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ZDM

, Volume 49, Issue 6, pp 865–880 | Cite as

The function concept at the transition to upper secondary school level: tasks for a situation of change

  • Mareike Best
  • Angelika Bikner-Ahsbahs
Original Article
First Online:

Abstract

This paper is about the development of a task sequence to help overcome the fragmented understanding of the ‘function’ concept that students often bring with them into the initial stage of upper secondary school level. Our aim is to make the students’ use of functions more flexible in certain respects, for example when functions are required to be used as tools for modelling. The core idea of our task design is to interpret formulas as functional relations. The tasks are developed along the lines of a Design-Based Research approach in which several theoretical approaches are employed in a complementary way. The paper will show how this complementarity frames and informs the design as well as the analysis of data about how a student solves the tasks. Mediated by the task sequence, students’ development in terms of how their use of functions becomes more flexible is reconstructed. In the analysis, a key constraint for developing a flexible use of functions is identified: their poor understanding of the coordinate system and its scaling and utilization as a reference space for graphical representations of functions.

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Notes

Acknowledgements

This paper is part of a project (http://www.uni-bremen.de/cu-fabit) that is funded by the Excellence Initiative of the German Government and Federal States for Promoting Science and Research at German Universities.

We would like to thank the reviewers for their auxiliary reviews, and the Master’s students Steffen Lühring, Janina Neukirch, and Valentin Wolff for their support in developing the concept of flexibility in the use of functions: The empirical study in their Master’s thesis substantiates the relevance of the aspect of robustness against flexible switching.

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Copyright information

© FIZ Karlsruhe 2017

Authors and Affiliations

  1. 1.University of BremenBremenGermany

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