7/19/2010 teaching students to “think like a physicist” paradigms in physics corinne manogue

7/19/2010 http://physics.oregonstate.edu/portfolioswiki

Teaching Students to “Think Like a Physicist”

Paradigms in Physics

Corinne Manogue

http://physics.oregonstate.edu/portfolioswiki


Support• National Science Foundation

– DUE-9653250, 0231194, 0618877– DUE-0088901, 0231032, 0837829

• Oregon State University

• Oregon Collaborative for Excellence in the Preparation of Teachers

• Grinnell College• Mount Holyoke College• Utah State University


Thank you for the warm welcome

to Colombia!


Paradigms in Physics

• I will not talk about the Paradigms arrangement of courses here.

• I will talk about teaching.

See our wiki: activities, courses, narratives, pedagogical strategies, textbooks.

physics.oregonstate.edu/portfolioswikiphysics.oregonstate.edu/portfolioswiki


Outline

• Classroom Norms

• The Hidden Curriculum

• Listening:

(Surprising Things Students Don’t Know)


Outline

• Things you already know.

• Ways you may never have imagined how to implement them!


Classroom Norms

What are your students expectations for what will happen in the classroom?


Foodin mouth:

Eat

Usehands

Useknife

and fork

Selectfood

Pay

Menuon paper

Menuon wall

In a Restaurant:1


Classroom Norms

• Everyone is welcome in my class.– Women & minorities– Foreigners– First generation students– Quiet, shy white men– Engineers– Foot in mouth—apologizing.


Classroom Norms

• High stakes, low stakes, no stakes.

• Everyone is expected to participate.– Start from the first day!!– Don’t expect them to do anything you don’t

model (looking foolish!)


Changing the Frame


Classroom NormsI think part of what was interesting.It was completely different than what you might be implicitly

expecting about even regular group work might be like.So preconceptions about what class was going to be like,It was effective at probably shattering a lot of those.You don’t terribly often have your professor standing on the

tablerole playing a fictional character for educational purposes.And I thought that was good as a way to sort of expand our expectations of what we might be doing at any

given time.rather than just sort of sit here, take notes, then do something and then sit here some more.


Classroom Norms

• Everyone makes lots of mistakes.– Small white boards

• Do you feel welcome?

– “Give a formula for the potential due to this point charge.”

– Saving face:• Allow question marks.

• Who summarizes?


Point Charge—Potential


Small White Board Questions

• Allow the instructor to see if everyone is on the same page.

• “Quiet” members of the class are encouraged to participate.

• Students vie to have their answers chosen.

• Keep everyone engaged and awake


Classroom Norms

• Mathematicians teach students to be precise => pay attention to language (good)

=> be afraid (bad)

• Physicists teach students to solve problems they’ve never seen before

=> must coordinate many strategies

=> jump in even if you can’t see the end


The Hidden Curriculum

• What is the middle-division?

• What are your hidden curriculum goals for the middle-division?


The Hidden Curriculum—Problem-Solving

• Moving away from templates

• Using advanced notation

• Breaking-up complicated problems

• Harmonic reasoning• Novice Expert

• Problem-solving confidence

• Using Reflective Judgment


Novice to Expert

• How do I use this method to solve problems?

• How do I get from this step to this step?

• How will I know if this will work?

• What else can I do if this won’t work?


Metacognition Matters

• How do I know that I know something?

• Why is she doing this to mc?

• What are the facets of problem-solving?

• How far have I come?

• How do I organize the content in my head?


The Hidden Curriculum

• Choose your pedagogical strategies to reflect your hidden curriculum goals.


The Hidden Curriculum—Lecture vs. Activities

• The Instructor:– Paints big picture.

– Inspires.

– Covers lots fast.

– Models speaking.

– Models problem-solving.

– Controls questions.

– Makes connections.

• The Students:– Focus on subtleties.

– Experience delight.

– Slow, but in depth.

– Practice speaking.

– Practice problem-solving.

– Control questions.

– Make connections.


Lecture vs. Activities

• Rule of thumb:– If the can get it from lecture—then lecture!!– If they can’t get it from lecture—then make

them fall in the trap when you are there to help them out.


Hidden Curriculum

• Kinesthetic Activities– students use their own bodies to represent

aspects of the physical situation – concrete representation of the geometric

situation – concrete representation of idealizations.


Current

“This went surprisingly smoothly and quickly. I had been a bit concerned that we'd have chaos, but students very quickly worked out what they were to do. Since all the students are working together, everyone stayed on the same page.”


Compare & Contrast

• Each small group solves a slightly different example of the same calculation.

• The focus of the activity, then, is often on the full-class wrap-up discussion that happens after the activity.


Eigenvectors & Eigenvalues

• Each group has a different matrix.

• The examples are all “tricky” (degeneracy)

• Find eigenvalues & eigenvectors.

See Narratives on the wiki,

physics.oregonstate.eduphysics.oregonstate.edu


Large Whiteboards

• Provide the opportunity:– to compare and contrast answers,– for mini-presentations,– to discuss problem-solving strategies, synthesis,

evaluation, decision-making, etc.


Chunking & Compiling

• When we are learning new things, they each appear in our memory as separate facts. This makes the load on working memory extremely high.

• What happens when the buffer gets full?

• Chunking/compiling.


Breaking Complex Problems into Smaller Pieces

• Potential Due to Pair of Charges

• Potential Due to Ring

• Electric Field Due to Ring

• Vector Potential Due to Spinning Ring

• Magnetic Field Due to Spinning Ring


Epistemological strategies

Reinventing College Physics for Biologists: Explicating an Epistemological Curriculum , E. F. Redish and D. Hammer, Am. J. Phys., 77, 629-642 (2009).

recognizing patterns

fleshing out formulas

applying learned mathematics

applying a principle to a specific case

sense making

10: Group begins.

2: Middle of group work.

8: Wrap-up


Structure

• Open-ended, short prompts.

• Break into pieces for different content goals.

• Scaffolded by high-quality roving instructors.

• Wrap-up discussions provide chance for reflection.


Listening

Surprising things students don’t know.• basis vectors that go with curvilinear coordinates • matrices as transformations • power series as approximations • eigenvectors as the things that are “unchanged” by a transformation • a geometric conception of fields • that zero is a number • how to add two functions pointwise • how to read equations as words • what is planar about plane waves?• geometric interpretations of dot and cross products • the meaning of the vertical axis on a graph • how to shift a graph left or right, up or down


Relating Multiple Representations

1. Flux is the total amount of electric field through a given area.

E da

2.

da

E

E da

3.


Socratic vs. Groups

classd questionsò

classd knowledgeò

How does it feel to teach in these ways?

vs.

Everyone knows everything vs. No one knows anything


Conclusions

• Linear vs. Holistic Thinking– Lecturing, textbooks are linear– Learning is holistic.

• Meet the diverse needs of your students by thinking about your curriculum on multiple levels.


Plane Wave Activity

Students connect points

with equal value of

What is

k r

cos k r t


Plane Wave Representations


Using Color to VisualizeSpherical Harmonics


Visualization—Table

-5 -4 -3 -2 -1 0 1 2 3 4 5

-5 0 9 16 21 24 25 24 21 16 9 0

-4 9 18 25 30 33 34 33 30 25 18 9

-3 16 25 32 37 40 41 40 37 32 25 16

-2 21 30 37 42 45 46 45 42 37 30 21

-1 24 33 40 45 48 49 48 45 40 33 24

0 25 34 41 46 49 50 49 46 41 34 25

1 24 33 40 45 48 49 48 45 40 33 24

2 21 30 37 42 45 46 45 42 37 30 21

3 16 25 32 37 40 41 40 37 32 25 16

4 9 18 25 30 33 34 33 30 25 18 9

5 0 9 16 21 24 25 24 21 16 9 0


Visualization—Level Curves

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5

05101520253035404550f(x,y)

x

y

f(x,y)=A(50-x^2-y 2)

45-50

40-45

35-40

30-35

25-30

20-25

15-20

10-15

5-10

0-5


Visualization—Graph

-5 -3 -1 1 3 5

-5

0

5

0

5

10

15

20

25

30

35

40

45

50

f(x,y)

x

y

f(x,y)=A(50-x^2-y^2)

45-50

40-45

35-40

30-35

25-30

20-25

15-20

10-15

5-10

0-5


Visualization—Gradient


Relating Multiple Representations

1. Flux is the total amount of electric field through a given area.

E da

2.

da

E

E da

3.


What is the electrostatic potential due to this point charge?


What is the electrostatic potential due to this pair of point charges?


Shifting/Superposition

• Superposition for solutions of linear differential equations:

0

0

1

4

1( )

4i

i i

qV

r

qV r

r r


What is the electrostatic potential due to this ring of charge?


Idealization

• Make the students think about the source:

0

0

1

4

1 ( )( )

4

qV

r

r dV r

r r


What is the electrostatic field due to this ring of charge?


Potentials or Fields

Should students study

• the electric field first (conventional)

or

• electrostatic potentials (Paradigms)?


The Spinning Ring

• Consider a very thin ring of charge with constant charge density, and total charge Q. The ring has radius R and is rotating about its axis with period T.

• For all groups: Create an integral expression for the vector potential caused by this ring everywhere in space. The expression should be complete enough to put into Maple or a similar mathematics package.


The Spinning Ring - Limits

• Approximate this vector potential near the center of the ring, in the plane of the ring.

• Approximate this vector potential near the center of the ring, along the z-axis.

• Approximate this vector potential far from the ring, in the plane of the ring.

• Approximate this vector potential far from the ring, along the z-axis.


Motto

My Agenda Is Irrelevant

If I Can’t

Take The Students With Me


An Example

• Typical of EARLY upper-division work for physics majors and many engineers.

• Solution requires:– many mathematical strategies,– many geometrical and visualization strategies,– only one physics concept.

• Demonstrates different use of language.


Potential Due to Charged Disk

What is the electrostatic potential at a point, on axis, above a uniformly charged disk?

z


One Physics Concept

• Coulomb’s Law:

0

1

4

qV

r


Superposition

• Superposition for solutions of linear differential equations:

0

0

1

4

1 ( )( )

4

qV

r

r daV r

r r


Chopping and Adding

Integrals involve chopping up a part of space and adding up a physical quantity on each piece.

2 2r z z

r


Computational Skill

• Can the students set-up and do the integral?

0

2

2 20 0 0

2 2

0

1( )

4

4

2

4

R

r daV r

r r

dr r d

r z

R z z


Constants vs. Variables

• Which of these symbols are constants and which are variables?

2

2 2 20 0

( , , )4 2 cos( )

R dV r z

r R rR z


Limits (Far Away)

2 2

0

2

20

2

20

2

0

2( )

4

21

4

2 11

4 2

1

4

V r R z z

Rz z

z

Rz z

z

R

z


The Spinning Ring

• Consider a very thin ring of charge with constant charge density, and total charge Q. The ring has radius R and is rotating about its axis with period T.

• For all groups: Create an integral expression for the vector potential caused by this ring everywhere in space. The expression should be complete enough to put into Maple or a similar mathematics package.


The Spinning Ring - Limits

• Approximate this vector potential near the center of the ring, in the plane of the ring.

• Approximate this vector potential near the center of the ring, along the z-axis.

• Approximate this vector potential far from the ring, in the plane of the ring.

• Approximate this vector potential far from the ring, along the z-axis.


Multiple Representations

Write on your small white board something about dot products.

1 1 2 2 3 3u v u v u v u v

cosu v u v

u u u v u

u

u

v


Steady Current


Small White Board Questions

• Allow the instructor to see if everyone is on the same page.

• “Quiet” members of the class are encouraged to participate.

• Students vie to have their answers chosen.

• Keep everyone engaged and awake

7/19/2010 teaching students to “think like a physicist” paradigms in physics corinne manogue

Documents

teaching students

students expectations

dont model

low stakes

warm welcome

shy white menengineersfoot

small white boardsdo

language good