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The Unease About the Mathematics-Society Relation as Learning Potential

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Practice-Oriented Research in Tertiary Mathematics Education

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Abstract

In this contribution, I present an inquiry that was prompted by an empirical observation that emerged in interviews with student-teachers: Speaking about their beliefs about mathematics and its teaching and learning was disrupted by expressions of unease about popular myths related to their future profession and the current status of the relation between mathematics and society. Based on a theoretical position of the subject-scientific approach, that also vague feelings – such as unease – entail the potential to gain further insights into the object at stake, I analysed its potential for learning. Since the unease is related to beliefs, I take a closer look at, and formulate a critique of, current trends in belief research and their practical implications. Instead of repeatedly designing more teaching interventions for students to align with certain beliefs along the way, I propose to understand the unease as a starting point for an intentional and collaborative learning process of mathematics education scholars and students.

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Notes

  1. 1.

    Because of the importance of interconnectedness for mathematics education, I consider both as common subject matter.

  2. 2.

    Here, ‘subject’ refers to human beings and their subjective perspectives, not to the subject of mathematics.

  3. 3.

    Introduction in Spanish: Vollmer and Holzkamp (2015); English introduction: Tolman (2013); Selected writings in English: Schraube and Osterkamp (2013).

  4. 4.

    The distinction is made analytically, in real life situations it is not distinctly classifiable.

  5. 5.

    This does not imply that it is not possible to become aware, or to consciously unlearn something in retrospect that has been initially learned along the way.

  6. 6.

    The study programmes vary in their structure and focus. In primary and lower secondary teacher education programmes more weight is put on pedagogical subjects, while in secondary school teacher education programmes, which prepare for teaching at lower and upper secondary level, the mathematical requirements are higher.

  7. 7.

    Arranging qualities in a continuum is an analytical strategy of grounded theory.

  8. 8.

    Names are changed.

  9. 9.

    Popular myths condense views regarding mathematics to images, these are often counter to desirable views from a mathematics education perspective.

  10. 10.

    Mathematics is an exact science on an axiomatic basis and is further developed by deduction.

  11. 11.

    Mathematics is a collection of terms, rules and formulae.

  12. 12.

    Mathematics concerned with problem-solving and the discovery of structure and regularities.

  13. 13.

    Mathematics is presented as a science relevant to society and life.

  14. 14.

    Regarding something as separate from intellect usually leads to consider it as not being part of intentional learning processes.

  15. 15.

    School and university.

  16. 16.

    His analysis is based on policies and research concerning the school level, but it could be argued that also on university level comparable contradictory requirements for university teachers prevail. For an example of contradictions that university teachers face, see Ruge et al. (2021).

  17. 17.

    A detailed argumentation can be found in Ruge (2017).

  18. 18.

    Degraded in the sense that commonly the cognitive is referred to as higher function.

  19. 19.

    Interestingly, it is not the student who is the agent of change but a scientific construct.

  20. 20.

    My belief in this interpretation was strengthened by the experiences I gathered at conferences (Sect. 3.3.3).

  21. 21.

    Central idea about the institution university in Germany.

  22. 22.

    Especially those practices that serve the allocation and selection function of educational institutions run counter to caring and mattering.

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Authors and Affiliations

  1. University of Hamburg, Hamburg, Germany

    Johanna Ruge

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  1. Johanna Ruge
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Editors and Affiliations

  1. Institute of Mathematics, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Rolf Biehler

  2. Institute of Mathematics, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Michael Liebendörfer

  3. University Paris Saclay, Orsay, France

    Ghislaine Gueudet

  4. Department of Mathematics and Statistics, San Diego State University, San Diego, CA, USA

    Chris Rasmussen

  5. Faculty of Science, University of Copenhagen, Copenhagen, Denmark

    Carl Winsløw

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Ruge, J. (2022). The Unease About the Mathematics-Society Relation as Learning Potential. In: Biehler, R., Liebendörfer, M., Gueudet, G., Rasmussen, C., Winsløw, C. (eds) Practice-Oriented Research in Tertiary Mathematics Education. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-031-14175-1_3

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