active learning in upper-division...

Active Learning in Upper-Division Physicslessons from the Paradigms

David RoundyOregon State University

DUE-0837829National Science Foundation

DUE-1141330

Paradigms in Physics Computational Lab and Electrostatics Energy and Entropy Conclusion

Teaching upper-division physics well

departmental culture

I what students learn depends on what students do

→ lecture is not enough (for most students)

I math in physics courses is not like math in math courses

→ intentional and planned just-in-time teaching of math

I faculty need to agree on what is taught

→ faculty need to discuss what is taught!!!

connecting math with the real world

I integration as summation

→ computational lab and integrated lab activities

I measurable partial derivatives

→ in-class activities and experiments in thermal physics

2 / 33


Organization of curriculum

I 16 years ago, we began a major reform of our upper-divisionphysics curriculum.

I ∼25 incoming majors (class size 33-40 students)

I 91% of incoming majors continue to second quarter

I 68% of incoming majors obtain a degree in Physics

Junior-year Paradigms

I intensive 7-hour-a-week 3-week-long courses (2 credits)

I forces us to talk with each other

I forces students to talk with each other

Senior-year Capstones

I more conventional 3-credit courses

3 / 33


Classroom norms

Breaking boundaries

Kinesthetic activities

Group work

Integrated labs

Group presentations

Small whiteboards

4 / 33


Passing it onI monthly meetings of upper-division group

I regular peer teaching observationI Paradigms in Physics wiki page

I documents what we do in each courseI documents why we do what we do (e.g. stand on table)I shared problem sets

5 / 33


Computational lab parallel to “traditional” courses

A computational lab for traditional courses

I reinforce learning in traditional courses

I save time by not having to introduce the physics

I students have a very busy schedule: just one credit

All work is done in the lab

I Today all physicists need to program

I Struggling students make little progress outside of class

I These are the students who need a computational course6 / 33


Python and matplotlib

Reasoning

I free software, readily available to students

I ease of use and power comparable to Matlab

I used by professional scientists

I tutorials and help readily available on web

7 / 33


Teaching programming to physics students

No templates needed

I students write their programs from scratch

I they google for help

Pair programming

I students work in pairs: a driver and a navigator

I swap roles every 30 minutes or so

I “show and tell” when projects are done

8 / 33


Electrostatics

The first two Paradigms cover electrostatics and magnetostatics.

Learning goals shared with the Paradigms

I how to compute distances

I curvilinear coordinates

I plotting with slices and lines through V (~r)

I integration as chopping and adding (how to set up integrals)

I taking advantage of symmetry

Learning goals specific to computing

I plotting

I writing functions and using loops

9 / 33


Electrostatics (student work)Day 1: 4 point charges

4 3 2 1 0 1 2 3 4Distance (m)

0.0

0.5

1.0

1.5

2.0

2.5

3.0Po

tent

ial (

V)

I how to compute distances I how to plot10 / 33


Electrostatics (student work)Day 2: 4 point charges

3 2 1 0 1 2 3X (m)

2.0

1.5

1.0

0.5

0.0

0.5

1.0

1.5

2.0

Y (m

)

15000000000.000 1500

0000

000.

000

v(X,Y,.1)

I plotting with slices11 / 33


Electrostatics (student work)Day 3: Square of charge

10 5 0 5 1010

5

0

5

10

4000.000 4000.000

4000.000 4000.000

6000.000

8000.000

10000.00012000.000

Simplest default with labels

I chopping and adding I googling for help12 / 33


Electrostatics (student work)Day 4: Square of charge (with varying density on left)

0 1 2 3 4 5z

0.0

0.5

1.0

1.5

2.0

2.5V

Sig = f, Potential @x=0, y=0

0 1 2 3 4 5z

01234567

V

Sig = 1, Potential @x=0, y=0

6 4 2 0 2 4 6x

6

4

2

0

2

4

6

y

Sig = f, Potential @z=.01

321

012345

6 4 2 0 2 4 6x

6

4

2

0

2

4

6

y

Sig = 1, Potential @z=.01

01234567

I visualizing in multiple dimensions13 / 33


Computational conclusion

I all physicists do computing

I teach physics that is relevant to students

I lab-style course works great

I no templates needed

I pair programming

I python + matplotlib

14 / 33


Challenges in thermal physics

I no thermo in our lower-division sequence

I variables p, V , T and S are unfamiliar

I students have never seen a differential in a math course

I partial derivative notation is new(∂T∂V

)p

I “everything else is held constant”I partial derivative manipulations are also new

I cyclic chain ruleI Clairaut’s theoremI ordinary chain ruleI inverse of a partial derivative

15 / 33


Math notation vs physics notation

Physics(∂p

∂V

)S

=1(

∂V∂p

)S

physical observables

p = p(V ,S)

p = p(V ,T )

V = V (p,S)

V = V (p,T )

Math

∂u

∂x6= 1

∂x∂u

functions

u(x , y)

v(x , y)

x(u, v)

y(u, v)(∂u

∂x

)y

6= 1(∂x∂u

)v

16 / 33


Mathematical interlude: a mechanical analogue for thermo

7 hours of thermodynamics math on a mechanical system

I integrating over a path to find work

I path independence to get potential energy

I small differences or tangent slope to find partial derivatives

I “holding everything else constant” is not possible

I partial derivative manipulations

I connection with experiment

I total differential for energy conservation

I Maxwell relations

I Legendre transformations

17 / 33


The partial derivative machineThe system

xy

xF

yF

I one hidden elastic system

I two controllable and measurable coordinates x and y

I two controllable forces Fx and FyI one potential energy U, not directly measurable

I can integrate work to find potential energy18 / 33


Measuring partial derivatives(∂x

∂Fx

)y

vs

(∂x

∂Fx

)Fy

I students consistently believe these are the same

I they are taught to “hold everything else constant”

19 / 33


Approaches for finding a derivative

I make a small change, measure a small change, take a ratioI mistake: use a very small change and get noiseI mistake: use a large change and assume linear responseI try a different small change to ensure “small enough”

I measure many values, make a plotI mistake: fit to a straight lineI find tangent line (by eye)

I mistake: seek analytic form to differentiate (black box helps)20 / 33


A mechanical analogue for thermo: First Law

I energy conservation and path independence: differentials

I looks like thermodynamic identity: dU = Fxdx + Fydy

I students integrate work to find potential energy

I paths from state A to state B (like pV plots)

21 / 33


A mechanical analogue for thermo: First Law

dU = Fxdx + Fydy

I Maxwell relation(∂(∂U∂x

)y

∂y

)x

=

∂(∂U∂y

)x

∂x

y(

∂Fx∂y

)x

=

(∂Fy∂x

)y

I can verify this experimentally

22 / 33


A mechanical analogue for thermo

I Legendre transform: imagine one mass is inside the black boxI you cannot change one force Fy

I you cannot measure the value y

I add potential energy of mass causing Fy :

V ≡ U − Fyy

I like enthalpy and Helmholtz free energy

I gives more Maxwell relations

23 / 33


What is this derivative?

(∂p

∂V

)S

24 / 33


Name the experiment!

I give student groups specific derivatives

I students sketch an experiment to measure that derivative

I groups share their experiments with the class

25 / 33


Name the experiment!Adiabatic compressibility

(∂p∂V

)S

=

26 / 33


Name the experiment!General learning goals

I operational definitions of thermodynamic quantitiesI how to measureI how to fix

I what is held constant matters

I “canonical” thought experiments

I thermodynamic derivatives are physically measurable

27 / 33


Name the experiment!Specific learning goals

I adiabatic processes:(∂T∂V

)S

,(∂T∂p

)S

and(∂V∂p

)S

I changing temperature without heating:(∂T∂V

)S

and(∂T∂p

)S

I the First Law:(∂U∂T

)V

and(∂U∂p

)S

I heat capacity:(∂S∂T

)V

and(∂S∂T

)p

I heating without changing temperature:(∂S∂V

)T

and(∂S∂p

)T

I using Maxwell relations:(∂S∂V

)T

,(∂S∂p

)T

,(∂S∂p

)V

and(∂S∂V

)p

I turning derivatives upside down: many of the above

28 / 33


Measuring partial derivatives with experiment

Integrated labs enable tight coupling ofcoursework with experiments, includingteaching 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 relations29 / 33


Thermal conclusion

I connect math with tangible reality

I partial derivative machine

I name the experiment

I perform actual experiments

30 / 33


Teaching upper-division physics well

departmental culture

I what students learn depends on what students do

→ lecture is not enough (for most students)

I math in physics courses is not like math in math courses

→ intentional and planned just-in-time teaching of math

I faculty need to agree on what is taught

→ faculty need to discuss what is taught!!!

connecting math with the real world

I integration as summation

→ computational lab and integrated lab activities

I measurable partial derivatives

→ in-class activities and experiments in thermal physics

31 / 33


Acknowledgements

Paradigms team

I Corinne Manogue

I Tevian Dray

I Mary Bridget Kustusch

I Henri Jansen

I Janet Tate

I David McIntyre

Energy and Entropy collaborators

I John Thompson (U. Maine)

I Michael Rogers (Ithaca College)

Students

I Eric Krebs and Jeff Schulte

I Grant Sherer

32 / 33


Resources

I These slides:physics.oregonstate.edu/~roundyd/education.html

I Paradigms in Physics wiki:http://physics.oregonstate.edu/portfolioswiki

I Computational lab course website:http://physics.oregonstate.edu/~roundyd/COURSES/ph365

I G. Sherer, M. B. Kustusch, C. A. Manogue, and D. Roundy,“The Partial Derivative Machine,” 2013 PERC Proceedings.

I D. Roundy, M. B. Kustusch and C. A. Manogue, “Name theexperiment! Interpreting thermodynamic derivatives asthought experiments,” AJP (in press).

I D. Roundy and M. Rogers, “Exploring the thermodynamics ofa rubber band,” AJP (2013).

I D. Roundy, A. Gupta, J. F. Wagner, T. Dray, M. B. Kustuschand C. A. Manogue, “From Fear to Fun in Thermodynamics,”2013 PERC Proceedings. 33 / 33

physics.oregonstate.edu/~roundyd/education.html

http://physics.oregonstate.edu/portfolioswiki

http://physics.oregonstate.edu/~roundyd/COURSES/ph365

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