Modeling Beyond Mechanics The Modeling Version of CASTLE

Modeling Beyond Mechanics: The Modeling Version of CASTLE Physics 287 - Fall Semester 2006 Illinois State University 1

What is CASTLE? A Bit of History. b Capacitor b Developed l b Aided l Project Director: Melvin S. Steinberg, l b System for l by Smith College, Editor: Camille Wainwright l b Teaching & b. Learning b Electricity l Pacific University b Authors l l Included: 12 high school teachers. 4 community college or university faculty. 2

Original CASTLE Philosophy b b b 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. b Something needed to be done. 3

CASTLE: Electricity Visualized b b b 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. 4

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 5

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. 6

The Pro’s & Con’s of the Original CASTLE Program. b Constructivist Approach: • Hands on Activities • Guided Discovery b A Complete Package: • Instructional Materials for Students • Matching Teachers Manual with answer keys and additional resources. • Commonly available materials except for CAPACITORS. b Qualitative Conceptual Approach • Minimal use of numbers which intimidate novices • Emphasizes qualitative conceptual understanding over quantitative solutions. 7

The Pro’s & Con’s of the Original CASTLE Program. b From a Modeling Perspective: Too guided • Each step is laid 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. 8

The Modeling Version of CASTLE: b 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. 9

What are the Models? b The Closed Loop Model. b Charge is a Fluid. b A Model for Resistance to Charge Flow b Charge is a Compressible Fluid. Footnote: The original CASTLE Materials further develop models to address electrostatic behaviors and electromagnetic interactions. 10

What are the Models? (continued): b 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. 11

What are the Models? (continued): b 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. 12

What are the Models? (continued): b 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. 13

What are the Models? (continued): b 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. 14

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. 15

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. 16

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. 17

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. 18

The Story Line: Unit III (continued) • 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. 19

The Story Line: Unit IV – 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. 20

The Story Line: Unit IV (continued) • Since the bulbs do light a second time, charge needs to be compressible like air rather than incompressible 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. 21

The Story Line: Unit IV (continued) • This unit also introduces a new representational tool: Color coding. RED Highest above Normal ORANGE Above Normal YELLOW Normal GREEN BLUE Below Normal Lowest below Normal. 22

The Story Line: 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. 23

The Story Line: Unit V • 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. 24

Unit VI Sequence: • 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. 25

How is the Modeling Version Different? b 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. b More open ended: • Students are free to develop their own procedures. 26

How is the Modeling Version Different? b b How are we less directed but still maintaining the focus? The “Vee-Diagram” • Reduced paper work – In the Original CASTLE Manual this activity takes up almost three pages. 27

How is the Modeling Version Different? b 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. 28

In Conclusion: b b 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. b Both versions emphasize the construction, deployment and revision of the causal model to explain the behavior of charge. 29

In Conclusion: (continued) b The Modeling Version closely follows the storyline of the original version of CASTLE with a few minor exceptions. b The Modeling Version reduces the volume of paper consumed by focusing activities on Vee diagrams. b The Modeling Version puts greater emphasis on the development and use of models. 30