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Theorems-in-Action for Problem-Solving and Epistemic Views on the Relationship Between Physics and Mathematics Among Preservice Physics Teachers

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Mathematics in Physics Education

Abstract

The difficulties students have with mathematics while trying to understand physics is one of the more remarkable, at least for physics teachers. In this chapter, we present our attempt to understand and to detect the cognitive aspects involved in the interrelationship between mathematics and physics when students try to understand physics concepts and solve problems in physics. The framework is based on the model proposed by Greca and Moreira (Investigações em Ensino de Ciências 7(1):30–45, 2002) that includes Johnson-Laird’s mental model theory and Vergnaud’s theory of conceptual fields. After, we present the construction and validation of a questionnaire with 15 (Likert scale) items, based in a previous case study in which those cognitive aspects that seemed to guide problem-solving were detected. The instrument was applied to 80 preservice physics teachers. The results show that students who think mathematics is just a tool for physics seem to use it only as a technique and to solve problems by trial and error. On the opposite side, students who use mathematical reasoning coherent with the situation outlined in problems consider that math has a structural role in physics theories. These variables also correlate with the difficulties perceived by the students for understanding physics concepts. Finally, we discuss how the questionnaire may be a resource that could be helpful for instructors to detect the behavior of students in relation to problem-solving before their instruction and, so, useful in their lessons design.

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Notes

  1. 1.

    It is worth stressing the similarities between epistemic games and theorems-in-action. Nevertheless, it must be noted that theorems-in-action can be used to understand many other cognitive behaviors, not only the ones related to problem-solving, which appears to be the case of the idea of epistemic games.

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Author information

Authors and Affiliations

  1. Department of Specifics Didactics, Faculty of Education, Universidad de Burgos, Burgos, Spain

    Ileana M. Greca & Ana Raquel Pereira de Ataíde

  2. Department of Physics, Universidade Estadual da Paraíba, Paraíba, Brazil

    Ileana M. Greca & Ana Raquel Pereira de Ataíde

Authors
  1. Ileana M. Greca
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  2. Ana Raquel Pereira de Ataíde
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Corresponding author

Correspondence to Ileana M. Greca .

Editor information

Editors and Affiliations

  1. Technische Universität Dresden, Dresden, Germany

    Gesche Pospiech

  2. DCFA - Section of Mathematics and Physics, University of Udine, Udine, Italy

    Marisa Michelini

  3. The Weizmann Institute of Science Rehovot, Israel

    Bat-Sheva Eylon

Appendix: Questionnaire (Likert Scale)

Appendix: Questionnaire (Likert Scale)

This questionnaire is a data collection instrument from a survey that aims to identify relations between epistemological views on the role of mathematics in physics and strategies used in problem-solving.

1.1 Identification

  • Name:_____________________________________________________________

  • Registration number: ______________ Semester that you are attending: ___________

1.2 About the Role of Mathematics in Physics

(Select one option)

  1. 1.

    Mathematics is an instrument that is used in physics to solve problems.

  2. 2.

    Math works for physics as a language that helps describe and translate the problems.

  3. 3.

    Math is a structure for physics; both are interrelated in such a way that mathematics is crucial in the construction of the concepts and theories of physics.

1.3 The Strategies Used in Solving Physics Problems

  1. 4.

    Equations are the first step in solving a physics problem.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  2. 5.

    The manipulation of equations is essential to solve a physics problem.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  3. 6.

    Adjust the equations to available data is essential to solving physics problems.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  4. 7.

    The use of charts and graphs facilitates the resolution of a problem.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  5. 8.

    Before solving a physics problem, you need to know how to explain it.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  6. 9.

    A detailed reading, with representation through charts and problem explanation, is essential to its resolution.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  7. 10.

    The identification and characterization of the variables involved in a problem are of fundamental importance for its resolution.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  8. 11.

    Solving a problem requires the placement of equations and an explanation of its use.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  9. 12.

    It is of fundamental importance in solving a physics problem to build meaning between equations and concepts, so as to understand how they are related.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

1.4 About the Performance and Difficulties in Curriculum Components of Physics

  1. 13.

    I have no difficulty with physics, and my performance in this curriculum component is very good.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  1. 14.

    I have difficulty with the understanding of the concepts of physics, and my performance in this curriculum component is weak.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

  1. 15.

    I have difficulty with math, and my performance in curriculum components of physics is weak.

    • ( ) Strongly agree ( ) Agree ( ) Neither agree nor disagree ( ) Disagree ( ) Strongly disagree

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Greca, I.M., de Ataíde, A.R.P. (2019). Theorems-in-Action for Problem-Solving and Epistemic Views on the Relationship Between Physics and Mathematics Among Preservice Physics Teachers. In: Pospiech, G., Michelini, M., Eylon, BS. (eds) Mathematics in Physics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-04627-9_7

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  • DOI: https://doi.org/10.1007/978-3-030-04627-9_7

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