1, Potential x 13 / 33

19 Computational conclusion all physicists do computing teach physics that is relevant to students lab-style course works great no templates needed pair programming python + matplotlib 14 / 33

20 Challenges in thermal physics no thermo in our lower-division sequence variables p, V, T and S are unfamiliar students have never seen a differential in a math course partial derivative notation is new ( ) T V p everything else is held constant partial derivative manipulations are also new cyclic chain rule Clairaut s theorem ordinary chain rule inverse of a partial derivative 15 / 33

21 Math notation vs physics notation Physics ( ) p = V S ( V p 1 ) S physical observables p = p(v, S) p = p(v, T ) V = V (p, S) V = V (p, T ) Math u x 1 x u functions ( ) u x y u(x, y) v(x, y) x(u, v) y(u, v) 1 ) ( x u v 16 / 33

22 Mathematical interlude: a mechanical analogue for thermo 7 hours of thermodynamics math on a mechanical system integrating over a path to find work path independence to get potential energy small differences or tangent slope to find partial derivatives holding everything else constant is not possible partial derivative manipulations connection with experiment total differential for energy conservation Maxwell relations Legendre transformations 17 / 33

controllable and measurable coordinates x and y I two controllable forces Fx and Fy I one

23 Paradigms in Physics Computational Lab and Electrostatics Energy and Entropy Conclusion The partial derivative machine The system Fx x y Fy I one hidden elastic system I two controllable and measurable coordinates x and y I two controllable forces Fx and Fy I one potential energy U, not directly measurable I can integrate work to find potential energy 18 / 33

24 Measuring partial derivatives ( ) x F x y vs ( ) x F x students consistently believe these are the same they are taught to hold everything else constant F y 19 / 33

Approaches for finding a derivative make a small change, measure a small change, take a ratio mistake: use a very small change and get noise mistake: use a large change and assume linear response try

25 Approaches for finding a derivative make a small change, measure a small change, take a ratio mistake: use a very small change and get noise mistake: use a large change and assume linear response try a different small change to ensure small enough measure many values, make a plot mistake: fit to a straight line find tangent line (by eye) mistake: seek analytic form to differentiate (black box helps) 20 / 33

26 A mechanical analogue for thermo: First Law energy conservation and path independence: differentials looks like thermodynamic identity: du = F x dx + F y dy students integrate work to find potential energy paths from state A to state B (like pv plots) 21 / 33

27 A mechanical analogue for thermo: First Law du = F x dx + F y dy Maxwell relation ( ( U ) ) x y y ( Fx y ) x x ( ) = U y x x = ( Fy x ) y y can verify this experimentally 22 / 33

28 A mechanical analogue for thermo Legendre transform: imagine one mass is inside the black box you cannot change one force F y you cannot measure the value y add potential energy of mass causing F y : V U F y y like enthalpy and Helmholtz free energy gives more Maxwell relations 23 / 33

29 What is this derivative? ( p V ) S 24 / 33

30 Name the experiment! give student groups specific derivatives students sketch an experiment to measure that derivative groups share their experiments with the class 25 / 33

31 Name the experiment! Adiabatic compressibility ( p V ) S = 26 / 33

32 Name the experiment! General learning goals operational definitions of thermodynamic quantities how to measure how to fix what is held constant matters canonical thought experiments thermodynamic derivatives are physically measurable 27 / 33

33 Name the experiment! Specific learning goals adiabatic processes: changing temperature without heating: the First Law: heat capacity: heating without changing temperature: ( using Maxwell relations: S ) ( ) V T, S p turning derivatives upside down: ( T ) ( ) V S, T p ) ( T V ( U S and ( V p S and ( T p ) ) ) ( ) T V and U p S ( S ) T V and ( ) S T p ( S ) ( ) V T and S p T ( ), S T p and ( ) S V V p many of the above S S 28 / 33

collected. I ice-water calorimetry I ice melting in water I rubber band tension vs.

34 Paradigms in Physics Computational Lab and Electrostatics Energy and Entropy Conclusion Measuring partial derivatives with experiment Integrated labs enable tight coupling of coursework with experiments, including teaching while data is being collected. I ice-water calorimetry I ice melting in water I rubber band tension vs. L and T Learning goals I heat, heat capacity, latent heat I work, free energy I integrating experimental data I measuring derivatives I integrating to find S I Maxwell relations 29 / 33

35 Thermal conclusion connect math with tangible reality partial derivative machine name the experiment perform actual experiments 30 / 33

36 Teaching upper-division physics well departmental culture what students learn depends on what students do lecture is not enough (for most students) math in physics courses is not like math in math courses intentional and planned just-in-time teaching of math faculty need to agree on what is taught faculty need to discuss what is taught!!! connecting math with the real world integration as summation computational lab and integrated lab activities measurable partial derivatives in-class activities and experiments in thermal physics 31 / 33

37 Acknowledgements Paradigms team Corinne Manogue Tevian Dray Mary Bridget Kustusch Henri Jansen Janet Tate David McIntyre Energy and Entropy collaborators John Thompson (U. Maine) Michael Rogers (Ithaca College) Students Eric Krebs and Jeff Schulte Grant Sherer 32 / 33

38 Resources These slides: physics.oregonstate.edu/~roundyd/education.html Paradigms in Physics wiki: Computational lab course website: G. Sherer, M. B. Kustusch, C. A. Manogue, and D. Roundy, The Partial Derivative Machine, 2013 PERC Proceedings. D. Roundy, M. B. Kustusch and C. A. Manogue, Name the experiment! Interpreting thermodynamic derivatives as thought experiments, AJP (in press). D. Roundy and M. Rogers, Exploring the thermodynamics of a rubber band, AJP (2013). D. Roundy, A. Gupta, J. F. Wagner, T. Dray, M. B. Kustusch and C. A. Manogue, From Fear to Fun in Thermodynamics, 2013 PERC Proceedings. 33 / 33

Interactive Engagement in Upper-Level Physics

Interactive Engagement in Upper-Level Physics Lessons from the Paradigms Program http://physics.oregonstate.edu/portfolioswiki Corinne Manogue & the whole Paradigms Team Support National Science Foundation