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Modeling Beyond Mechanics:Modeling Beyond Mechanics:The Modeling Version of CASTLEThe Modeling Version of CASTLE
Physics 287 - Fall Semester 2006Physics 287 - Fall Semester 2006
Illinois State UniversityIllinois State University
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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 PhilosophyOriginal CASTLE Philosophy
Many physics teachers are converted biologist or Many physics teachers are converted biologist or chemistschemists
Because of their lack of experience with ‘electricity’, Because of their lack of experience with ‘electricity’, their comfort level is LOW.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 electricity.They still have many naïve conceptions about 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 models of Fosters development of effective causal models of
charge and its flow in DC circuits.charge and its flow in DC circuits.• Allows models to break down and demonstrates Allows models to break down and demonstrates
the need for revising the model.the need for revising the model.
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How is CASTLE different from How is CASTLE different from Traditional E&M Curricula?Traditional E&M 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 than ‘+’ and Ben Franklin’s single ‘flavor’ of charge rather than ‘+’ and
‘-’‘-’– Alessandro Volta’s conception of electric pressureAlessandro Volta’s conception of electric pressure
• Avoids use of ‘jargon’ in place of more meaningful Avoids use of ‘jargon’ in place of more meaningful terms: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 problem Avoids equations and quantitative problem solving.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 to Uses multiple representational tools to facilitate abstract reasoning. 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:• Instructional Materials for StudentsInstructional Materials for Students• Matching Teachers Manual with answer keys and additional Matching Teachers Manual with answer keys and additional
resources.resources.• Commonly available materials except for CAPACITORS.Commonly available materials except for 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 laid out in manual for the Each step is laid out in manual for the student to follow.student to follow.
• Commentaries allow students to read Commentaries allow students to read ahead and make “post”-dictions rather ahead and make “post”-dictions rather than predict and experience.than predict and experience.
• Model building, evaluation and revision is Model building, evaluation and revision is present, but not a primary focus.present, but not a primary 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 and development, deployment, evaluation and revision.revision.
• Greater emphasis on using multiple Greater emphasis on using multiple representational tools. representational tools.
• Central focus of all activities is modeling of Central focus of all activities is modeling of observed behaviors. 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 electromagnetic models to address electrostatic behaviors and electromagnetic
interactions.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 conducting Identifies the need for a continuous conducting
path for bulbs to light.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 bulbs Identifies the path through the sockets and bulbs
which cause bulb lighting.which cause bulb lighting.
• Identifies that both ends of the battery must be in Identifies that both ends of the battery must be in
the circuit for bulbs to light.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 through all The same amount of charge is moving through all
the wires.the wires.• Charge is already present in all the conductors in Charge is already present in all the conductors in
the circuit. 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’ Some conductors have ‘constrictions’
which reduce the rate of charge flow which reduce the rate of charge flow through them.through them.
• These restrictions are related to the These restrictions are related to the thickness and length of the conductor.thickness 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 charge By compressing or depleting the amount of charge
in a conductor the pressure is raised or lowered in a conductor the pressure is raised or lowered respectively. 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 matches pressure difference across the capacitor matches the pressure difference across the battery.the pressure difference across the battery.
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The Story Line: Unit IThe Story Line: Unit I
• Activities 1-4 develop the idea that a continuous Activities 1-4 develop the idea that a continuous path of conductors including both ends of a battery path of conductors including both ends of a battery are the essential elements required to cause bulb are the essential elements required to cause bulb lighting. lighting.
• Worksheets 1 & 2 provide opportunities to deploy Worksheets 1 & 2 provide opportunities to deploy this model. this model.
• Activity 5 uses compasses to provide evidence of Activity 5 uses compasses to provide evidence of activity in the wires. activity in the wires.
• Because deflection depends battery orientation, Because deflection depends battery orientation, there is strong evidence that flow is circuital.there is strong evidence that flow is circuital.
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The Story Line: Unit IIThe Story Line: Unit II
• After introducing electrical schematics, Activity 1 After introducing electrical schematics, Activity 1 introduced the capacitor. 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 light The requirement for an ‘insulator-free’ circuit. (bulbs light with insulator present in circuit.)with insulator present in circuit.)
– The non-battery origin of charge. (bulbs down stream of The non-battery origin of charge. (bulbs down stream of the capacitor still light.)the capacitor still light.)
– The need for a battery to cause charge flow. (bulbs light The need for a battery to cause charge flow. (bulbs light during discharge with no battery in the circuit.)during discharge with no battery in the circuit.)
• Hand crank generators (Genecons) reinforce the Hand crank generators (Genecons) reinforce the non-battery origin of charge & introduce energy. non-battery origin of charge & introduce 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 air Activity 4 asks the question “How is an air circuit analogous to an electrical circuit?” circuit analogous to an electrical circuit?” and introduces the Air Capacitor.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 air use a “charge is like water” analogy, the air analogy is seeded by this activity. 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 fluid students can practice articulating the fluid model in terms of the air analogy. 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 long bulbs. Activity 1 introduces higher resistance long bulbs. Students examine the different lighting times Students examine the different lighting times during capacitor charging and discharging. during capacitor charging and discharging.
• Students examine long and round bulb filaments Students examine long and round bulb filaments under magnification to see that thickness and under magnification to see that thickness and length are key difference between the filaments.length are key difference between the filaments.
• Students then examine and practice analyzing Students then examine and practice analyzing series and parallel combinations of resistors.series and parallel 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 brightness are Representational tools for flow rate and bulb brightness are introduced:introduced:
– flow rate is represented by arrow with increasing numbers of flow rate is represented by arrow with increasing numbers of tails to show increasing flow rates. 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 circuit By adding a second battery pack to a circuit which contains an charged capacitor, students which contains an charged capacitor, students are forced to confront the limitations of the are forced to confront the limitations of the ‘charge is like water’ analogy.‘charge is like 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, charge Since the bulbs do light a second time, charge needs to be compressible like air rather than needs to be compressible like air rather than incompressible like water. incompressible 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 depletion electric pressure is due to the compression or depletion of charge in a conductor. 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 difference capacitor charging stops when the pressure difference
across the capacitor is equal to the pressure difference across the capacitor is equal to the pressure difference across the battery.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 represent Color coding permits students to represent electric pressure at different points in electric pressure at different points in circuits. 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 relationship can better identify the causal relationship between resistance and flow rate. between resistance and flow rate.
• Once again, this is a non-quantitative tool Once again, this is a non-quantitative tool which allows for qualitative reasoning of which allows for qualitative reasoning of many non-trivial problems. 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 directly how pressure is reached in wires not directly
connected to a battery.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 internal why batteries die due to the build up of internal
resistance. resistance.
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Unit VI Sequence:Unit VI Sequence:
• This unit introduces voltmeters and This unit introduces voltmeters and ammeters. ammeters.
• Quantifies pressure difference and Quantifies pressure difference and flow rates. flow rates.
• Confirms the predictions from color Confirms the predictions from color coding, flow rate arrow tails and bulb coding, flow rate arrow tails and bulb brightness rays. brightness rays.
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How is the Modeling Version How is the Modeling Version Different?Different?
Less directed:Less directed:• Experiments are developed in a Socratic dialogue Experiments are developed in a Socratic dialogue
vs. presented in writing. vs. presented in writing. • Prediction are elicited prior to activity.Prediction are elicited prior to activity.• Conclusions are discussed rather than read from a Conclusions are discussed rather than read from a
handout. handout.
More open ended:More open ended:• Students are free to develop their own procedures. Students are free to develop their own procedures.
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How is the How is the Modeling Version Different?Modeling Version Different?
How are we less How are we less directed but still directed but still maintaining the focus?maintaining the 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 Different?Modeling Version 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 student Provides space for student
conclusionconclusion• Also space for consensus Also space for consensus
from the post activity from the post activity discussion.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 circuits, approach to electricity which starts with circuits, (rather than electrostatics.)(rather than electrostatics.)
Both versions use multiple representation tools to Both versions use multiple representation tools to facilitate learning: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 to deployment and revision of the causal model to explain the behavior of charge. 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 CASTLE storyline of the original version of CASTLE with a few minor exceptions. with a few minor exceptions.
The Modeling Version reduces the volume of The Modeling Version reduces the volume of paper consumed by focusing activities on Vee paper consumed by focusing activities on Vee diagrams.diagrams.
The Modeling Version puts greater emphasis The Modeling Version puts greater emphasis on the development and use of models. on the development and use of models.
