Learning Difficulties and Teaching Strategies Related to Electric Circuits David E. Meltzer Department of Physics and Astronomy Iowa State University Ames, Iowa

Research on Learning of Electric Circuit Concepts Pre-college students –Shipstone (1984) Early work with college students –Fredette and Lochhead (1980) –Cohen, Eylon and Ganiel (1982) Extended investigations with college students –Shaffer and McDermott (1992) –Harrington (1995)

Why do students have such difficulty learning about circuits? Lack of practical experience with circuits Widespread linguistic imprecision in dealing with subtle physical concepts confounding of “current,” “voltage,” “energy,” and “power” Abstract and counterintuitive nature of closely related concepts e.g., charge, field, force, potential, etc.

General Problems with Circuits Students retain confusion with “building block” concepts such as charge, field, potential, etc. Students struggle with common representations of circuits e.g., relating circuit diagrams to drawings, and drawings to actual equipment Students do not have separate concepts attached to the words “current,” “power,” “energy,” and “voltage.” (it’s all “electricity”) This exacerbates tendency toward confusion “batteries have constant current” [instead of voltage] “current gets used up in circuit elements” [instead of energy]

(1) Draw a circuit diagram for the physical layout shown below (assume bulbs are identical) (2) Draw a physical layout that corresponds to the circuit diagram shown below. Example: Exercise given in an elementary physics course: Results: Many students drew physical layout for #2 to be same as shown in first diagram!

The two most universal conceptual difficulties regarding circuits: Most students believe strongly that electric current gets used up as it moves through circuit elements. The overwhelming majority of students are certain that a battery will always produce the same amount of current regardless of the circuit to which it is attached. It is EXTREMELY DIFFICULT to persuade students that these ideas are not correct!

Pitfalls of All Instructional Methods Students are very good at devising theoretical justifications (for observations) that conform to their original beliefs. Students will frequently “observe” nonexistent phenomena (e.g., differences in bulb brightness) that they believe should be present. Students may greatly exaggerate the significance of minor observational discrepancies (to match their theoretical preconceptions). [It is possible that some physicists may occasionally behave in a similar manner...]

Observation: Bulbs in two-bulb circuit are dimmer than bulb in one-bulb circuit

Students’ Theorizing to Explain Observations Student: Same current goes through battery in each case; battery always has to produce the same amount of current. Instructor: But since these bulbs are dimmer, doesn’t that mean that less current goes through these bulbs than through the bulb in the one-bulb circuit? Student: Yes. The same current flows out of battery, but it is shared between the two bulbs, so each gets only half.

Effect of “successful” intervention by instructor on student understanding: After discussion with instructor, students agree that less current goes through battery in case of two bulbs in series. (Concept of “current conservation” is reviewed.) Five minutes later, students make observations of two-bulbs in parallel: this time, both bulbs are same brightness as one bulb alone. Question to students: How does amount of current through the battery now compare to single-bulb case? Answer [given by % of students]: Current is the same!

What about using ammeters... Randal Harrington asked physics majors (who had completed E&M + lab course) to compare ammeter readings in these circuits: A A Result: 20% said readings would be different.

Difficulties with “Voltage” “Potential Energy” is a difficult concept in itself; “Electric Potential” is still more confusing. Students are very slow to understand that difference in electric potential between two points is what is proportional to current flow. Common usage of “voltage” and “V” in Ohm’s law seriously aggravates this problem. After study of loop rule, students will frequently confuse “voltage drops” with current drops (i.e., re- emergence of idea that “current gets used up” )

Instructional Strategy Developed at University of Washington Physics Education Group led by L. C. McDermott “ Physics By Inquiry” and “Tutorials in Introductory Physics”: Extended hands-on investigations using batteries and bulbs. 1) Introduce concept of complete circuit: try to light bulb with wire and battery 2) Introduce concept of current: current not “used up”; current through a battery depends on circuit configuration. 3) Introduce concepts of resistance and equivalent resistance: “indicator” bulb with various configurations. 4) Introduce ammeters, voltmeters, and concept of potential difference. 5) Finally, introduce concepts of energy and power.

Advantages of “Current First” Strategy Avoids need for immediate grappling with “potential” concept. Notion of “flow” relatively easy for students to accept. Averts probable early confusion of “energy loss” with current “non-conservation.” Allows much deduction and model-building based on qualitative observation.

Another Strategy: Emphasis on Potential “Workbook for Introductory Physics” by Meltzer and Manivannan; for in-class use without relying on lab. Extended development of electric forces and fields, electric potential energy, and electric potential; Intensive study of current, “voltage” [potential difference], and Ohm’s law before discussion of circuits; Step-by-step analysis of very simple circuits.

Balance Sheet of “Workbook” Strategy Advantages: –close contact between circuit theory and preceding development of field, force and energy concepts –provides an option when lab work is not required or not available Disadvantages: –confusion between current and potential is aggravated –only very simple circuit configurations are dealt with –lack of “hands-on” a potentially fatal constraint on understanding

Summary If universally held misconceptions regarding circuits are not explicitly addressed, most students will never give them up. Methodical attention to subtle distinctions among key circuit concepts is essential. Whatever strategy is adopted, common conceptual difficulties will make their presence evident in numerous guises.