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Comparison of students’ understanding of functions in classes following English and Israeli national curricula

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Abstract

This paper arises from a study of how concepts related to understanding functions develop for students across the years of secondary/high school, using small samples from two different curricula systems: England and Israel. We used a survey consisting of function tasks developed in collaboration with teachers from both curriculum systems. We report on 120 higher achieving students, 10 from each of English and Israeli, 12–18 years old. Iterative and comparative analysis identified similarities and differences in students’ responses and we conjecture links between curriculum, enactment, task design, and students’ responses. Towards the end of school, students from both curriculum backgrounds performed similarly on most tasks but approached these by different routes, such as intuitive or formal and with different understandings, including correspondence and covariational approaches to functions.

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Notes

  1. The current curriculum is similar to this description, but with more modelling and applications. There has been no major change in the age at which function is introduced explicitly.

  2. By dividing class size by 10 to get n and then selecting approximately every nth script.

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Authors and Affiliations

  1. University of Oxford, Oxford, England

    Anne Watson

  2. University of Haifa, Hayarden 21, Rehovot, Israel

    Michal Ayalon

  3. London South Bank University, London, England

    Stephen Lerman

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  1. Anne Watson
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  2. Michal Ayalon
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  3. Stephen Lerman
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Correspondence to Michal Ayalon.

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Watson, A., Ayalon, M. & Lerman, S. Comparison of students’ understanding of functions in classes following English and Israeli national curricula. Educ Stud Math 97, 255–272 (2018). https://doi.org/10.1007/s10649-017-9798-8

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