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Progression Towards Functions: Students’ Performance on Three Tasks About Variables from Grades 7 to 12


Identifying and expressing relations between quantities is a key aspect of understanding and using functions. We are aiming to understand the development of functions understanding throughout school years in Israel. A survey instrument was developed with teachers and given to 20 high and average achieving students from each of years 7–11 and to 10 high achieving students from year 12, a total of 110 students. Our analytical approach is to identify qualitatively what students appeared to do and whether their approaches led to complete solutions. We look for progress in understanding variables and relations between them, and we found that there does not appear to be a strong link between curriculum and informal understandings of variables and covariation, but there are other strengths.

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  1. Straight line graphs include proportional and affine relations; we use ‘linear’ for all these in common with curricula and school-based use of the term.


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Correspondence to Michal Ayalon.

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Ayalon, M., Watson, A. & Lerman, S. Progression Towards Functions: Students’ Performance on Three Tasks About Variables from Grades 7 to 12. Int J of Sci and Math Educ 14, 1153–1173 (2016).

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  • Covariation
  • Correspondence
  • Functions
  • Rate of change
  • Variables