Promoting Conceptual Development in Physics Teacher Education: Cognitive-Historical Reconstruction of Electromagnetic Induction Law

Abstract

In teaching physics, the history of physics offers fruitful starting points for designing instruction. I introduce here an approach that uses historical cognitive processes to enhance the conceptual development of pre-service physics teachers’ knowledge. It applies a method called cognitive-historical approach, introduced to the cognitive sciences by Nersessian (Cognitive Models of Science. University of Minnesota Press, Minneapolis, pp. 3–45, 1992). The approach combines the analyses of actual scientific practices in the history of science with the analytical tools and theories of contemporary cognitive sciences in order to produce knowledge of how conceptual structures are constructed and changed in science. Hence, the cognitive-historical analysis indirectly produces knowledge about the human cognition. Here, a way to use the cognitive-historical approach for didactical purposes is introduced. In this application, the cognitive processes in the history of physics are combined with current physics knowledge in order to create a cognitive-historical reconstruction of a certain quantity or law for the needs of physics teacher education. A principal aim of developing the approach has been that pre-service physics teachers must know how the physical concepts and laws are or can be formed and justified. As a practical example of the developed approach, a cognitive-historical reconstruction of the electromagnetic induction law was produced. For evaluating the uses of the cognitive-historical reconstruction, a teaching sequence for pre-service physics teachers was conducted. The initial and final reports of twenty-four students were analyzed through a qualitative categorization of students’ justifications of knowledge. The results show a conceptual development in the students’ explanations and justifications of how the electromagnetic induction law can be formed.

Appendices

Appendix 1: Task Given to the Students

1.1 Experiments and Models in Forming a Law: Electromagnetic Induction Law

The task is to explore how the electromagnetic induction law can be formed and how experiments and models are used in forming the law. In this, you can use the following questions as aids:

• What phenomenon is related to the law?

• What are the varying or constant features of the phenomenon that make it possible to identify the phenomenon, based on known theory?

• What are the varying or constant features of the phenomenon that form the basis of a quantifying experiment?

• What are the essential quantities in the case of induction law, and how are they measured?

• How is the law quantified? Short description and/or picture of the setup.

• What theory or models enable the interpretation of the experiment?

• How the law is incorporated to the existing theory?

• What kind of position does the law obtain in the structure of physics knowledge (e.g., independent, derived, restricted, general)?

The formation of the electromagnetic induction law is presented as a flow chart, which is complemented with a separate essay. DRP was discussed in the lectures (the flow chart in Fig. 2 without the induction law related content) and is used as a basis for the flow chart. The essay explains or elaborates upon the chart and is attached to the chart.

The level of discussion is commensurate with upper secondary school physics and it is assumed that the direct circuits, electro- and magnetostatics, are already familiar to you.

Appendix 2: Student Simeoni’s Initial Report (Flow Chart in Fig. 3 and Essay)

2.1 Explanation of Chart

Homogeneous magnetic field is produced using Helmholtz coils. The magnitude of the field can be measured with a meter based on the Hall effect. The voltage is measured with voltmeter and the speed with using MBL.

Fig. 3

Flow chart in Simeoni’s initial report

A metal rod is placed to move in a homogeneous magnetic field. The rod is allowed to move steadily along the parallel conducting rails, and the resulting voltage between the rails is measured. The rod, the rails, and the field are set perpendicular to each other. By varying one factor at a time, it can be noticed that the measured induction voltage E is proportional to the distance between the rails L, the velocity of the rod v and the magnetic flux density of the field B (Fig. 4).

Fig. 4

Picture of the setup of the quantitative experiment

E = LvB (electromagnetic magnetic induction law of motional emf)

From this, the general form is attained.

When the rod moves with velocity v = Δx/Δt, the area of the conducting loop A formed by the experimental setup changes with the velocity

$$ \Updelta {\text{A}}/\Updelta {\text{t}} = {\text{L}}\Updelta {\text{x}}/\Updelta {\text{t}} = {\text{Lv}} $$

The expression of the induced emf is obtained in form

$$ {\text{E}} = {\text{LVB}} = \Updelta {\text{AB}}/\Updelta {\text{t}} $$

A new quantity is introduced, the magnetic flux permeating through the loop

$$ \Upphi = {\text{AB}} $$

and the following form is obtained

$$ {\text{E}} = \Updelta \Upphi /\Updelta {\text{t}} $$

because the induced voltage tends to always resist the change, the induction law is obtained

$$ {\text{E}} = - {\text{d}}\Upphi /{\text{dt}} $$

This form is known as Faraday’s and Henry’s law. The law applies to all forms of magnetic induction, regardless of the cause of the change in magnetic flux due to the conductor’s motion, the movement of the source of the field, or the change of the field.

Appendix 3: Student Noora’s Final Report (Flow Chart in Fig. 5 and Essay)

3.1 Explanations

3.1.1 Experiment 1

The qualitative experiments are conducted using coils, bar magnets, current sources, and ammeters. Such ammeters are used, where the direction of current can be observed.

Fig. 5

Flow chart in Noora’s final report

First, the poles of test coil are connected through the ammeter. A bar magnet is moved through the coil back and forth. It is observed that when the magnet is moving, there is current in the coil. If the magnet is not moving, the current disappears. Similar results are also obtained so that the magnet is stationary and the coil is moved. The electric current is the bigger, the faster the magnet is moved.

In the second experiment, two coils are set side by side, from which the other, “field coil”, is connected from its poles to the current source. The other coil, “test coil”, is connected to an ammeter. A current is observed in the test coil if one of the coils is moved. The magnitude of the induced current in the test coil depends now on the magnitude of the current in the field coil.

In the third experiment, two coils are also used. The field coil is connected with the current source and a switch and the test coil is connected with the ammeter. When the switch of the field coil is on and the current is moving in the coil, it is observed a current moving in the test coil. When the switch is released, the current is moving in the opposite direction. The phenomenon can be made more strength using joint iron bar in the coils.

Based on the first and second experiment, it could be thought that the current induced in the test coil somehow depends on the movement of the coil or magnet. However, the third experiment shows that this is not the case. Clearly, only the change of magnetic field is essential. From the directions of induced currents, it is observed that the direction of the induced current is such that it resists the change of magnetic field that has caused the current (Fig. 6).

Fig. 6

Pictures of the setups of qualitative experiments in Experiment 1

3.1.2 Experiment 2

An adjustable current source, an ammeter and a field coil are connected to each other. The test coil is connected to the voltmeter. The current in field coil and the voltage in test coil are measured using computer. The current in field coil is changed using the adjustable current source (Fig. 7).

Fig. 7

Picture of the setup of the quantitative experiment in Experiment 2

3.1.3 Explanation 3

It is observed that that the current’s rate of change in field coil is proportional to the voltage induced in the test coil. Thus, U_t~dI_f/dt. As in the case of the qualitative experiments, here, it can also be observed that the direction of the induced voltage is such that is resists the change of magnetic field.

3.1.4 Explanation 4

Magnetic flux, Φ, and magnetic flux density, B, are proportional, so Φ~B. On the other hand, according to the Biot-Savart law, the magnetic flux density, B, and current, I, are proportional to each other, B ~ I. Thus, Φ~B~I.

According to the energy principle, the energy cannot disappear or arise out of nothing. So, the induction current consumes energy, e.g., in order to outdo resistance. This energy must be received from the system causing induction. The direction of the induction phenomenon must be opposing the change causing it, because the cause of induction must do work in order to outdo the counter-effect of the induction current.

3.1.5 Explanation 5

Induction law E = −dΦ/dt, where E is the induced voltage and Φ is the magnetic flux. According to Lenz’s law, the direction of induction current is such that it resists the change causing the induction.

Induction law is an independent law; it cannot be derived from other laws of electromagnetism. Induction law combines the disciplines of electricity and magnetism. The electric current induces magnetic field, the induction is the inverse phenomenon of this, and the changing magnetic field causes electric current.

Appendix 4: Categorization Examples

Table 10 shows how contents in Simeoni’s initial report (Appendix 2) and Noora’s final report (Appendix 3) are categorized.

Table 10 Categorizations of Simeoni’s and Noora’s reports