1 vanderbilt univ. onr project assessing student understanding of electrical concepts to inform...

1Vanderbilt Univ. ONR Project

Assessing Student Understanding of Electrical Concepts to Inform

Instructional DecisionsGautam Biswas, Dan Schwartz

Bharat Bhuva, John Bransford

Sean Brophy, Amit Verma, Doug Holton,

Jay Pfaffman

Vanderbilt University

ONR Contractor’s Meeting, CMU – April 2000


GoalInvestigate individual’s understanding and misconceptions when problem solving with

AC and DC circuits

Larger GoalLarger GoalHow to better train naval technicians for How to better train naval technicians for

maintenance, upkeep, and troubleshooting of maintenance, upkeep, and troubleshooting of complex electrical and electronic equipment complex electrical and electronic equipment

deployed by the Navydeployed by the Navy

Focus: BEE CourseFocus: BEE Course


Experimental StudiesMotivation

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?


Initial StudiesProtocol 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 lightSchwartz, Biswas, et al., “Computer Tools that link assessment and instruction:Investigating what makes electricity hard to learn.”


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?


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.


Protocol AnalysisSignificant 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 learningelectricity? Can they be easily remediated by instruction?


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

- what would happen if

will bulb flicker ?

wires to bulb were madelonger and longer


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 ?


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.


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



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



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


Protocol Analysis AC circuits: Role of components

Circuit with capacitor in parallel with light bulb (e.g., in car doors)- DC versus AC case


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)


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.


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”

More advanced students did not have these difficulties.But do they have a true physical understanding of AC concepts?


Protocol StudiesPhysical 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?


Protocol StudiesPhysical Understanding of AC waveforms

Voltage waveform – amplitude, frequency, power delivered to load (resistor).

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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Protocol StudiesPhysical Understanding of AC waveforms: results

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 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.


Protocol StudiesPhysical Understanding of AC waveforms: results

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 havemuch physical intuitions or knowledgeAppeal to everyday physical phenomena did not help much either.Students focus is very much on mathematical formulations and manipulation of mathematical formulations


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 behaviorbehavior from structurestructure and link to circuit functionfunction.


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)


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.


Misconceptions TestAC Misconceptions Test noqMisconceptions/Question Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21spatial waveform d bc(Q)Negative is mathematical artifact b(Q)Negative cancels dempty pipe (or current as substance) abc(Q) abd(Q) ab bc(Q)I->R same as DC a ab(Q) aCap behavior same in DC and AC bc d c d cunderstanding combined AC & DCwaveforms with multiple frequencies

failure to differentiate c a b(Q) b(Q) ab c a(Q)minimum causality bc(Q)overly local reasoningbad framingexperiential impov. a(Q)

generalized strengthground is goodstatic dischargeR impedes energyR engenders heat/energy b b

lack of Ohm's law abd(Q)lack of KCL abc(Q) abd(Q) abc(Q) ab(Q) bc(Q)lack of KVL b bcd(Q) bc ab b(Q) b(Q) ablack of power equations abd(Q) bc ab(Q)lack of knowledge about Capacitors (Q = CV) bc(Q)lack of Xc in AC & DC ac(Q) bc(Q)topographic misunderstanding (e.g., series vs. parallel) (Q) a(Q) bc(Q) a(Q)


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.


AC Circuit Analysis: Focus on Instruction

Instruct students to derive invariantsinvariants from circuit topologytopology

InvariantsInvariants 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.)


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 Goal: Deeper understanding of principles and circuit behaviorbehavior


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


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


The Inductor SystemTest Taking InterfaceMatrix of questions


Question:

Student picks invariants

Step 2, Pick right answer

Student explainsanswer


Student withCorrect Answer

Feedback


Student with Incorrect Answer


Student with Incorrect Answer

FeedbackFeedback

Compare Invariants

Hints and pointersto resources

Student reflectsand revises


Feedback for Incorrect Answer: Screen 3


Another Question:AC Domain


Feedback from StudentsQuestionnaire


Inductor test -- results

Percent Correct Answers to Questions

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DC AC DCcap ACRC

Category of Question

Per

centa

ge

Corr

ect

1st test taken

2nd test taken

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

Results: Correct answers versus correct choice of invariants

Some problems:

tests unequal

wording of questions

not enough resources


Selection of Invariants for Questions

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DC AC DCcap ACRC


Yule

's Q 1st test taken

2nd test taken

Selection of InvariantsInvariants -- not properly motivated

Fatigue factor

Yule’s Q:

h – hit rate; f – false alarm rateQ=1 perfect discriminationQ=0 chance performance

Results:Avg. Q when correct = 0.53, when incorrect = 0.39

)2(

)(

ffhh

fh



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DC AC DCcap ACRC


Test A 1st

Test B 2nd


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DC AC DCcap ACRC


Test B 1st

Test A 2nd

Invariants by Question category


DC - Invariants vs. Answers (R=.33)

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Percent Correct Answers

Ave

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Yule

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AC - Invariants vs. Answers(R=.13)

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Ave

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Yule

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Capacitors - Invariants vs. Answers(R=0.0)

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Ave

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Yule

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ACRC - Invariants vs. Answers(R=.18)

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Ave

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Yule

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Invariants versus Correct Answers


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


Inductor: Dynamic Self-Assessment SystemPractical Problem

IdentifyPrimary

Invariants

ExplainAnswer

GenerateSolution

Compare withexpert’ssolution

Revise ResourcesResourcesResourcesResources

1 vanderbilt univ. onr project assessing student understanding of electrical concepts to inform...

Documents

current switch

pieces n metaphors

pieces n failure

learning n failure

onr project goal

ac circuits voltage

basic concepts n series

variations n fundamentals