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Modeling Beyond Mechanics: The Modeling Version of CASTLE. C apacitor A ided S ystem for T eaching & L earning E lectricity. Developed by Project Director: Melvin S. Steinberg, Smith College, Editor: Camille Wainwright Pacific University Authors Included :

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Modeling beyond mechanics the modeling version of castle l.jpg

Modeling Beyond Mechanics:The Modeling Version of CASTLE

What is castle a bit of history l.jpg



System for

Teaching &



Developed by

Project Director:

Melvin S. Steinberg,

Smith College,


Camille Wainwright

Pacific University


12 high school teachers.

4 community college or university faculty.

What is CASTLE? A Bit of History.

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Original CASTLE Philosophy

  • Many physics teachers are converted biologist or chemists

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

  • Therefore:

    • They do minimal treatments of electricity.

    • They do little in the way of lab work.

    • They still have many naïve conceptions about electricity.

  • Something needed to be done.

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CASTLE:Electricity Visualized

  • Funded by NSF Grant MDR-9050189

  • Contains instructional materials, homework and quizzes.

  • Emphasizes:

    • Hands-on Investigations.

    • Targets common naïve conceptions.

    • Fosters development of effective causal models of charge and its flow in DC circuits.

    • Allows models to break down and demonstrates the need for revising the model.

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How is CASTLE different from Traditional E&M Curricula?

  • Starts with circuits rather than electrostatics

  • Follows a more historical development of concepts:

    • Ben Franklin’s single ‘flavor’ of charge rather than ‘+’ and ‘-’

    • Alessandro Volta’s conception of electric pressure

  • Avoids use of ‘jargon’ in place of more meaningful terms:

    • flow rate rather than current

    • electric pressure difference rather than voltage

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How is CASTLE different?(cont.)

  • Avoids equations and quantitative problem solving.

  • Emphasizes qualitative reasoning and proportional thinking.

  • Emphasizes the development of operational definitions

  • Uses multiple representational tools to facilitate abstract reasoning.

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Constructivist Approach:

Hands on Activities

Guided Discovery

A Complete Package:

Intructional Materials for Students

Matching Teachers Manual with answer keys and additional resources.

Commonly available materials except for CAPACITORS.

Qualitative Conceptual Approach

Minimal use of numbers which intimidate novices

Emphasizes qualitative conceptual understanding over quantitative solutions.

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

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From a Modeling Perspective:

Too guided

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

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

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

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

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The Modeling Version of CASTLE:

  • Fundamental Differences:

    • More open ended investigations

    • More distinction between model development, deployment, evaluation and revision.

    • Greater emphasis on using multiple representational tools.

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

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What are the Models?

  • The Closed Loop Model.

  • Charge is a Fluid.

  • A Model for Resistance to Charge Flow

  • Charge is a Compressible Fluid.

  • Footnote: The original CASTLE Materials further develop models to address electrostatic behaviors and electromagnetic interactions.

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What are the Models?(continued):

  • The Closed Loop Model:

    • Identifies the need for a continuous conducting path for bulbs to light.

    • Accounts for fact that conductors allow bulb lighting but insulators don’t.

    • Identifies the path through the sockets and bulbs which cause bulb lighting.

    • Identifies that both ends of the battery must be in the circuit for bulbs to light.

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What are the Models?(continued):

  • Charge is a Fluid Model: (like water)

    • Charge moves around the loop.

    • The battery is like a pump which pushes the charge around the loop.

    • Charge moves in the same direction in all the wires.

    • The same amount of charge is moving through all the wires.

    • Charge is already present in all the conductors in the circuit.

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What are the Models?(continued):

  • The Resistance to Charge Flow Model:

    • Not all conductors are created equally.

    • Some conductors are better than others.

    • Some conductors have ‘constrictions’ which reduce the rate of charge flow through them.

    • These restrictions are related to the thickness and length of the conductor.

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What are the Models?(continued):

  • Charge is a Compressible Fluid:

    • Charge behaves more like air than water.

    • By compressing or depleting the amount of charge in a conductor the pressure is raised or lowered respectively.

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

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

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The Story Line: Unit I

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

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

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

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

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The Story Line: Unit II

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

  • The capacitor is used extensively to confront several naive conceptions:

    • The requirement for an ‘insulator-free’ circuit. (bulbs light with insulator present in circuit.)

    • The non-battery origin of charge. (bulbs down stream of the capacitor still light.)

    • The need for a battery to cause charge flow. (bulbs light during discharge with no battery in the circuit.)

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

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The Story Line: Unit II (continued)

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

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

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

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The Story Line: Unit III

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

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

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

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Representational tools for flow rate and bulb brightness are introduced:

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

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

The Story Line: Unit III (continued)

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The Story Line: Unit IV introduced:

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

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The Story Line: introduced:Unit IV (continued)

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

  • The activities and readings lead students to conclude:

    • electric pressure is due to the compression or depletion of charge in a conductor.

    • charge flows due to differences in electric pressure.

    • capacitor charging stops when the pressure difference across the capacitor is equal to the pressure difference across the battery.

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The Story Line: introduced:Unit IV (continued)

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

RED Highest above Normal

ORANGE Above Normal


GREEN Below Normal

BLUE Lowest below Normal.

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The Story Line: introduced:Unit IV (continued)

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

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

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

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The Story Line: Unit V introduced:

  • This unit is essentially a whole set of deployment activities in which the compressible fluid model is used to explain:

    • how pressure is reached in wires not directly connected to a battery.

    • what happens during transients and how steady state is achieved.

    • why batteries die due to the build up of internal resistance.

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Unit VI Sequence: introduced:

  • This unit introduces voltmeters and ammeters.

  • Quantifies pressure difference and flow rates.

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

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How is the Modeling Version Different? introduced:

  • Less directed:

    • Experiments are developed in a Socratic dialogue vs. presented in writing.

    • Prediction are elicited prior to activity.

    • Conclusions are discussed rather than read from a handout.

  • More open ended:

    • Students are free to develop their own procedures.

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

The “Vee-Diagram”

Reduced paper work

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

How is the Modeling Version Different?

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How is the introduced:Modeling Version Different?

  • The “Vee-Diagram”

    • Provides a focus question

    • Provides space for predictions

    • Provides space for student conclusion

    • Also space for consensus from the post activity discussion.

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In Conclusion: introduced:

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

  • Both versions use multiple representation tools to facilitate learning:

    • bulb rays/starbursts for brightness.

    • arrows with multiple tails for flow rate

    • color coding to represent electric pressure.

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

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In Conclusion: (continued) introduced:

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

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

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