Transcript SAMPLE EXAMS: Do They Help or Do They Hinder the

Resources in Understanding
Electromagnetism: Building a
Conceptual Bridge for Physics
Learners and Teachers
Carolann Koleci
Assistant Professor of Physics
Worcester Polytechnic Institute
Department of Physics
[email protected]
Friday, May 2, 2008
University at Albany, SUNY
PRELUDE
Ask yourself a question
Is it what, where, or why?
Solving problems requires inquiry
So why not give it a try.
2
Worcester Polytechnic Institute
Why is Physics Perceived as
Difficult?
3
Fox Trot Cartoon Strip, by: Bill Amend
Worcester Polytechnic Institute
HERE’S WHAT REALLY
HAPPENED…
4
Worcester Polytechnic Institute
Never Underestimate Creativity
lim [ 1/(t – 8) ] = ∞
t→8
Now what do you get
for:
lim [1/(t – 4) ] =
t→4
5
Worcester Polytechnic Institute
ORGANIZATION
•
•
•
•
•
•
Theory/Statement of the Problem
Learning Resources in EM
Assessment Tools
Pilot Study at WPI (Spring 2006)
Current Results (some excerpts)
Future Directions
6
Worcester Polytechnic Institute
ACKNOWLEDGMENT
• Special thanks to Prof. John Belcher, Prof.
Sen-Ben Liao, Prof. Peter Dourmashkin,
Prof. Sahana Murthy, and the MIT
Visualizations Team for their inspiration,
collaboration, and support.
• We kindly acknowledge support from the
Davis Foundation and the NSF.
• Thank you to UAlbany (Department of
Physics) for the opportunity to share our
work.
7
Worcester Polytechnic Institute
STATEMENT OF THE PROBLEM
• “I read the book, take notes on the
chapter, attend all lectures and
recitations, do all of the sample
problems from the book, and get
‘good’ grades on my homework, yet I
still cannot do well on the exams.”—
anonymous introductory physics
student
8
Worcester Polytechnic Institute
EM Road Blocks (excerpts)
• Electricity flows like water in a pipe
to the receiver. Only needs one wire.
• Electrons flow at the speed of light.
• Electric companies supply electrons
to your house.
• Magnets only attract.
• Magnets only attract to iron.
• Only magnets have magnetic fields.
Worcester Polytechnic Institute
9
More Impediments
• The Three Principles of EM: V = IR,
I = V/R, R = V/I
• Coulomb Syndrome
• Students accept the existence of a
cause only when they can imagine an
effect (i.e. to calculate E, only need
q(enc) )
• When the RHR becomes the LHR
10
Worcester Polytechnic Institute
Learning Resources in EM
• Physlets; Belloni & Christian; Davidson
College:
http://webphysics.davidson.edu/cise_qm/
• PHysics Education Technology Project
(PHET); University of Colorado (Boulder):
http://www.colorado.edu/physics/Educatio
nIssues/research/research_projects.htm
• Technology Enabled Active Learning
(TEAL); MIT:
http://web.mit.edu/8.02t/www/802TEAL3D/
visualizations/electrostatics/index.htm
11
Worcester Polytechnic Institute
ON CREATING EXAMS…
What it is that a test item measures (that is,
its content validity) depends not on what
adult experts or critics think it measures
nor on what item statistics suggest about
the item but rather on how individual testtakers perceive and react to the test or
item.... To delve into what it is that a test
or test item measures for particular testtakers requires some kind of observation
or communication with them on an
individual basis (Haney & Scott).
Worcester Polytechnic Institute
12
ON CREATING EXAMS…
Likewise, students' classroom experiences play
into their perceptions and response to the
fairness of testing. Reporting on her
interviews with students, Thorkildsen (1999)
found that their judgment of how much testing
is fair had to do, in part, with the curriculum
and instruction they experienced on a day-today basis. Consequently, those taking a test
that differs radically in mode or content from
their classroom learning may respond
negatively to the test itself, especially if the
test does not allow them to demonstrate what
13
they know how to do.
Worcester Polytechnic Institute
LEARNING AND TRANSFER
“Learning often cannot be translated
into a generic form until there has
been enough mastery of the
specifics of the situation to permit
the discovery of lower order
regularities which can then be
recombined into higher-order, more
generic coding systems.”—Jerome
Bruner, Going Beyond the
Information Given (1973)
Worcester Polytechnic Institute
14
LEARNING
• Thorndike, Woodworth, et al. were among
the first to use transfer tests to examine
assumptions about learning (1901)
• Initial learning is necessary for transfer
• Knowledge that is overly contextualized
can reduce transfer
• Transfer is an active, dynamic process All
new learning involves transfer based on
previous learning
Mestre et al., Rebello et al., etc.
Worcester Polytechnic Institute
15
FACTORS THAT INFLUENCE
TRANSFER
• Time on Task (e.g. Garner 1974)
• Motivation to Learn (e.g. Schwartz et
al., 1999)
• Context (e.g. Lave, 1988)
• Problem Representations (e.g. Spiro
et al., 1991)
• Relationship between Learning and
Transfer Conditions (e.g. Brown
1986)
16
Worcester Polytechnic Institute
Assessment Tools in E&M
• CSEM: Conceptual Survey in Electricity
and Magnetism; Hieggelke, Maloney,
O’Kuma, Van Heuvelen
• DEEM: Diagnostic Exam in Electricity and
Magnetism; Marx
• DIRECT: Determining and Interpreting
Resistive Electric Circuits Concepts
Test ; Engelhardt and Beichner
• BEMA: Brief Electricity and Magnetism
Assessment; Ding, Chabay, Sherwood,
Beichner
Worcester Polytechnic Institute
17
18
Worcester Polytechnic Institute
DEEM
To fill the need for a tool testing introductory, undergraduates' knowledge of
basic concepts in electricity and magnetism (EM), the investigator has
developed a sixty-six item, multiple-choice diagnostic exam (DEEM). The
exam is intended to provide physics instructors with a psychometrically
sound instrument that serves three general purposes: (1) gauge students'
pre-instructional knowledge (baseline assessment), assess students' postinstructional achievement, and provide scores to determine students'
conceptual learning gains; (2) yield results that are maximally diagnostic
to instructors by highlighting students' most common misconceptions and
reveling patterns of responses which are easily interpreted by physics
instructors; and (3) provide the physics education research community
with a tool to measure the relative effectiveness of various curricula.
The exam covers the following basic concepts of EM: forces on charged
particles in electric or magnetic fields; properties of electric fields and
magnetic fields; properties of electrostatic potential and potential energy;
Maxwell's Equations; and induction, with Lenz's Law. Items comprising the
DEEM do not require calculus, explicit calculations, or memorization of
fundamental constants; are pictorially based; and generally explore highsymmetry scenarios.
Reference: http://www.compadre.org/per/items/detail.cfm?ID=3786
Worcester Polytechnic Institute
19
20
Worcester Polytechnic Institute
BEMA
Evaluating an electricity and magnetism assessment tool: Brief
electricity and magnetism assessment
written by Lin Ding, Ruth Chabay, Bruce Sherwood, and Robert J.
Beichner
The Brief Electricity and Magnetism Assessment (BEMA), developed
by Chabay and Sherwood, was designed to assess student
understanding of basic electricity and magnetism concepts
covered in college-level calculus-based introductory physics
courses. To evaluate the reliability and discriminatory power of
this assessment tool, we performed statistical tests focusing both
on item analyses (item difficulty index, item discrimination index,
and item point biserial coefficient) and on the entire test (test
reliability and Ferguson's delta). The results indicate that BEMA is
a reliable assessment tool.
Physical Review Special Topics - Physics Education Research:
Volume 2, Issue 1, Pages 7
Reference: http://prst-per.aps.org/abstract/PRSTPER/v2/i1/e010105
Worcester Polytechnic Institute
21
Pilot Study at WPI (Spring 06)
• Sophomore/Junior Level Course in
Electricity and Magnetism at the level
of Griffiths (N = 26: Frsh=4,
Soph=18, Jr=2, Sr=2)
• 85% class = PH majors; 15% = ECE
majors
• Female = 5 (19%), male = 21 (81%)
22
Worcester Polytechnic Institute
Course Background
• Vector/Tensor Analysis is a
prerequisite for the course
• Material Discussed: Griffiths,
Chapters 1,2,3,5
• 2/3 of HW is traditional, 1/3 are
visualizations in the
MasteringPhysics framework (MP
problems done in special classroom)
23
Worcester Polytechnic Institute
24
Worcester Polytechnic Institute
Hint for Question One
25
Worcester Polytechnic Institute
26
Worcester Polytechnic Institute
27
Worcester Polytechnic Institute
28
Worcester Polytechnic Institute
29
Worcester Polytechnic Institute
30
Worcester Polytechnic Institute
31
Worcester Polytechnic Institute
32
Worcester Polytechnic Institute
33
Worcester Polytechnic Institute
34
Worcester Polytechnic Institute
Problem One (35 points): As shown in the diagram below, a rod of length L
consists of a uniform line charge λ. (a) With V = 0 at infinity, what is V at P?
(10 points) (b) On the diagram below, for the situation described in part (a),
sketch the direction of the net electric field at point P (5 points). (c)
Problempotential,
One (35 points):
in the
a rodcharge
of length L consists
of a is
Determine the electric
V,Asatshown
point
P,diagram
if thebelow,
linear
density
uniform line charge λ
V = 0 at infinity, what is V at P? (10 points) (b) On the diagram
non-uniform and obeys
relationship
λ =(a),cx,
where
c isofatheconstant
having
below, for the
the situation
described in part
sketch
the direction
net electric field
at point
P
(5
points).
(c)
Determine
the
electric
potential,
V,
at
point
P,
if
the
linear
charge
density
is
units of charge per
length
squared
(15
points).
(d)
Set
up,
but
do
not
non-uniform and obeys the relationship λ = cx, where c is a constant having units of charge per
evaluate, an expression
for(15the
electric
P,anfor
the situation
length squared
points).
(d) Set up,field
but doat
notPoint
evaluate,
expression
for the electric field
at Point P, for the situation described in part (c). (5 points)
described in part (c).
(5 points)
.
(
a
)
W
i
t
h
35
Worcester Polytechnic Institute
Problem Three: Short Answer Questions: Please answer the following
possibly unrelated questions, using a minimum of mathematics (5 points
each, 30 points total).
a.
We give below three possible expressions for the z
(vertical) component of the electric field at point P, Ez. Which one of
these is correct? The circular loop has radius r and carries a
uniform line charge λ.
i.) Ez = (2πr)(λ/(4πεo)) [z/(z2 + r2 )5/2 ]
ii.) Ez = (πr)(λ/(4πεo)) [1/(z2 + r2 ) ]
iii.) Ez = (2πr)(λ/(4πεo)) [z/(z2 + r2 )3/2 ]
36
Worcester Polytechnic Institute
Preliminary Data
Average
(%)
Standard
Deviation
Mastering Physics Assignment
80
14
Traditional Homework Assignment
86
8
Exam Two
85
13
Exam Two, Question One
89
17
Exam Two, Question Three, Part A
99
0.39
Student Ranked Degree of Helpfulness***
2.96
0.87
37
Worcester Polytechnic Institute
***Likert Scale: 1-5
Correlation Matrix****
(1)
(2)
(3)
(4)
Variables
(1) MasteringPhysics Assignment
1.00 0.41 0.37 0.26
(2) Traditional Homework Assignment
0.41 1.00 0.21 0.01
(3) Exam Two
0.37 0.21 1.00 0.81
(4) Exam Two, Question One
0.26 0.01 0.81 1.00
38
Worcester Polytechnic Institute
****Product Moment Correlation
39
Worcester Polytechnic Institute
40
Worcester Polytechnic Institute
41
Worcester Polytechnic Institute
Student Feedback
“The Java applets were moderately interesting,
as were many of the visuals. However, many
of the better ones were hidden in the hints,
which the grade system encourages users to
not view.”—WPI Student
“It was a good summary of the concepts we
learned, but some of the visualizations were a
little ambiguous.”—Another WPI Student
42
Worcester Polytechnic Institute
FUTURE DIRECTIONS
MasteringPhysics and Visualizations Pilot Study is
currently ongoing at MIT. Findings?
Run more Comparison Tests: Academic Major, Gender,
Class Year, CSEM gains
Interview students at both WPI and MIT to learn specific
misconceptions and revise curricular materials as needed
Should the MasteringPhysics assignment be more
difficult than the traditional homework assignment
(addressing the context morphology issue)?
43
Worcester Polytechnic Institute
EPILOGUE
“We talk about transfer of learning when
learning is displayed in a situation
somewhat different from that in which the
original learning occurred. If the transfer
situation is so different that the use of
learning encounters some barrier or
difficulty, we speak of problem solving.
When the situation is greatly different and
the distance of transfer needed is greater
still, we speak of creativity.”—Wilbert
McKeachie, Teaching and Learning in the
College Classroom (1986).
44
Worcester Polytechnic Institute