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Calculus in European classrooms: curriculum and teaching in different educational and cultural contexts

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Abstract

In this paper we provide a first overview of the landscape with respect to calculus teaching in European classrooms, an area where research is very limited. In particular through a small expert-based survey and a literature review, we trace the development of calculus teaching at schools in a number of European countries and identify commonalities and differences. In the current curriculum developments, we notice a reduction in the content of calculus and a more informal approach. The use of digital tools has started to be integrated in calculus teaching in most countries. However in some nations, teaching of calculus in the classroom is rather traditional, focusing on procedural aspects of knowledge. Moreover, in cases where more informal and conceptual teaching approaches are used in the classroom, often contradictions seem to exist with other contextual matters such as examination requirements. Finally, we discuss the future of calculus teaching in Europe.

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Author information

Authors and Affiliations

  1. University of Duisburg-Essen, Duisburg, Germany

    Günter Törner

  2. University of Athens, Athens, Greece

    Despina Potari & Theodossios Zachariades

Authors
  1. Günter Törner
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  2. Despina Potari
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  3. Theodossios Zachariades
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Corresponding author

Correspondence to Despina Potari.

Appendices

Appendix 1: Questionnaire

Dear Colleagues,

We intend to investigate the teaching of Calculus in European classrooms. Thus we prepared some questions around which we would like to obtain some answers from you. We do not expect you to be able to address all our issues, but would greatly appreciate your giving us some information and insights about the status of calculus at school in your country.

  1. 1.

    Beginning of calculus at school: Since when is calculus part of the curriculum at secondary school?

  2. 2.

    Survey articles in literature on calculus as a school subject: Are there historical surveys (in literature) on calculus in your country?

  3. 3.

    Subject matter of secondary school calculus: To be compact: In the 1950s, the gap between school mathematics and university calculus was not large, however this gap is broadening gradually. Thus we want to know about the differences between school calculus and university calculus.

  4. 4.

    How many lesson hours and for how many years is calculus taught at school (in what years)?

  5. 5.

    Role of calculus in the school curriculum: How important is calculus within the math curriculum?

  6. 6.

    What are actual issues in maths education discussion on calculus in your country? Any project work within calculus?

  7. 7.

    What are the tools (calculators, what type) used and allowed in calculus teaching?

  8. 8.

    What is your vision about where calculus will be/should be in 10 years in your curriculum?

Thank you for your collaboration!

Appendix 2: Points addressed in the interview

  1. 1.

    Historical development of calculus teaching in your country

    1. (a)

      When was it introduced?

    2. (b)

      Basic milestones in the process of development

    3. (c)

      Relevant papers

  2. 2.

    Calculus content

    1. (a)

      What is the content today?

    2. (b)

      What changes have occurred during the last 20 years

  3. 3.

    Classroom teaching

    1. (a)

      Years taught/duration/percentage of teaching time in mathematics

    2. (b)

      Main teaching approach (informal–formal; conceptual–procedural; applied–pure)

    3. (c)

      Tools (graphic calculators/computers/other materials)

    4. (d)

      Relevant papers

  4. 4.

    Wider context

    1. (a)

      Need to connect to university calculus (in what ways?)

    2. (b)

      National examinations

    3. (c)

      Research in mathematics education (curriculum–teaching)

    4. (d)

      Teachers’ background–professional development

    5. (e)

      Other factors (e.g. needs of industry)

    6. (f)

      Relevant papers

  5. 5.

    How was the information for the initial questionnaire collected?

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Törner, G., Potari, D. & Zachariades, T. Calculus in European classrooms: curriculum and teaching in different educational and cultural contexts. ZDM Mathematics Education 46, 549���560 (2014). https://doi.org/10.1007/s11858-014-0612-0

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