A research-validated approach
to transforming upper-division
physics courses
Steven Pollock
Physics Dept.
University of Colorado at Boulder
Tufts 2014
Upper-Level Course Transformation
Univ. of Colorado
Physics Education Research at CU
Boulder
Faculty:
Postdocs/ Scientists:
Melissa Dancy
Michael Dubson
Noah Finkelstein
Heather Lewandowski
Valerie Otero
Robert Parson
Kathy Perkins
Steven Pollock
Carl Wieman*
Stephanie Chasteen
Karina Hensberry
Katie Hinko
Emily Moore*
Ariel Paul
Qing Ryan
Grad Students:
Teachers / Partners /
Staff:
Funded by:
Shelly Belleau, John Blanco
Kathy Dessau, Jackie Elser
Molly Giuliano, Kate Kidder
Trish Loeblein, Chris Malley
Susan M. Nicholson-Dykstra
Oliver Nix, Jon Olson
Emily Quinty, Sam Reid
Sara Severance
National Science Foundation
William and Flora Hewlett Foundation
American Association of Physics
Teachers
Physics Teacher Education Coalition
American Institute of Physics
American Physical Society
National Math & Science Initiative
Howard Hughes Medical Institute
Ian Her Many Horses
George Ortiz
Mike Ross
Ben Spike
Enrique Suarez
Ben Van Dusen
Bethany Wilcox
Rosemary Wulf
+recent grads (4 PhD)
+ many participating
faculty and LAs
Univ. of Colorado
Outline
• Overview, and some background
• Building on a research base:
– Why transform E&M I?
– What changed?
– Data collection
– Assessment
– Outcomes and research questions
Upper-Level Course Transformation
Univ. of Colorado
Background at CU Boulder
Physics Department
55 faculty
350 undergrad majors
230 graduate students
Upper-Level Course Transformation
Univ. of Colorado
Background at CU Boulder
• Clickers & Peer Instruction
• Tutorials in Introductory Physics
• Pre/post assessments
Upper-Level Course Transformation
Univ. of Colorado
Force Concept Inventory Learning gains
traditional lecture
Fraction of Courses
0.6
<g> = post-pre
0.5
100-pre
0.4
0.3
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
R. Hake, ”…A six-thousand-student survey…” AJP 66, 64-74 (‘98).
Univ. of Colorado
FCI Learning gains
traditional lecture interactive engagement
Fraction of Courses
0.6
<g> = post-pre
0.5
100-pre
0.4
0.3
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
R. Hake, ”…A six-thousand-student survey…” AJP 66, 64-74 (‘98).
Univ. of Colorado
FCI/FMCE Learning gains
traditional lecture interactive engagement
Fraction of Courses
0.6
0.5
0.4
0.3
CU for last 18 semesters
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
S. Pollock and N. Finkelstein, Phys. Rev. ST Phys. Educ. Res. 4, 010110 (2008)
Univ. of Colorado
S. Pollock Physics Ed Res. Conference Proc. 2012
FCI/FMCE Learning gains
traditional lecture interactive engagement
Fraction of Courses
0.6
0.5
0.4
Traditional Recitation at CU
(peer instruction in lectures)
0.3
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
S. Pollock and N. Finkelstein, Phys. Rev. ST Phys. Educ. Res. 4, 010110 (2008)
Univ. of Colorado
S. Pollock Physics Ed Res. Conference Proc. 2012
FCI/FMCE Learning gains
traditional lecture interactive engagement
Fraction of Courses
0.6
0.5
0.4
Peer instruction @ CU, also
with UW Tutorials and LAs
0.3
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
S. Pollock and N. Finkelstein, Phys. Rev. ST Phys. Educ. Res. 4, 010110 (2008)
Univ. of Colorado
S. Pollock Physics Ed Res. Conference Proc. 2012
Longitudinal
Upper division majors’ BEMA scores
After upper div. E&M.
(Only students who took intro without Tutorials)
S. Pollock, 2007 PERC, and Phys. Rev STPER 5 (2009)
Upper-Level Course Transformation
Univ. of Colorado
Longitudinal
Upper division majors’ BEMA scores
BLUE: students who took freshman E&M with Tutorials
S. Pollock, 2007 PERC, and Phys. Rev STPER 5 (2009)
Upper-Level Course Transformation
Univ. of Colorado
Longitudinal
Upper division majors’ BEMA scores
Grade in course
(3.1 ±.1)
(3.3 ±.1)
(3.2)
(3.0 ±.1)
Yellow: students who had been E&M LAs
S. Pollock, 2007 PERC, and Phys. Rev STPER 5 (2009)
Upper-Level Course Transformation
Univ. of Colorado
Why transform junior E&M I?
Lecture with clickers
Washington Tutorials
?
Can our majors learn
better from interactive
techniques adapted from
introductory physics?
Upper-Level Course Transformation
Univ. of Colorado
Model of Course Transformation
Establish
learning goals
Using Research
& Assessment
Faculty & Staff
Apply research-based
teaching techniques &
measure progress
Chasteen, Perkins, Beale, Pollock, & Wieman, JCST 40 (4), 70, 2011
Chasteen et al., AJP 80, 923, 2012, PRSTPER 8 020108, 2012
• E&M 1 & II
• QM I
• Class
Mech/Math
Methods
Univ. of Colorado
What Changed?
• Faculty collaboration
• Explicit learning goals
• Collect student data!
• Interactive classroom
techniques
• Concept Tests
• Modified Homework
• Homework Help Sessions
• Tutorials
Students debate a concept test
Pepper et al, Chasteen et al, Pollock et al. PERC 2010
Upper-Level Course Transformation
Univ. of Colorado
What’s special about upper-div?
???
• More experienced students
• Faculty and student identity
• More complex
physics
• Smaller classes
Univ. of Colorado
Learning Goals
• From faculty working group
• Framed course transformations
• Made explicit to students
Students should
… be able to achieve physical insight
through the mathematics of a problem
… be able to choose and apply the
appropriate problem-solving technique
… demonstrate intellectual maturity
Pepper et al, PERC 2011
Upper-Level Course Transformation
Univ. of Colorado
Research on student difficulties
Research-based
Research-validated
• Tutorials
• Clicker Questions
•Class activities
•Homeworks
• Consensus learning goals
reflective
development
• valid/reliable instruments
• interviews and class
observations
•pre/post assessments
(intermediate or course
scale)
Upper-Level Course Transformation
Univ. of Colorado
Did it Work? Assessments
• Compared Traditional (9 courses) & Transformed
(9 courses) at CU and elsewhere (N=515).
• Common traditional exam questions (5)
• Developed Colorado Upper-Division Electrostatics
Assessment (CUE)
Chasteen et al, JCST 40 (2011) , Phys Rev STPER (2012)
Upper-Level Course Transformation
Univ. of Colorado
CUE assessment:
DO NOT SOLVE the problem, we just want to know:
- The general strategy (half credit)
- Why you chose that method (half credit)
A grounded conducting plane with a point charge Q at a distance
a. Find E (or V) at point P.
Illinois ‘13
Upper-Level Course Transformation
Univ. of Colorado
Univ. of Colorado
CUE results: Trad courses
CUE Total Post-test Score
80
Common CUE Score (%)
Average (Across Courses)
Post: Standard
70
60
50
40
30
20
10
0
S1
S2
S3
CU
S4
S5
S6
S7
S8
Non-CU
Standard Lecture-Based Courses
Chasteen et al , Phys Rev STPER 8 (2012)
Course Transformation
Univ. of Colorado
S9
CUE results
CUE Total Post-test Score
80
Common CUE Score (%)
70
Average (Across Courses)
Post-test: Standard
Post-test: Research-based
60
50
40
30
20
10
0
Non-CU
Standard Lecture-Based Courses (STND)
‘13
Non-CU
CU
Physics Education Research-Based Courses (PER)
Course Transformation
Univ. of Colorado
CUE results
CUE Total Post-test Score
80
Common CUE Score (%)
70
Post-test: Standard
Post-test: Research-based
Post-test: Graduate Students
Average (Across Courses)
60
50
40
30
20
10
0
Non-CU
Standard Lecture-Based Courses (STND)
‘13
CU
Non-CU
Physics Education Research-Based Courses (PER)
Course Transformation
Univ. of Colorado
CUE score distribution
Fraction of classes
traditional lecture
interactive engagement
50
45
40
35
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Score (as %)
Ntot=540
‘13
Course Transformation
Univ. of Colorado
FCI Learning gains
traditional lecture interactive engagement
Fraction of Courses
0.6
<g> = post-pre
0.5
100-pre
0.4
0.3
0.2
0.1
0
0.08
0.14
0.20
0.26
0.32
Less Learning
0.38
<g>
0.44
0.50
0.56
0.62
0.68
More Learning
R. Hake, ”…A six-thousand-student survey…” AJP 66, 64-74 (‘98).
Univ. of Colorado
Traditional exam questions
Exam Results by Learning Goal
STND
100
PER‐C
PER‐D
5 exam questions
80
60
40
20
0
Calcula on
Reasoning Expecta on
Method 1
(Gauss)
Method 2
(Ampere)
Chasteen et al, PERC 2011, AJP 80 (#10) 2012
Upper-Level Course Transformation
Univ. of Colorado
Classroom Techniques
• Traditional lecture
blended with interactive
engagement (e.g.
concept tests)
• Simulations & demos
• Small handheld
whiteboards
• Concept tests, +…
S. Chasteen et al, AJP 80 (#10) 2012, Phys Rev STPER 8 (2012)
Upper-Level Course Transformation
Univ. of Colorado
Concept Tests
• Allowed students to discuss & debate challenging,
high-level ideas
• 2-4 per 50 minute lecture
• Active debate
Pollock et al, PERC 2010
Upper-Level Course Transformation
Univ. of Colorado
Concept Tests
Upper-Level Course Transformation
Univ. of Colorado
Concept Tests
Upper-Level Course Transformation
Univ. of Colorado
Tutorials
Optional, weekly. 30-50% attendance. Test-bed, chance to do demos.
Chasteen, PERC 2011
Upper-Level Course Transformation
Univ. of Colorado
Upper-div Clickers at CU
Term
04
05
06
07
08
09
10
11
S F S F S F S F S F S F S F S F
Mech Math I
Mech MathII
EM I
EM II
QM I
QM II
Stat Mech
Solid State
Plasma
Nuclear/HE
Perkins et al, PERC 2009
Upper-Level Course Transformation
Univ. of Colorado
Upper-div Clickers at CU
Term
04
05
06
07
08
✔
✔
10
11
S F S F S F S F S F S F S F S F
Mech Math I
✔
Mech MathII
EM I
EM II
QM I
QM II
Stat Mech
09
✔
Solid State
✔
✔✔
✔
✔
✔✔✔✔
✔✔✔
✔✔✔✔
✔
✔
✔✔✔✔
✔
✔
✔
✔✔✔
✔
✔✔
✔✔
✔✔✔
✔
✔✔
✔
Plasma
Nuclear/HE
PER faculty
Upper-Level Course Transformation
Univ. of Colorado
Students Find Clickers Useful
Q: How useful for your learning is the addition of clicker
questions compared to pure lecture with no clicker questions?
Lecture with clickers
much more useful
79% of
students
Lecture with clickers
more useful
Same
Pure lecture
more useful
Upper-div courses using clickers:
12 courses, 264 student responses
Pure lecture
much more useful
0%
10%
20%
30%
40%
Perkins and Turpen, PERC 2009
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Student’s can’t predict value
Q: Would you recommend using clicker
questions in upper-level physics courses?
Highly
Recommend
Recommended
In highly rated pure lecture,
No clickers (QM II, n=17)
Neutral
Add Clickers (QM I, n=30)
Missing clickers? (EM II, n=16)
Not recommended
Definitely not
recommended
0%
10% 20% 30% 40% 50%
Perkins and Turpen, PERC 2009
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Student difficulties:
Where in space (if anywhere)
does the divergence of E
vanish?
Ñ× E = r / e0
correct complete,
18%
other, 21%
correct where no
charges, 8%
origin, 8%
infinity, 6%
inside, 31%
outside, 8%
Midterm exam, N = 59
R. Pepper et al, PR-STPER 8 010111 (2012)
Modified version in Sp ‘13, N=64: 79% correct, with 49% “correct-complete”
Univ. of Colorado
Topical Pre-post shifts
1
(effect size)
Early term
0.9
Early term
0.8
Effect size
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Delta Function
math
‘13
Delta function
interp
Vector potential Vector Potential
fully correct
direction only
Course Transformation
Bound Current
location
Univ. of Colorado
Topical Pre-post shifts
(effect size)
1
0.9
Early term
0.8
Modified
Effect size
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Delta Function
math
‘13
Delta function
interp
Vector potential Vector Potential
fully correct
direction only
Course Transformation
Bound Current
location
Univ. of Colorado
More resources
www.colorado.edu/sei/physics
Univ. of Colorado
Summary
Course transformation (and broader questions)
focusing on upper-div are still at an early stage
- What is the nature of UD student difficulties?
- Do the means to address these differ in
substantial ways from lower division?
FFPER ‘13
Upper-Level Course Transformation
Univ. of Colorado
Summary
Course transformation (and broader questions)
focusing on upper-div are still at an early stage
- What is the nature of UD student difficulties?
- Do the means to address these differ in
substantial ways from lower division?
- Can we improve student performance in
“the canon”?
- What forms of data support faculty buy-in, &
how far and how fast can/should we push?
FFPER ‘13
Upper-Level Course Transformation
Univ. of Colorado
Summary
We are transforming upper division classes:
- Impact on content learning
- Impact
on
participation
It’s not about our teaching,
it’sfaculty
about(buy-in?)
student
Included
learning
Developing materials and resources
Developing assessment instruments
Upper-Level Course Transformation
Univ. of Colorado
Upper-Level Course Transformation
Univ. of Colorado
Questions!
Lower division: per.colorado.edu/cts
Upper division: per.colorado.edu/sei
Upper-Level Course Transformation
Univ. of Colorado
EXTRA SLIDES
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
CUE Total Post-test Score
80
Average (Across Courses)
Post-test: Standard
Post-test: Research-based
Common CUE Score (%)
70
Post-test: Graduate Students
Gain
60
50
40
30
20
10
0
Non-CU
Standard Lecture-Based Courses (STND)
Illinois ‘13
CU
Non-CU
Physics Education Research-Based Courses (PER)
Upper-Level Course Transformation
Univ. of Colorado
pre-test (post lecture)
Which of the following could be a physically allowable
static charge distribution?
Why/why not?
20%
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Common Mathematical Difficulties:
(From R. Pepper) –
• Can do calculation – difficulty setting up
and interpreting results (e.g. Thompson)
• Don’t connect math to physical
situation (e.g. Manogue et al., Singh)
• Do not access all the math tools that
instructors expect (e.g. Bing & Redish)
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
• accessing math tools
Examples:
• Gauss’s Law
– Precise symmetry arguments
– Inverse problems
– Impossible vs. difficult
• Vector Fields
– Making meaning of div, grad, curl
– Magnitude and direction
• Potential
Univ. of Colorado
Vector calculus difficulties
•
•
•
•
Divergence
Gradient and Curl
Line integrals
Surface and volume integrals
Univ. of Colorado
Student troubles with divergence
r
Ñ× E =
e0
+
Univ. of Colorado
You have a thin spherical shell of uniform negative charge -Q
centered at the origin with no other charge anywhere (i.e. all the
charge is concentrated in a hollow shell at r=R). Where in space
(if anywhere) does the divergence of E vanish?
r
Ñ× E =
e0
Univ. of Colorado
Where in space (if anywhere) does the
divergence of E vanish?
other, 21%
origin, 8%
correct complete,
18%
correct where no
charges, 8%
infinity, 6%
inside, 31%
outside, 8%
Midterm exam, N = 59
Univ. of Colorado
Electric potential
V (r) º - òO E× dl
r
Ñ V = r /e 0
2
V (r) =
1
4 pe 0
ò
E = -ÑV
r(r')
Â
dt '
Univ. of Colorado
You have a thin spherical shell of uniform negative charge -Q
centered at the origin with no other charge anywhere What is the
sign of (V(r=0) – V(r=R))?
other, 2%
positive, 18%
zero, 57%
negative, 23%
V (r) º - òO E× dl
r
Midterm exam, N = 59
Univ. of Colorado
3310 Results (Perceived Utility)
Univ. of Colorado
© S. Chast
Questions: Conceptual
74% incorrect
freshmen: 33%
ud: 80% correct
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Questions: “Next step”
• Next step
– Derivation
– Proof
– Calculation
84% correct
Part of generalized uncertainty
principle proof in QM
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Questions: “Application”
• Application
–
–
–
–
Of abstract idea
To new situation
To real-world
Variations on a theme
Mostly correct,
but good discussions
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Questions: Math/Physics
• Math/Physics
– Apply mathematics to a physical situation
– Translate physical situation into math
Understanding
E=-(grad)V
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
pre-test (post lecture)
Which of the following
could be a physically
allowable static charge
distribution?
Why/why not?
~10% pre
~50% post
Upper-Level Course Transformation
Univ. of Colorado
Outcomes
UPDER 10
Upper-Level Course Transformation
Univ. of Colorado
Using Gauss’s law is hard
ò E× da =
Qenc
e0
Univ. of Colorado
Lower and upper division students
struggle (Singh AJP 2006)
• 25 question multiple choice test to 541
introductory students and 28 upper-level
students
• Introductory students: 49%
• Upper-level: 44%(pre) –> 49% (post)
• Graduate students: 75%
Univ. of Colorado
We also quantify student difficulties:
• CUE concept survey: Do not solve, but give “the easiest method
you would use to solve the problem” and “why you chose that method
(half credit):
r(r) = r0e
-r 2 / a 2
33% of students do not recognize Gauss’s law
as the easiest way to solve. (N=325)
Univ. of Colorado
We also quantify student difficulties:
• CUE concept survey: Do not solve, but give “the easiest method
you would use to solve the problem” and “why you chose that method
(half credit):
33% of students do not recognize Gauss’s law
as the easiest way to solve. (N=325)
24% of students incorrectly choose
Gauss’s law as the easiest way to
solve. (N=325)
Univ. of Colorado
Midterm question:
Suppose I evenly fill a cube (length L on a side) with electric charges.
I then imagine a larger, closed cubical surface neatly surrounding this
cube (length 2L on a side).
Is Gauss' law TRUE in this situation? Briefly, why or why not?
89% correct (N = 59)
Can one use Gauss' law (written above) to simply compute
the value of the electric field at arbitrary points outside the
charged cube (Don't try, just tell me if you could, and why/why not?)
46% correct (N = 59)
31% receive no points
AAPT 2010
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Univ. of Colorado
Probing student difficulties with interviews
• 4 students interviewed after transformed E&M 1
course
• Think-aloud protocol
• Interviewer asked for
clarification and asked
follow-up questions
AAPT 2010
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Univ. of Colorado
Upper-division student have difficulty with:
•
Difficulties with Gauss’s law
The inverse nature of the problem
observed in 3310:
• Precise symmetry arguments
• In less symmetric situations thinking it would
be “difficult” or “messy” rather than
impossible to use Gauss’s law
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical geometry
Examples:
• Gauss’s Law
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• access all the
mathematical tools
that an expert does
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
Incorrect inferences about the integrand
“The E-field...
that Q
passes
“’Cause
if there’s
on the
through the
a Gaussian
surface
is is
outside,
charge, you
know,
only dependent
Q and
making
an E-fieldonasthe
well...
enclosed…On
inside,
therefore
it mustthe
affect
the once
E field
again
it’s [points
[ρ is] constant,
at
that ifpoint
to the then
that’s fine,
because
s...I’m
Gaussian
surface]
asthere
well. ’So
because
doesn
t matter
what
still...
I’m itstill
not ’really
happy
the shape
with
Gaussis
’slooking
law.” like ‘cause
we’re not looking on the outside.
We’re only looking... it’s only
dependent on the Q enclosed.”
• Similar to previous reported difficulties.
(Singh, 2006; Chasteen & Wallace 2010, Guisasola et al., 2008)
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical geometry
Examples:
• Gauss’s Law
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• access all the
mathematical tools
that an expert does
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
We also quantify student difficulties:
• Midterm exam question:
Suppose I evenly fill a cube (length L on a side with electric charges. I
then imagine a larger, closed cubical surface neatly surrounding this
cube (length 2L on a side).
Is Gauss' law TRUE in this situation? (Briefly, why or why not?)
Can one use Gauss' law (written above) to simply compute the value of
the electric field at arbitrary points outside the charged cube (Don't
try, just tell me if you could, and why/why not?)
AAPT 2010
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Univ. of Colorado
Can one use Gauss' law to simply compute the value of the
electric field at arbitrary points outside the charged cube?
• Correct : “It cannot be used to simply calculate the E
field because over the outer box, E is not constant so
the E × da cannot be replaced with EA.”
ò
• Incorrect - over generalize from highly symmetric
charge distributions: “Since the two are the same
type of surfaces they will have the same normal
vectors you could easily calculate the |E| for both
surfaces”
• Incorrect – messy rather than impossible: “I don’t
think so. It probably wouldn’t be “simple” because
there’s no easy symmetry that allows E to be pulled
out of the integral, so it’d be mess. Perhaps
someone with crazy math skills could.”
AAPT 2010
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Univ. of Colorado
Answers from a recent transformed E&M
class
All 4 students
interviewed gave this
type of explanation for a
different question.
Other, 5%
Incorrect messy ;
36%
Common intro-level
difficulty observed by
Singh. (AJP 2006)
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Correct, 37%
Incorrect generalized, 22%
Univ. of Colorado
Indicates?
• Students not yet familiar with solving inverse
problems - sometimes not possible to solve
• Students are not thinking through the problem
(interviews indicate maybe not this)
• Students at the upper division have faith that
there is a fancy math trick for every problem
• Your ideas?
AAPT 2010
Dealing with Mathematical Difficulties
in Lower and Upper Division Physics
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
• accessing math tools
Examples:
• Gauss’s Law
– Precise symmetry arguments
– Inverse problems
– Impossible vs. difficult
• Vector Fields
– Making meaning of div, grad, curl
– Magnitude and direction
• Potential
Univ. of Colorado
Students in interviews struggle to make
complete symmetry arguments
• Two types of arguments used by experts:
– Geometry: invariant to rotations/translations
– Superposition: Add-up E from symmetric pieces
• Which do students prefer? Do they use both?
Are they proficient?

∞
∞
Univ. of Colorado
Students in interviews struggle to make
complete symmetry arguments
• Two types of arguments used by experts:
– Geometry: invariant to rotations/translations
– Superposition: Add-up E from symmetric pieces
• Students in interviews seem to predominantly
use superposition

– Even when not applicable ∞
– May lead to problems assessing novel charge
distributions
Univ. of Colorado
∞
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
Examples:
• Gauss’s Law
(PERC paper
and poster)
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• accessing math tools
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
Examples:
• Gauss’s Law
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• accessing math tools
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
Examples:
• Gauss’s Law
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• accessing math tools
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
Common Mathematical Difficulties:
• set up and interpret
results
• connect math to
physical situation
Examples:
• Gauss’s Law
– Inverse problems
– Precise symmetry
arguments
– Impossible vs. difficult
• Vector Fields
• accessing math tools
– Making meaning of div,
grad curl
– Magnitude and direction
• Potential
Univ. of Colorado
Arguments against upper-div
clickers
• Chews up time
Ideas are complex
• Discussion easy in small classes
Students can still hide
• Students are sophisticated learners
Clickers used to aid learning
• Students may resist
But perhaps only initially…
• Extra effort for faculty
Question banks available if you want to try
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
???
What do upper-division students think?
Code
Positives
Improved mastery
Type of Activity
APS ‘10
# of responses*
(out of 70)
%
64
91%
35
31
50%
44%
Wh
Upper-Level Course Transformation
Univ. of Colorado
“Clicker questions encourage me to pay attention in class as well as help me to come to firm
understanding of material through argument.”
“They were useful because they were challenging but used the knowledge we just learned in the
lecture portion. They are a great way to go from hearing the information to actually using the
information.”
“It helps a lot to be able to check your understanding of the concepts before moving on to the
next, especially when we're going over complex topics that we may not have seen before. Also,
discussing the topic with others, as we did when a clicker question was posed, is a great way to
develop intuition and stay focused.”
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
What do upper-division students think?
Code
# of responses*
(out of 70)
%
64
91%
35
31
44
20
20
18
50%
44%
63%
29%
29%
26%
16
23%
Positives
Improved mastery
Type of Activity
Active processing/activity
Discussion with others
Feedback to students
Time/pause to think, OR Immediacy
Engagement
Wh
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Preferred types of questions
N=4 courses, 66 students
How useful for learning?
91%
35%
36%
18%
Very useful
Useful
Somewhat useful
Types of clicker questions:
Mostly useless
Challenging conceptual
Recalling a previous fact
Completely useless
Recalling a recent fact
Plugging numbers into equation
% of students 0% 10% 20% 30% 40% 50% 60%
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
Student Difficulties
•
•
•
•
•
•
•
•
•
•
•
•
Surface and line integrals
Curvilinear coordinates (esp. cylindrical)
Recognizing and exploiting symmetry
Divergence and Stokes’ Theorems (visualizing, using)
Script-r and notation
Laplace’s Equation (what is it?)
Applicability of solution methods
Following through steps of Sep of Variables
Recognizing boundary conditions
What is a dielectric? What is bound charge/current?
What is D? H? A?
Volume and surface currents (calculating, visualizing)
APS ‘10
Upper-Level Course Transformation
Univ. of Colorado
3310 Results (CUE)
90
80
Post-Test
Gain
70
60
50
40
30
20
10
0
N=493
UMd ‘11
Physics Education Research-Based
Courses (PER)
Standard Lecture-Based Courses
(STND)
Univ. of Colorado
1120 BEMA pre/post
20
PreF04
18
PreS05
PostF04
PostS05
% of students
16
14
12
g(F04) = .44+/- .01 g(S05)=.43+/- .01
10
8
6
4
2
0
0
6 12 18 24 30 36 42 48 55 61 67 73 79 85 91 97
Score (%)
F04 (N=319) Post: 59%
S05 (N=232): 59%
Univ. of Colorado
1120 BEMA LA’s
TA(post)
(post)
TA(pre)
(pre)LA
LA
LA2
(post)
NCSU post
CU
upper
division (trad)
NCSU
honors,
CMU trad post
Univ. of Colorado