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Modeling Beyond Modeling Beyond Mechanics:Mechanics:

The Modeling Version of The Modeling Version of CASTLECASTLE

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What is CASTLE?What is CASTLE?A Bit of History.A Bit of History.

CCapacitorapacitor

AAided ided

SSystem ystem for for

TTeachingeaching & &

LLearning earning

EElectricitylectricity

Developed byDeveloped by Project Director: Melvin S. Steinberg,

Smith College, Editor:

Camille Wainwright Pacific University

AuthorsAuthors IncludedIncluded:: 12 high school

teachers. 4 community

college or university faculty.

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Original CASTLE Original CASTLE PhilosophyPhilosophy

Many physics teachers are converted biologist Many physics teachers are converted biologist or chemistsor chemists

Because of their lack of experience with Because of their lack of experience with ‘electricity’, their comfort level is LOW.‘electricity’, their comfort level is LOW.

Therefore:Therefore:• They do minimal treatments of electricity.They do minimal treatments of electricity.• They do little in the way of lab work.They do little in the way of lab work.• They still have many naïve conceptions about They still have many naïve conceptions about

electricity.electricity.

Something needed to be done.Something needed to be done.

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CASTLE:CASTLE:Electricity VisualizedElectricity Visualized

Funded by NSF Grant MDR-9050189Funded by NSF Grant MDR-9050189 Contains instructional materials, homework and Contains instructional materials, homework and

quizzes.quizzes. Emphasizes:Emphasizes:

• Hands-on Investigations.Hands-on Investigations.• Targets common naïve conceptions.Targets common naïve conceptions.• Fosters development of effective causal Fosters development of effective causal

models of charge and its flow in DC circuits.models of charge and its flow in DC circuits.• Allows models to break down and Allows models to break down and

demonstrates the need for revising the model.demonstrates the need for revising the model.

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How is CASTLE different How is CASTLE different from Traditional E&M from Traditional E&M Curricula?Curricula?

• Starts with circuits rather than electrostaticsStarts with circuits rather than electrostatics• Follows a more historical development of Follows a more historical development of

concepts:concepts:– Ben Franklin’s single ‘flavor’ of charge rather Ben Franklin’s single ‘flavor’ of charge rather

than ‘+’ and ‘-’than ‘+’ and ‘-’– Alessandro Volta’s conception of electric pressureAlessandro Volta’s conception of electric pressure

• Avoids use of ‘jargon’ in place of more Avoids use of ‘jargon’ in place of more meaningful terms:meaningful terms:– flow rate rather than currentflow rate rather than current– electric pressure difference rather than voltageelectric pressure difference rather than voltage

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How is CASTLE different?How is CASTLE different?(cont.)(cont.)

• Avoids equations and quantitative Avoids equations and quantitative problem solving.problem solving.

• Emphasizes qualitative reasoning and Emphasizes qualitative reasoning and proportional thinking. proportional thinking.

• Emphasizes the development of Emphasizes the development of operational definitionsoperational definitions

• Uses multiple representational tools Uses multiple representational tools to facilitate abstract reasoning. to facilitate abstract reasoning.

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The Pro’s & Con’s of the The Pro’s & Con’s of the Original CASTLE Program.Original CASTLE Program.

Constructivist Approach:Constructivist Approach:• Hands on ActivitiesHands on Activities• Guided DiscoveryGuided Discovery

A Complete Package:A Complete Package:• Intructional Materials for StudentsIntructional Materials for Students• Matching Teachers Manual with answer keys and Matching Teachers Manual with answer keys and

additional resources.additional resources.• Commonly available materials except for Commonly available materials except for

CAPACITORS.CAPACITORS. Qualitative Conceptual ApproachQualitative Conceptual Approach

• Minimal use of numbers which intimidate novicesMinimal use of numbers which intimidate novices• Emphasizes qualitative conceptual understanding over Emphasizes qualitative conceptual understanding over

quantitative solutions.quantitative solutions.

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The Pro’s & Con’s of the The Pro’s & Con’s of the Original CASTLE Program.Original CASTLE Program.

From a Modeling Perspective:From a Modeling Perspective: Too guidedToo guided

• Each step is layed out in manual for Each step is layed out in manual for the student to follow.the student to follow.

• Commentaries allow students to read Commentaries allow students to read ahead and make “post”-dictions ahead and make “post”-dictions rather than predict and experience.rather than predict and experience.

• Model building, evaluation and Model building, evaluation and revision is present, but not a primary revision is present, but not a primary focus.focus.

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The Modeling Version of The Modeling Version of CASTLE:CASTLE:

Fundamental Differences:Fundamental Differences:• More open ended investigationsMore open ended investigations• More distinction between model More distinction between model

development, deployment, evaluation development, deployment, evaluation and revision.and revision.

• Greater emphasis on using multiple Greater emphasis on using multiple representational tools. representational tools.

• Central focus of all activities is Central focus of all activities is modeling of observed behaviors. modeling of observed behaviors.

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What are the Models?What are the Models?

The Closed Loop Model.The Closed Loop Model. Charge is a Fluid.Charge is a Fluid. A Model for Resistance to Charge FlowA Model for Resistance to Charge Flow Charge is a Compressible Fluid.Charge is a Compressible Fluid.

Footnote: The original CASTLE Materials further develop Footnote: The original CASTLE Materials further develop models to address electrostatic behaviors and models to address electrostatic behaviors and

electromagnetic interactions.electromagnetic interactions.

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What are the Models?What are the Models?(continued):(continued):

The Closed Loop Model:The Closed Loop Model:• Identifies the need for a continuous Identifies the need for a continuous

conducting path for bulbs to light.conducting path for bulbs to light.• Accounts for fact that conductors allow bulb Accounts for fact that conductors allow bulb

lighting but insulators don’t.lighting but insulators don’t.• Identifies the path through the sockets and Identifies the path through the sockets and

bulbs which cause bulb lighting.bulbs which cause bulb lighting.• Identifies that both ends of the battery must Identifies that both ends of the battery must

be in the circuit for bulbs to light.be in the circuit for bulbs to light.

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What are the Models?What are the Models?(continued):(continued):

Charge is a Fluid Model: (like water)Charge is a Fluid Model: (like water)• Charge moves around the loop.Charge moves around the loop.• The battery is like a pump which pushes the The battery is like a pump which pushes the

charge around the loop.charge around the loop.• Charge moves in the same direction in all the Charge moves in the same direction in all the

wires.wires.• The same amount of charge is moving The same amount of charge is moving

through all the wires.through all the wires.• Charge is already present in all the Charge is already present in all the

conductors in the circuit. conductors in the circuit.

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What are the Models?What are the Models?(continued):(continued):

The Resistance to Charge Flow Model:The Resistance to Charge Flow Model:• Not all conductors are created equally. Not all conductors are created equally. • Some conductors are better than others.Some conductors are better than others.• Some conductors have ‘constrictions’ which Some conductors have ‘constrictions’ which

reduce the rate of charge flow through them.reduce the rate of charge flow through them.• These restrictions are related to the thickness These restrictions are related to the thickness

and length of the conductor.and length of the conductor.

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What are the Models?What are the Models?(continued):(continued):

Charge is a Compressible Fluid:Charge is a Compressible Fluid:• Charge behaves more like air than water.Charge behaves more like air than water.• By compressing or depleting the amount of By compressing or depleting the amount of

charge in a conductor the pressure is raised or charge in a conductor the pressure is raised or lowered respectively. lowered respectively.

• Charge flows from region of higher to regions of Charge flows from region of higher to regions of lower pressures. lower pressures.

• Capacitor charging stops because the electric Capacitor charging stops because the electric pressure difference across the capacitor pressure difference across the capacitor matches the pressure difference across the matches the pressure difference across the battery.battery.

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The Story Line: Unit IThe Story Line: Unit I

• Activities 1-4 develop the idea that a Activities 1-4 develop the idea that a continuous path of conductors including both continuous path of conductors including both ends of a battery are the essential elements ends of a battery are the essential elements required to cause bulb lighting. required to cause bulb lighting.

• Worksheets 1 & 2 provide opportunities to Worksheets 1 & 2 provide opportunities to deploy this model. deploy this model.

• Activity 5 uses compasses to provide Activity 5 uses compasses to provide evidence of activity in the wires. evidence of activity in the wires.

• Because deflection depends battery Because deflection depends battery orientation, there is strong evidence that flow orientation, there is strong evidence that flow is circuital.is circuital.

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The Story Line: Unit IIThe Story Line: Unit II

• After introducing electrical schematics, Activity After introducing electrical schematics, Activity 1 introduced the capacitor. 1 introduced the capacitor.

• The capacitor is used extensively to confront The capacitor is used extensively to confront several naive conceptions:several naive conceptions:– The requirement for an ‘insulator-free’ circuit. (bulbs The requirement for an ‘insulator-free’ circuit. (bulbs

light with insulator present in circuit.)light with insulator present in circuit.)– The non-battery origin of charge. (bulbs down stream The non-battery origin of charge. (bulbs down stream

of the capacitor still light.)of the capacitor still light.)– The need for a battery to cause charge flow. (bulbs The need for a battery to cause charge flow. (bulbs

light during discharge with no battery in the circuit.)light during discharge with no battery in the circuit.)

• Hand crank generators (Genecons) reinforce Hand crank generators (Genecons) reinforce the non-battery origin of charge & introduce the non-battery origin of charge & introduce energy. energy.

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The Story Line: Unit II The Story Line: Unit II (continued)(continued)

• Activity 4 asks the question “How is an Activity 4 asks the question “How is an air circuit analogous to an electrical air circuit analogous to an electrical circuit?” and introduces the Air Capacitor.circuit?” and introduces the Air Capacitor.

• While students are allowed to continue to While students are allowed to continue to use a “charge is like water” analogy, the use a “charge is like water” analogy, the air analogy is seeded by this activity. air analogy is seeded by this activity.

• This unit ends with a worksheet where This unit ends with a worksheet where students can practice articulating the students can practice articulating the fluid model in terms of the air analogy. fluid model in terms of the air analogy.

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The Story Line: Unit IIIThe Story Line: Unit III

• Activity 1 introduces higher resistance Activity 1 introduces higher resistance long bulbs. Students examine the long bulbs. Students examine the different lighting times during capacitor different lighting times during capacitor charging and discharging. charging and discharging.

• Students examine long and round bulb Students examine long and round bulb filaments under magnification to see that filaments under magnification to see that thickness and length are key difference thickness and length are key difference between the filaments.between the filaments.

• Students then examine and practice Students then examine and practice analyzing series and parallel analyzing series and parallel combinations of resistors.combinations of resistors.

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The Story Line: Unit III The Story Line: Unit III (continued)(continued)

• Representational tools for flow rate and bulb Representational tools for flow rate and bulb brightness are introduced:brightness are introduced:

– flow rate is represented by arrow with increasing flow rate is represented by arrow with increasing numbers of tails to show increasing flow rates. numbers of tails to show increasing flow rates.

– bulb rays or starbursts are used to represent bulbs bulb rays or starbursts are used to represent bulbs brightness with increasing numbers of rays to show brightness with increasing numbers of rays to show increasing brightness.increasing brightness.

STANDARD GREATESTNon-zero but insignificant

STANDARD BRIGHTESTDIMMESTOUT

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The Story Line: Unit IV The Story Line: Unit IV

– By adding a second battery pack to a By adding a second battery pack to a circuit which contains an charged circuit which contains an charged capacitor, students are forced to confront capacitor, students are forced to confront the limitations of the ‘charge is like the limitations of the ‘charge is like water’ analogy.water’ analogy.

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The Story Line: The Story Line: Unit IV (continued)Unit IV (continued)

• Since the bulbs do light a second time, Since the bulbs do light a second time, charge needs to be compressible like air charge needs to be compressible like air rather than imcompressible like water. rather than imcompressible like water.

• The activities and readings lead students to The activities and readings lead students to conclude:conclude:– electric pressure is due to the compression or electric pressure is due to the compression or

depletion of charge in a conductor. depletion of charge in a conductor. – charge flows due to differences in electric pressure.charge flows due to differences in electric pressure.– capacitor charging stops when the pressure capacitor charging stops when the pressure

difference across the capacitor is equal to the difference across the capacitor is equal to the pressure difference across the battery.pressure difference across the battery.

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The Story Line: The Story Line: Unit IV (continued)Unit IV (continued)

• This unit also introduces a new This unit also introduces a new representational tool: Color coding. representational tool: Color coding.

RED Highest above Normal

ORANGE Above Normal

YELLOW Normal

GREEN Below Normal

BLUE Lowest below Normal.

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The Story Line: The Story Line: Unit IV (continued)Unit IV (continued)

• Color coding permits students to Color coding permits students to represent electric pressure at different represent electric pressure at different points in circuits. points in circuits.

• By examining the pressure differences By examining the pressure differences across various circuit elements, students across various circuit elements, students can better identify the causal can better identify the causal relationship between resistance and flow relationship between resistance and flow rate. rate.

• Once again, this is a non-quantitative Once again, this is a non-quantitative tool which allows for qualitative tool which allows for qualitative reasoning of many non-trivial problems. reasoning of many non-trivial problems.

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The Story Line: Unit VThe Story Line: Unit V

• This unit is essentially a whole set of This unit is essentially a whole set of deployment activities in which the deployment activities in which the compressible fluid model is used to compressible fluid model is used to explain:explain:– how pressure is reached in wires not how pressure is reached in wires not

directly connected to a battery.directly connected to a battery.– what happens during transients and how what happens during transients and how

steady state is achieved. steady state is achieved. – why batteries die due to the build up of why batteries die due to the build up of

internal resistance. internal resistance.

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Unit VI Sequence:Unit VI Sequence:

• This unit introduces voltmeters This unit introduces voltmeters and ammeters. and ammeters.

• Quantifies pressure difference Quantifies pressure difference and flow rates. and flow rates.

• Confirms the predictions from Confirms the predictions from color coding, flow rate arrow tails color coding, flow rate arrow tails and bulb brightness rays. and bulb brightness rays.

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How is the Modeling How is the Modeling Version Different?Version Different?

Less directed:Less directed:• Experiments are developed in a Socratic Experiments are developed in a Socratic

dialogue vs. presented in writing. dialogue vs. presented in writing. • Prediction are elicited prior to activity.Prediction are elicited prior to activity.• Conclusions are discussed rather than Conclusions are discussed rather than

read from a handout. read from a handout. More open ended:More open ended:

• Students are free to develop their own Students are free to develop their own procedures. procedures.

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How is the How is the Modeling Version Modeling Version Different?Different?

How are we less How are we less directed but still directed but still maintaining the maintaining the focus?focus?

The “Vee-Diagram”The “Vee-Diagram”• Reduced paper workReduced paper work

– In the Original In the Original CASTLE Manual this CASTLE Manual this activity takes up activity takes up almost three pages.almost three pages.

Name

Date Pd

CASTLE Unit 1: Activity 5

Describe the relative strength ofelectrical activity in each wire as

indicated by the compass.

Describe the direction of charge motion ineach wire as indicated by the compass.

Describe the direction of charge motion ineach wire when the battery pack is reversed.

Predict the relative strength ofelectrical activity in each wire.e.g. A = B, B < C

Predict the direction of chargemotion in each wire bydrawing arrows on thediagram above.

What would be the effect ofreversing the battery pack onthe motion of charge?

Prediction(s) Observation(s)

Conclusion:

Consensus:

What does a compass tellyou about what is

happening in the wires?

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How is the How is the Modeling Version Modeling Version Different?Different?

Name

Date Pd

CASTLE Unit 1: Activity 5

Describe the relative strength ofelectrical activity in each wire as

indicated by the compass.

Describe the direction of charge motion ineach wire as indicated by the compass.

Describe the direction of charge motion ineach wire when the battery pack is reversed.

Predict the relative strength ofelectrical activity in each wire.e.g. A = B, B < C

Predict the direction of chargemotion in each wire bydrawing arrows on thediagram above.

What would be the effect ofreversing the battery pack onthe motion of charge?

Prediction(s) Observation(s)

Conclusion:

Consensus:

What does a compass tellyou about what is

happening in the wires?

The “Vee-Diagram”The “Vee-Diagram”• Provides a focus Provides a focus

questionquestion• Provides space for Provides space for

predictionspredictions• Provides space for Provides space for

student conclusionstudent conclusion• Also space for Also space for

consensus from the post consensus from the post activity discussion.activity discussion.

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In Conclusion:In Conclusion:

CASTLE is an activity based, guided inquiry CASTLE is an activity based, guided inquiry approach to electricity which starts with approach to electricity which starts with circuits, (rather than electrostatics.)circuits, (rather than electrostatics.)

Both versions use multiple representation tools Both versions use multiple representation tools to facilitate learning:to facilitate learning:• bulb rays/starbursts for brightness.bulb rays/starbursts for brightness.• arrows with multiple tails for flow ratearrows with multiple tails for flow rate• color coding to represent electric pressure. color coding to represent electric pressure.

Both versions emphasize the construction, Both versions emphasize the construction, deployment and revision of the causal model deployment and revision of the causal model to explain the behavior of charge. to explain the behavior of charge.

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In Conclusion: (continued)In Conclusion: (continued)

The Modeling Version closely follows the The Modeling Version closely follows the storyline of the original version of storyline of the original version of CASTLE with a few minor exceptions. CASTLE with a few minor exceptions.

The Modeling Version reduces the The Modeling Version reduces the volume of paper consumed by focusing volume of paper consumed by focusing activities on Vee diagrams.activities on Vee diagrams.

The Modeling Version puts greater The Modeling Version puts greater emphasis on the development and use emphasis on the development and use of models. of models.