Download Presentation at ONR Contractor Meeting, CMU, April 2001

Assessing Student Understanding
of Electrical Concepts to Inform
Instructional Decisions
Gautam Biswas, Dan Schwartz
Bharat Bhuva, John Bransford
Sean Brophy, Amit Verma, Doug Holton,
Jay Pfaffman
Vanderbilt University
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ONR Contractor’s Meeting, CMU – April 2000
Vanderbilt Univ. ONR Project
Goal
Investigate individual’s understanding and
misconceptions when problem solving with
AC and DC circuits
Larger Goal
How to better train naval technicians for
maintenance, upkeep, and troubleshooting of
complex electrical and electronic equipment
deployed by the Navy
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Focus: BEE Course
Vanderbilt Univ. ONR Project
Experimental Studies
Motivation
What concepts in electricity are difficult to
understand and use in problem solving?
 How do people use knowledge when problem
solving in the domain?
 What misconceptions and omissions result in
problem solving errors?
 What form of instruction improves
understanding and avoids misconceptions?

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Vanderbilt Univ. ONR Project
Initial Studies
Protocol Analysis: DC Circuits
Problems anchored in simple flashlight
circuit and its variations
 Fundamentals: component roles, basic
concepts
 Series and Parallel: paired comparisons
 5 Watt versus 10 Watt bulb
 Troubleshooting Tasks: flashlight bulb will
not light

Schwartz, Biswas, et al., “Computer Tools that link assessment and instruction:
Investigating what makes electricity hard to learn.”
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Vanderbilt Univ. ONR Project
Classes of Difficulty
that affect Learning

Failure to differentiate among concepts in domain
(Bransford and Nitsch, 1978); voltage and current -- “voltage flows
…” , “voltage across open switch = 0, closed switch = high”

Incorrect simplifying assumptions, e.g., minimum
causality error -- single change in outcome must be a result of
single change in cause (White, Frederiksen, and Sphorer, 1993); e.g., 5W
versus 10w bulb.

Overly Local Reasoning -- local propagation versus
global constraints, e.g., movement of current from point to point
-- where to insert fuse to protect components in a circuit?
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Vanderbilt Univ. ONR Project
Classes of Difficulty
that affect Learning

Bad Framing - incorrect generalizations lead to
suboptimal framing (diSessa 1993); electricity - (no single
canonical model). experts and novices switch from
equations to physical explanations to analogical models.
Novices make mistakes -- e.g., two resistors in parallel draw more
current from a battery. (Gentner and Gentner, 1983) (i) water analogy not
good; (ii) crowds pushing through gates. Good analogy for parallel resistors
(emphasis on paths), but novices think of charges pile up on one side of gate;
i.,e., flow not uniform.

Experiential Impoverishment -- electricity is
invisible except for its end products. Misconceptions
typically not a result of perceptual intuition but more because of
analogies and representational methods used.
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Vanderbilt Univ. ONR Project
Protocol Analysis
Significant Findings
Difficulties result from interaction of
cognitive tendencies and the domain of
electricity
 Student Knowledge - “In Pieces”

- Attempts to switch metaphors when impasses
occur
Question: How serious are these difficulties wrt learning
electricity? Can they be easily remediated by instruction?
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Vanderbilt Univ. ONR Project
Protocol Analysis
Questions -simple AC concepts

DC battery replaced by AC source in flashlight circuit
- explain voltage and current at different points in circuit
- effects on bulb - power delivered,
- Effect of frequency changes
will bulb flicker ?
- what would happen if
wires to bulb were made
longer and longer
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Vanderbilt Univ. ONR Project
Protocol Analysis
Questions -simple AC concepts

Light bulb circuit with sinusoidal versus square
wave AC source
- differences in power delivered

Where to place fuse in AC circuit to protect
expensive bulb ?

Series-parallel resistive circuit
- plot voltage and current waveforms at different points in
circuit
- oscilloscope reading: displaced sine wave - is it possible ?
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Vanderbilt Univ. ONR Project
Protocol Analysis
“Knowledge in Pieces”

Metaphors: Flow of electricity and Flow of water.
- Creates empty pipe misconception
» electrons take time to flow from the battery to the light bulb
» when you place two bulbs in series the second will light up after
the first one does
» (AC) since electrons just stop, turn around and go the other way,
they might never reach the light bulb, and the bulb may never
light up.
» (AC) how can current flow from one source terminal to another if
it reverses
» (fuses) in DC you place it at the top, in AC you need it at both
places.
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Vanderbilt Univ. ONR Project
Protocol Analysis
“Knowledge in Pieces”

Failure to differentiate
- the difference between voltage and current
» flow of voltage
» voltage drop through the resistor, therefore, current at one end of
resistor different from current at other end.
- sinusoidal time varying voltage and current versus
pulses (voltage and current switch on and off): AC
circuits
» voltage and current go on and off
» voltage and current switch between positive and negative
- importing DC models to explain AC
» increasing voltage implies build up of charge at terminal;
when sufficient charge accumulates, current flows . current
turns on and off.
» alternating current going through a resistor is constant in time
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Vanderbilt Univ. ONR Project
Protocol Analysis
“Knowledge in Pieces”

Incorrect Simplifying Assumptions:
minimum causality error
- using one relation to derive cause-effect
relation in problem solving and ignoring others
» a 10 Watt bulb must have greater resistance than a
5W bulb
» in an AC circuit voltage can vary sinusoidally but
current must remain constant to allow electrons to
flow from one terminal of battery to another
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Vanderbilt Univ. ONR Project
Protocol Analysis
“Knowledge in Pieces”

Experential Impoverishmnet
- in AC: flow of current to sinusoidal waveform
» sinusoidal waveform is a spatial property of
current; describes current values at different points
in the circuit
- meaning of negative current and voltage
» voltage or current cannot really be negative, the absolute
value is what is really happening; a minus sign appears in
some calculations, and you should not worry about it.
» It’s ok to have something negative - it’ll fix itself; it’s not really
a negative value
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Vanderbilt Univ. ONR Project
Protocol Analysis
AC circuits: Role of components

Circuit with capacitor in parallel with light
bulb (e.g., in car doors)
- DC versus AC case
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Vanderbilt Univ. ONR Project
Protocol Analysis Advanced AC
concepts - Significant Findings

Capacitor + light bulb
- (novices)
- capacitor is always an open circuit
- capacitor will take time to charge up (time constant =
RC)
- capacitor will behave the same in AC and DC because
battery and AC source put out constant current
- bulb will take longer to light up
- (advanced students had no trouble with this problem)
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Vanderbilt Univ. ONR Project
Summary of conceptual difficulties with
AC basics -- 2nd Semester EE Students

Physical models
» Current can’t reverse because if "electrons just stop, turn
around, and go the other way, they might never reach the
light bulb, and the bulb may never light up."

Temporal and graphical representations
» The different positions of the sine wave are often mapped
onto different positions in a wire.
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Vanderbilt Univ. ONR Project
Basic Conceptual Difficulties (cont.)

Mathematical models
» "voltage or current cannot really be negative, the absolute
value is what is really happening, a minus appears
sometimes in calculations, and you should not worry about
it."

Circuit implications
» “a capacitor behaves the same in AC and DC because AC
source always puts out a constant current.”

Physical implications of changing voltage and current
» “a DC current makes a magnet out of a coil”
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More advanced students did not have these difficulties.
But do they have a true physical understanding of AC concepts?
Vanderbilt Univ. ONR Project
Protocol Studies
Physical Understanding of AC waveforms
(Students were juniors in their 3rd EE course)

Could a radio work if the signals were
carried on a wire instead of through the air?
- Role of the transmission tower
- How is the waveform propagated
- Does the wire limit the amplitude and
frequency of the signal that can be transmitted
- Why can’t my AM radio pick up FM stations
- What if I designed an AM receiver to operate at
FM frequencies?
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Vanderbilt Univ. ONR Project
Protocol Studies
Physical Understanding of AC waveforms

Voltage waveform – amplitude, frequency, power delivered
to load (resistor).
1
0.8
0.6
0.4
0.2
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-0.2
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0
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9 10 11 12 13 14 15 16 17 18 19 20
RC and RL circuits: What happens when we vary the
frequency of the AC source in circuit B (capacitor and
inductor)?
Amplitude Modulation: addition of waveforms
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Vanderbilt Univ. ONR Project
Protocol Studies
Physical Understanding of AC waveforms: results

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8 of 10 students were confused between temporal and spatial
representation of waveform. Some tried “ripple in a pond”
metaphor to explain electromagnetic wave.
8 of 10 said you could get bigger waveform amplitudes in air. 6
of 10 thought you needed thicker wires to support larger
amplitude signals. 2 of 10: Waveform amplitude a wire
thickness. (“thicker wire has more resistance, and so amplitude of current will be
smaller.”)
4 of 10 thought wire could carry only one frequency at a time.
6 of 10 – larger amplitude waves travel further.
Higher frequency of signal implies necessarily more power
delivered. (one student “average power delivered by AC signal is zero.”). In general,
all students found it hard to compare change in power delivered
as frequency and amplitude of signal changed.
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Vanderbilt Univ. ONR Project
Protocol Studies
Physical Understanding of AC waveforms: results




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Some students said, frequency = 1 / t
Most students had difficulty expressing how a capacitor charged
and discharged with an AC voltage source. Confusion among
charge, voltage, and current. With prompting 8 of 10 students
correct reasoning for capacitor.
Same problems with inductor, but 6 of 10 said inductor would
reduce flickering of light bulb in circuit.
AM signals – 6 of 10 did not know what it means to “translate
signal to another frequency.” Two students “base and carrier frequencies are
multiplied for AM”. Some students thought TV cables had multiple
wires, one for each station.
Primary conclusions: More advanced students do not have
much physical intuitions or knowledge
Appeal to everyday physical phenomena did not help much either.
Students focus is very much on mathematical formulations and
manipulation of mathematical formulations
Vanderbilt Univ. ONR Project
Physical Understanding of AC Concepts




Students have very little understanding of
underlying physical phenomena
Developing understanding of time varying
characteristics of circuit components, such as
capacitors and inductors are hard
Instead build up from primary relations describing
time-varying behavior of components
Study how students apply these problems to
circuit analysis
Focus: Students ability to develop behavior from structure
and link to circuit function.
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Vanderbilt Univ. ONR Project
Protocol Studies: Function, Structure,
and Behavior Analysis



Present students with simple low (high) pass filter circuit
Prompt students by guided simulation
Present students with variations of original circuit
(contrasting cases)
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Vanderbilt Univ. ONR Project
Protocol Studies: Function, Structure,
and Behavior Analysis - Results

Capacitor – Resistor interactions cause confusions
- capacitor cannot fully discharge because of resistor
- resistor produces phase shift
- current through resistor and capacitor cannot be the same

Reasoned at two extreme points:
- capacitor open circuit for DC
- capacitor short circuit for AC

No idea of how to deal with frequencies in between
No confidence in circuit equations
- first wrote down capacitor current = resistor current; when challenged said that was
not correct
- wrote down mathematical equations, but often had no idea of how to apply them (“I
know a of equations and I will try them one by one and find the ones that fit”)


Concepts like phase shift and cut-off frequency very vague terms; one student
tried to get rid of frequency dependence by computing RMS values, but when
pushed did not know what RMS really meant.
Lot of problems with two capacitor circuit.
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Vanderbilt Univ. ONR Project
Misconceptions Test
AC Misconceptions Test
Misconceptions/Question Number
spatial waveform
Negative is mathematical artifact
Negative cancels
empty pipe (or current as substance)
I->R same as DC
Cap behavior same in DC and AC
understanding combined AC & DC
waveforms with multiple frequencies
failure to differentiate
minimum causality
overly local reasoning
bad framing
experiential impov.
generalized strength
ground is good
static discharge
R impedes energy
R engenders heat/energy
lack of Ohm's law
lack of KCL
lack of KVL
lack of power equations
lack of knowledge about Capacitors
(Q = CV)
lack of Xc in AC & DC
topographic misunderstanding (e.g.,
series vs. parallel)
1
2
3
d
4
bc(Q)
5
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12
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noq
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ab
c
a(Q)
b(Q)
d
abc(Q) abd(Q)
ab
a
ab(Q)
bc(Q)
a
bc
d
c
d
c
c
a
b(Q)
b(Q)
bc(Q)
a(Q)
b
b
abd(Q)
abc(Q) abd(Q) abc(Q)
ab(Q)
bc(Q)
b
bcd(Q) bc ab
bc ab(Q)
abd(Q)
b(Q)
b(Q)
ab
bc(Q)
ac(Q)
bc(Q)
(Q)
a(Q) bc(Q) a(Q)
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Vanderbilt Univ. ONR Project
Misconceptions Test
Spatial AC misconception.
Negative part of AC cycle is just a mathematical artifact.
Alternate form of this misconception. The negative current "cancels" out the
positive current.
Empty pipe misconception (similar to Chi's current as substance).
Incorrectly importing DC models to explain AC.
alternating current through a resistor is constant in time.
capacitor behaves the same in AC as in DC.
Difficulties understanding circuit behavior when AC and DC signals are
combined.
More generally have difficulty thinking of circuit behavior when
multiple waveforms, frequencies are combined.
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Vanderbilt Univ. ONR Project
AC Circuit Analysis: Focus on Instruction

Instruct students to derive invariants from circuit
topology
Invariants directly linked to conservation principles
that govern domain behavior (Kirchoff’s laws)
(in some way linked to Piaget’s experiments – subjects
unable to see conservation relations when their focus is
perception bound – experiments with pennies, liquid in
tall and wide containers, etc.)
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Vanderbilt Univ. ONR Project
Problem Solving with Invariants
What laws apply in a given circuit situation
(map structure and function to behavior)
 How to simplify analysis of situation using
these laws?

- Determine invariant parameters and variables
- Solve problems by qualitative reasoning
Goal: Deeper understanding of principles and circuit
behavior
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Vanderbilt Univ. ONR Project
Assessing Student Understanding of Electrical
Concepts to Inform Instructional Decisions

PROBLEM: (Mis)understanding in analysis of RLC circuits
- Voltage, current and power relationships
- Frequency, phase and waveforms for AC
- Everyday phenomena

METHOD: Dynamic Assessment Model + Preparedness for learning
- Teaching during student evaluation
- Assessment of domain learnability (ADL)
- Protocol and experimental evaluations

TECHNOLOGY: Software Support Development
- Software Technology for Action and Reflection (STAR-Legacy)
- Software shells for integrating multiple resources
- Simulations and interactive analogies
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Vanderbilt Univ. ONR Project
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Vanderbilt Univ. ONR Project
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Vanderbilt Univ. ONR Project
Inductor: Web-based Self Assessment System
for Learning in the AC Domain
Students choose question to answer from
Test Matrix
 Pick primary invariant, answer question and
see results
 Continual feedback allows them to evaluate
their performance
 Answer and reflect
 Opportunity to access resources

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Vanderbilt Univ. ONR Project
The Inductor System
Test Taking Interface
Matrix of questions
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Vanderbilt Univ. ONR Project
Question:
Student picks
invariants
Step 2, Pick right
answer
Student explains
answer
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Vanderbilt Univ. ONR Project
Student with
Correct Answer
Feedback
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Vanderbilt Univ. ONR Project
Student with
Incorrect Answer
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Vanderbilt Univ. ONR Project
Student with
Incorrect Answer
Feedback
Compare Invariants
Hints and pointers
to resources
Student reflects
and revises
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Vanderbilt Univ. ONR Project
Feedback for Incorrect Answer: Screen 3
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Vanderbilt Univ. ONR Project
Another Question:
AC Domain
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Vanderbilt Univ. ONR Project
Feedback from Students
Questionnaire
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Vanderbilt Univ. ONR Project
Inductor test -- results
Two tests: A and B
Four categories of questions
Students in 2 groups – one
did test A and then test B
other group did the opposite
Some problems:

tests unequal
0.9
0.8
Percentage Correct
Results: Correct answers
versus correct choice of
invariants
Percent Correct Answers to Questions
0.7
0.6
1st test taken
2nd test taken
0.5
0.4
0.3
0.2
DC

wording of questions

not enough resources
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AC
DCcap
ACRC
Category of Question
Vanderbilt Univ. ONR Project
Selection of Invariants
Invariants -- not
properly motivated
Selection of Invariants for Questions
Fatigue factor
1
0.9
0.8
Yule’s Q:
h – hit rate; f – false alarm rate
Q=1  perfect discrimination
Q=0  chance performance
Yule's Q
(h  f )
(h  2 fh  f )
0.7
0.6
1st test taken
0.5
2nd test taken
0.4
0.3
0.2
0.1
0
DC
AC
DCcap
ACRC
Category of Question
Results:
Avg. Q when correct = 0.53, when incorrect = 0.39
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Vanderbilt Univ. ONR Project
Invariants by Question category
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Vanderbilt Univ. ONR Project
Invariants versus Correct Answers
DC - Invariants vs. Answers
(R=.33)
AC - Invariants vs. Answers
(R=.13)
1
1
0.8
0.6
Average Yule's Q
Average Yule's Q
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1
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-0.6
Percent Correct Answ ers
Percent Correct Answ ers
Capacitors - Invariants vs. Answers
(R=0.0)
ACRC - Invariants vs. Answers
(R=.18)
1
1
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0.8
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0.2
0
-0.2 0
0.2
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1
Average Yule's Q
Average Yule's Q
0.4
0.4
0.2
0
-0.2
0
0.2
0.4
0.6
-0.4
-0.6
-0.6
Percent Correct Answ ers
Percent Correct Answ ers
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Vanderbilt Univ. ONR Project
Next Steps



Administer Misconceptions Tests – Corry Station,
Naval Academy; Analyze data to determine student
understanding, potential for learning, and
instructional materials
Develop Inductor – progression of problems solving
modules dealing with power supplies, filters,
amplifiers, and communication equipment
Perform formative and summative assessments
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Vanderbilt Univ. ONR Project
Inductor: Dynamic Self-Assessment
System
Practical
Problem
Compare with
expert’s
solution
Revise
Identify
Primary
Invariants
Resources
Explain
Answer
Generate
Solution
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Vanderbilt Univ. ONR Project