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Didactical Reconstruction of Processes in Knowledge Construction: Pre-service Physics Teachers Learning the Law of Electromagnetic Induction

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Abstract

In physics teacher education, two central goals are first to learn the structures of physics knowledge, and second the processes of its construction. To know the structure is to know the framework of concepts and laws; to know the processes is to know where the knowledge comes from, how the framework is constructed, and how it can be justified. This article introduces a way to approach these goals in the form of a graphical tool called the didactical reconstruction of processes (DRP), where knowledge is constructed to the extent that experiments and models have an equally important role in the construction process. In practice, the DRP is a graphical network representation or a ‘flow chart’ with a specific structure, which aims to give an image of the processes of physical concept formation, while at the same time bearing in mind the educational goals. The DRP was tested in an instruction unit for pre-service physics teachers, where students drew flow charts for representing how the law of electromagnetic induction is formed. In addition to flow charts, students also wrote essays clarifying the content of the flow charts. The flow charts and essays were analysed through a qualitative categorisation of structural and knowledge claim patterns. The results show that the DRP helps students in arguing how to form the electromagnetic induction law and that the experiments and models have a distinct role in supporting students’ knowledge claims.

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Acknowledgements

This work was supported by the Academy of Finland through grant SA1133369.

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Authors and Affiliations

  1. Department of Physics, University of Helsinki, P.O. Box 64, FIN-00014, Helsinki, Finland

    Terhi Mäntylä

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  1. Terhi Mäntylä
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Correspondence to Terhi Mäntylä.

Appendices

Appendices

Appendix A: Student Matti’s Initial Report (flow chart in Fig. 4a and essay)

Fig. 4
figure 4

Student Matti’s Initial Report (Fig. 4a and Essay) and Redrawn Flow Chart (Fig. 4b)

Full size image
  1. (1)

    In the induction phenomenon, the change of the magnetic field induces voltage in a current loop in a magnetic field.

  2. (2)

    For forming the induction law a few concepts concerning electricity and magnetism have to be known. Quantities voltage (U) and electric current (I) must be known. Also magnetic flux (Φ) and density of magnetic flux (B) are assumed to be known. The dependency between them is Φ = BA. In that equation A is an area inside of a current loop.

  3. (3)

    The simplest way to implement the induction phenomenon is to push a bar magnet inside the coil. The coil is connected to an ammeter. With the help of a meter, the current induced in the coil is observed.

  4. (4)

    When pushing the bar magnet inside the coil, the magnetic field of the coil is changing. A voltage, which produces the current, is induced in the coil.

  5. (5)

    A straight conductor in a magnetic field. The experiment is conducted by moving a conductor rod on two rails in a magnetic field. The rails are connected to each other through an ammeter. The conductor rod is moved, i.e. the area of a loop is changed. It is observed that the current depends on the speed of the conductor. The greater the speed is the greater the current is.

  6. (6)

    A voltage is induced between the ends of the conductor: e = Blv = BlΔx/Δt = BΔA/Δt. l is the length of the conductor. v is the speed of the conductor. When the dependency Φ = BA is known we get: e = ΔΦ/Δt.

  7. (7)

    On the basis of the Lenz’ law the induced current tends to resist the change of the magnetic field.

  8. (8)

    The direction is according to Lenz’s law and is the reason for the minus sign. As the induction law, we then get e = -dΦ/dt.

Appendix B: Student Matti’s Final Report (flow chart in Fig. 5 and essay)

figure 5

 

  1. (1)

    Induction phenomenon

    A new phenomenon is identified through qualitative experiments. First a circuit with a coil and an ammeter is constructed. Based on previous knowledge it is inferred that there should be no electric current in this circuit due to the absence of a voltage source. A bar magnet is pushed inside the coil. An electric current is observed when the magnet is moving. It is also observed that the direction of current is changing when the magnet is pulled in the opposite direction.

    Next, two circuits are considered. The first circuit consists of a voltage source and a coil. The second circuit consists of an ammeter and a coil. When the other circuit is moved, the same kind of phenomenon is observed, i.e. the emergence of a current as in the experiment conducted with the bar magnet.

    Finally the situation in which the coils of the previous experiment are stationary is explored. A switch is added to the circuit consisting of the voltage source. When switching the circuit on and off, an electric current is observed in the other circuit.

    The phenomenon is interesting because, with its help, it is possible to produce an electric current without a voltage source. This was not possible on the basis of previous knowledge. On the other hand we know that an electric current causes magnetism. So is it possible that magnetism could produce electricity?

  2. (2)

    Measurement

    The measurement is conducted by way of two electric circuits. The first circuit consists of an adjustable voltage source, an ammeter and a coil. The second circuit consists of a voltmeter and a coil. In practice the measurement is conducted by using a computer and electric current and voltage sensors. Two graphs are drawn: the electric current in the function of time and voltage in the function of time.

  3. (3)

    Quantity or law

    From the graph, the rate of change of the electric current in the first circuit is calculated by derivation. The connection between the rate of change of the electric current and the voltage induced in the other circuit is observed. The following dependence is found: U = dI/dt.

  4. (4)

    Model for the measurement system

    A measurement system is used similar to that in a qualitative experiment. Knowledge about direct current circuits and measuring voltages and electric currents is needed. Also the use of a microcomputer-based laboratory (MBL) system and interpretation of graphs must be available.

  5. (5)

    Model for measurement results

    From the definition of magnetic flux, the dependence B ~ Φ is obtained. On the basis of Biot’s and Savart’s law the dependence B ~ I is obtained.

  6. (6)

    The theory needed for interpretation of measurement

    For interpreting the measurement, the concept of magnetic flux must be known. Magnetic flux is Φ = BA, where B is the density of magnetic flux and A is the area of loop perpendicular to the magnetic field. Also the Biot’s and Savart’s law must be known. For the straight conductor, the law is B = μ 0 I/2πR, where μ 0 is a physical constant, I electric current and R distance.

  7. (7)

    Extension of theory

    On the basis of the dependence obtained through the quantifying experiment and the dependencies presented in step (5) the theory can be extended: U ~ dI/dt ~ dB/dt ~ dΦ/dt. The following dependence is obtained: U ~ -dΦ/dt. From this dependence, the induction law is derived: U = -dΦ/dt. However to verify this [tentative law] would require several further experiments. One could e.g. investigate the effect of different coils (area, number of revolutions).

  8. (8)

    The theory related to the explanation of phenomenon

    In order to explain the phenomenon the concepts of magnetic fields and magnetic field lines must be known. The induction phenomenon can be explained through changing magnetic fields. In accordance with Lenz’s law, the induced voltage tends to resist the change of the magnetic field.

Appendix C: The Interview Protocol

  1. A.

    Student’s flow chart of the induction law (initial and final interview)

    • Tell me about your flow chart in your own words, where do you start and how do you proceed?

    • What does the content of this ‘box’/‘arrow’ represent in your representation? (going through the flow chart representation in detail)

    • What is the role of (only final interview)

      • ◦ the observation of phenomenon

      • ◦ qualitative experiments

      • ◦ quantitative experiment

      • ◦ models and theories

      in the case of the induction law?

  2. B.

    The Didactical Reconstruction of Process (DRP) (Initial and Final Interview)

    • What is your opinion on what the DRP represents?

    • Do you think that it is possible to use this DRP in the case of some other law?

  3. C.

    The Comparison of the Initial and Final Flow Charts (Only Final Interview)

    • Compare your initial and final flow charts; what are their greatest

      • ◦ differences?

      • ◦ similarities?

    • What factors made the flow charts different?

  4. D.

    The Utilisation and Usefulness of the DRP (Only Final Interview)

    • How was it to apply the DRP in the case of the induction law?

    • Did you find the DRP useful?

      • ◦ If the answer is yes → Why?

      • ◦ If the answer is no → Why not?

    • What was difficult in applying the DRP?

    • What was easy in applying the DRP?

    • Did the DRP help you to organise things discussed in the exercises?

    • Was the DRP discussed adequately during lectures?

    • Were the exercises enough support in using the DRP?

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Mäntylä, T. Didactical Reconstruction of Processes in Knowledge Construction: Pre-service Physics Teachers Learning the Law of Electromagnetic Induction. Res Sci Educ 42, 791–812 (2012). https://doi.org/10.1007/s11165-011-9217-6

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