Teaching Students to
“Think Like a Physicist”
Paradigms in Physics
http://physics.oregonstate.edu/portfolioswiki
Corinne Manogue
7/19/2010
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
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Thank you
for the warm welcome
to Colombia!
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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/portfolioswiki
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Outline
• Classroom Norms
• The Hidden Curriculum
• Listening:
(Surprising Things Students Don’t Know)
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Outline
• Things you already know.
• Ways you may never have imagined how to
implement them!
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Classroom Norms
What are your students expectations for
what will happen in the classroom?
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In a Restaurant:1
Food
in mouth:
Eat
Use
knife
and fork
Use
hands
Pay
Select
food
Menu
on paper
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Menu
on wall
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Classroom Norms
• Everyone is welcome in my class.
–
–
–
–
–
–
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Women & minorities
Foreigners
First generation students
Quiet, shy white men
Engineers
Foot in mouth—apologizing.
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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!)
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Changing the Frame
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Classroom Norms
I 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
table
role 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.
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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?
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Point Charge—Potential
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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
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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
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The Hidden Curriculum
• What is the middle-division?
• What are your hidden curriculum goals for
the middle-division?
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The Hidden Curriculum
—Problem-Solving
• Moving away from
templates
• Using advanced
notation
• Breaking-up
complicated problems
• Harmonic reasoning
• Novice Expert
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• Problem-solving
confidence
• Using Reflective
Judgment
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Novice to Expert
• How do I use this
method to solve
problems?
• How do I get
from this step to
this step?
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• How will I know
if this will work?
• What else can I
do if this won’t
work?
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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?
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The Hidden Curriculum
• Choose your pedagogical strategies to
reflect your hidden curriculum goals.
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The Hidden Curriculum
—Lecture vs. Activities
• The Instructor:
–
–
–
–
–
Paints big picture.
Inspires.
Covers lots fast.
Models speaking.
Models problemsolving.
– Controls questions.
– Makes connections.
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• The Students:
–
–
–
–
–
Focus on subtleties.
Experience delight.
Slow, but in depth.
Practice speaking.
Practice problemsolving.
– Control questions.
– Make connections.
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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.
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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.
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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.”
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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.
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Eigenvectors & Eigenvalues
• Each group has a different matrix.
• The examples are all “tricky” (degeneracy)
• Find eigenvalues & eigenvectors.
See Narratives on the wiki,
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Large Whiteboards
• Provide the opportunity:
– to compare and contrast answers,
– for mini-presentations,
– to discuss problem-solving strategies, synthesis,
evaluation, decision-making, etc.
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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.
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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
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Epistemological strategies
recognizing patterns
10: Group begins.
fleshing out formulas
2: Middle of group
work.
applying learned
mathematics
8: Wrap-up
applying a principle to a
specific case
sense making
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Reinventing College Physics for Biologists:
Explicating an Epistemological Curriculum , E. F.
Redish and D. Hammer, Am. J. Phys., 77, 629-642
(2009).
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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.
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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
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Relating Multiple
Representations
1. Flux is the total amount of electric field through a given area.
2.
r r
F=× ò E da
r r
E × da
3.
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r
E
r
da
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Socratic
vs.
Groups
How does it feel to teach in these ways?
ò d knowledge
vs.
class
Everyone knows everything
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ò d questions
class
vs.
No one knows anything
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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.
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Plane Wave Activity
Students connect points
with equal value of
k ×r
What is

cos k × r   t
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
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Plane Wave Representations
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Using Color to Visualize
Spherical Harmonics
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Visualization—Table
-5
-4
-3
-2
-1
0
1
2
3
4
5
9 16 21 24 25 24 21 16
-5
0
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
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4
9 18 25 30 33 34 33 30 25 18
5
0
9
9 16 21 24 25http://physics.oregonstate.edu/portfolioswiki
24 21 16 9 0
Visualization—Level Curves
f(x,y)=A(50-x^2-y^2)
5
4
45-50
3
40-45
2
35-40
1
30-35
0 y
25-30
-1
20-25
-2
-3
-4
f(x,y)
-5
50
45
40
35
30
25
20
15
10
5
0
-5 -4 -3 -2 -1 0
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x
1
2
3
4
15-20
10-15
5-10
0-5
5
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Visualization—Graph
f(x,y)=A(50-x^2-y^2)
45-50
40-45
50
35-40
45
30-35
40
35
25-30
30
f(x,y)
20-25
25
15-20
20
15
10-15
5
10
5-10
5
0
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x
5
3
1
-1
-3
-5
0
y
0-5
-5
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Visualization—Gradient
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Relating Multiple
Representations
1. Flux is the total amount of electric field through a given area.
2.
r r
F=× ò E da
r r
E × da
3.
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r
E
r
da
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What is the electrostatic potential
due to this point charge?
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What is the electrostatic potential
due to this pair of point charges?
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Shifting/Superposition
• Superposition for solutions of linear
differential equations:
1 q
V=
4 0 r
 V (r ) =
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1
4 0

i
qi
r  ri
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What is the electrostatic potential
due to this ring of charge?
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Idealization
• Make the students think about the source:
1 q
V=
4 0 r
 V (r ) =
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1
4 0
ò
 (r )d 
r  r
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What is the electrostatic field due
to this ring of charge?
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Potentials or Fields
Should students study
• the electric field first (conventional)
or
• electrostatic potentials (Paradigms)?
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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.
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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.
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Motto
My Agenda Is Irrelevant
If I Can’t
Take The Students With Me
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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.
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Potential Due to Charged Disk
z
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What is the electrostatic
potential at a point, on
axis, above a uniformly
charged disk?
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One Physics Concept
• Coulomb’s Law:
1 q
V=
4 0 r
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Superposition
• Superposition for solutions of linear
differential equations:
1 q
V=
4 0 r
 V (r ) =
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1
4 0
ò
 ( r )da 
r  r
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Chopping and Adding
z
r 2  z 2
Integrals involve
chopping up a part of
space and adding up a
physical quantity on
each piece.
r
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Computational Skill
• Can the students set-up and do the integral?
V (r ) =
1
4 0

=
4 0
2
=
4 0
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ò
  r  da 
r  r
2 R
òò
0 0

dr  r  d 
r 2  z 2
R2  z2  z

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Constants vs. Variables
• Which of these symbols are constants and
which are variables?

V ( r,  , z ) =
4 0
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2
ò
0
R d 
2

r  R  2rR cos(   )  z
2
2
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Limits (Far Away)
2
V (r ) =
4 0

R2  z2  z


2 
R2
=
 z 1 2  z 

4 0 
z

2   1 R 2
=

 z 1 
2
4 0   2 z
 
 z
 
1  R 2

4 0 z
7/19/2010
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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.
7/19/2010
http://physics.oregonstate.edu/portfolioswiki
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.
7/19/2010
http://physics.oregonstate.edu/portfolioswiki
Multiple Representations
Write on your small white board something about
dot products.
u × v = u1v1  u2 v2  u3v3
v
u × v = u v cos
u = u ×u
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v ×u
u
u
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Steady Current
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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
http://physics.oregonstate.edu/portfolioswiki