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1 Vanderbilt Univ. ONR Project 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 ONR Contractor’s Meeting, CMU – April 2000

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2 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 Focus: BEE Course

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3 Vanderbilt Univ. ONR Project Experimental Studies Motivation n What concepts in electricity are difficult to understand and use in problem solving? n How do people use knowledge when problem solving in the domain? n What misconceptions and omissions result in problem solving errors? n What form of instruction improves understanding and avoids misconceptions?

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4 Vanderbilt Univ. ONR Project Initial Studies Protocol Analysis: DC Circuits n Problems anchored in simple flashlight circuit and its variations n Fundamentals: component roles, basic concepts n Series and Parallel: paired comparisons n 5 Watt versus 10 Watt bulb n 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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5 Vanderbilt Univ. ONR Project Classes of Difficulty that affect Learning n Failure to differentiate among concepts in domain (Bransford and Nitsch, 1978); voltage and current -- “voltage flows …”, “voltage across open switch = 0, closed switch = high” n 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. n 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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6 Vanderbilt Univ. ONR Project Classes of Difficulty that affect Learning n 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. n 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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7 Vanderbilt Univ. ONR Project Protocol Analysis Significant Findings n Difficulties result from interaction of cognitive tendencies and the domain of electricity n 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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8 Vanderbilt Univ. ONR Project Protocol Analysis Questions -simple AC concepts n 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 made longer and longer

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9 Vanderbilt Univ. ONR Project Protocol Analysis Questions -simple AC concepts n Light bulb circuit with sinusoidal versus square wave AC source -differences in power delivered n Where to place fuse in AC circuit to protect expensive bulb ? n 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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10 Vanderbilt Univ. ONR Project Protocol Analysis “Knowledge in Pieces” n 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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11 Vanderbilt Univ. ONR Project Protocol Analysis “Knowledge in Pieces” n 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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12 Vanderbilt Univ. ONR Project Protocol Analysis “Knowledge in Pieces” n 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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13 Vanderbilt Univ. ONR Project Protocol Analysis “Knowledge in Pieces” n 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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14 Vanderbilt Univ. ONR Project Protocol Analysis AC circuits: Role of components n Circuit with capacitor in parallel with light bulb (e.g., in car doors) -DC versus AC case

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15 Vanderbilt Univ. ONR Project Protocol Analysis Advanced AC concepts - Significant Findings n 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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16 Vanderbilt Univ. ONR Project Summary of conceptual difficulties with AC basics -- 2nd Semester EE Students n 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." n Temporal and graphical representations »The different positions of the sine wave are often mapped onto different positions in a wire.

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17 Vanderbilt Univ. ONR Project Basic Conceptual Difficulties (cont.) n 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." n Circuit implications »“a capacitor behaves the same in AC and DC because AC source always puts out a constant current.” n 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 ?

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18 Vanderbilt Univ. ONR Project Protocol Studies Physical Understanding of AC waveforms (Students were juniors in their 3 rd EE course) n 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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19 Vanderbilt Univ. ONR Project Protocol Studies Physical Understanding of AC waveforms n 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)? n Amplitude Modulation: addition of waveforms

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20 Vanderbilt Univ. ONR Project Protocol Studies Physical Understanding of AC waveforms: results n 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.” ) n 4 of 10 thought wire could carry only one frequency at a time. n 6 of 10 – larger amplitude waves travel further. n 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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21 Vanderbilt Univ. ONR Project Protocol Studies Physical Understanding of AC waveforms: results n Some students said, frequency = 1 / t n 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. n Same problems with inductor, but 6 of 10 said inductor would reduce flickering of light bulb in circuit. n 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

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22 Vanderbilt Univ. ONR Project Physical Understanding of AC Concepts n Students have very little understanding of underlying physical phenomena n Developing understanding of time varying characteristics of circuit components, such as capacitors and inductors are hard n Instead build up from primary relations describing time-varying behavior of components n Study how students apply these problems to circuit analysis behaviorstructure Focus: Students ability to develop behavior from structure function and link to circuit function.

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23 Vanderbilt Univ. ONR Project Protocol Studies: Function, Structure, and Behavior Analysis n Present students with simple low (high) pass filter circuit n Prompt students by guided simulation n Present students with variations of original circuit (contrasting cases)

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24 Vanderbilt Univ. ONR Project Protocol Studies: Function, Structure, and Behavior Analysis - Results n 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 n 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 n 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”) n 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. n Lot of problems with two capacitor circuit.

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25 Vanderbilt Univ. ONR Project Misconceptions Test

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26 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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27 Vanderbilt Univ. ONR Project AC Circuit Analysis: Focus on Instruction invariants topology n Instruct students to derive invariants from circuit topology Invariants 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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28 Vanderbilt Univ. ONR Project Problem Solving with Invariants n What laws apply in a given circuit situation (map structure and function to behavior) n 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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29 Vanderbilt Univ. ONR Project Assessing Student Understanding of Electrical Concepts to Inform Instructional Decisions n PROBLEM: (Mis)understanding in analysis of RLC circuits -Voltage, current and power relationships -Frequency, phase and waveforms for AC -Everyday phenomena n METHOD: Dynamic Assessment Model + Preparedness for learning -Teaching during student evaluation -Assessment of domain learnability (ADL) -Protocol and experimental evaluations n 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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30 Vanderbilt Univ. ONR Project

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31 Vanderbilt Univ. ONR Project

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32 Vanderbilt Univ. ONR Project Inductor: Web-based Self Assessment System for Learning in the AC Domain n Students choose question to answer from Test Matrix n Pick primary invariant, answer question and see results n Continual feedback allows them to evaluate their performance n Answer and reflect n Opportunity to access resources

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33 Vanderbilt Univ. ONR Project The Inductor System Test Taking Interface Matrix of questions

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34 Vanderbilt Univ. ONR Project Question: Student picks invariants Step 2, Pick right answer Student explains answer

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35 Vanderbilt Univ. ONR Project Student with Correct Answer Feedback

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36 Vanderbilt Univ. ONR Project Student with Incorrect Answer

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37 Vanderbilt Univ. ONR Project Student with Incorrect AnswerFeedback Compare Invariants Hints and pointers to resources Student reflects and revises

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38 Vanderbilt Univ. ONR Project Feedback for Incorrect Answer: Screen 3

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39 Vanderbilt Univ. ONR Project Another Question: AC Domain

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40 Vanderbilt Univ. ONR Project Feedback from Students Questionnaire

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41 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 Results: Correct answers versus correct choice of invariants Some problems: tests unequal wording of questions not enough resources

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42 Vanderbilt Univ. ONR Project Selection of Invariants Invariants -- not properly motivated Fatigue factor Yule’s Q: h – hit rate; f – false alarm rate Q=1 perfect discrimination Q=0 chance performance Results: Avg. Q when correct = 0.53, when incorrect = 0.39

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43 Vanderbilt Univ. ONR Project Invariants by Question category

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44 Vanderbilt Univ. ONR Project Invariants versus Correct Answers

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45 Vanderbilt Univ. ONR Project Next Steps n Administer Misconceptions Tests – Corry Station, Naval Academy; Analyze data to determine student understanding, potential for learning, and instructional materials n Develop Inductor – progression of problems solving modules dealing with power supplies, filters, amplifiers, and communication equipment n Perform formative and summative assessments

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46 Vanderbilt Univ. ONR Project Inductor: Dynamic Self-Assessment System Practical Problem Identify Primary Invariants Explain Answer Generate Solution Compare with expert’s solution Revise Resources

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