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Scripting Tasks as a Springboard for Extending Prospective Teachers’ Example Spaces: a Case of Generating Functions

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Abstract

In this paper, we highlight a further use of scripting tasks in the work of researchers-teacher-educators, which we present in two parts. In Part 1, we study prospective secondary school mathematics teachers’ responses to a scripting task on the topic of functions. The generated examples for a function that satisfies certain constraints provide a lens for examining participants’ example spaces and concept images of a function. In Part 2, we demonstrate how the script analysis is subsequently used by teacher educators as a springboard for broadening prospective teachers’ personal example spaces for a function, strengthening their understanding of the concept, and extending connections between tertiary and school mathematics.

Résumé

Dans cet article comprenant deux parties, nous mettons l’accent sur une utilisation accrue des tâches de script dans le travail des chercheurs-enseignants-éducateurs. Dans la première partie, nous étudions les réactions des futurs enseignants du secondaire devant une tâche de script traitant des fonctions. En ce sens, les exemples générés pour une fonction spécifique soumis à certaines contraintes permettent d’examiner plus précisément le niveau de compréhension des participants face à l’espace d’échantillonnage et aux schémas conceptuels d’une fonction. Dans la deuxième partie, nous démontrons comment l’analyse du script est ensuite utilisée par les formateurs comme un tremplin permettant aux futurs enseignants d’élargir leur propre espace d’échantillonnage pour une fonction, de renforcer leur compréhension du concept et de mieux arrimer entre elles les mathématiques tertiaires et les mathématiques scolaires.

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Notes

  1. We cannot determine whether Jamie’s incorrect claim, which is acknowledged by the teacher-character as “correct,” is simply a “slip of a tongue” or points to the writer’s incorrect definition of a function. This claim contributed to our design of activities in Part 2 (see “Function Definition”).

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Funding

The study was funded by the grant no. 435-2013-0230 from the Social Sciences and Humanities Council of Canada.

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  1. Faculty of Education, Simon Fraser University, 8888 University Drive, Burnaby, BC, V5A 1S6, Canada

    Rina Zazkis & Ofer Marmur

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  1. Rina Zazkis
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  2. Ofer Marmur
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Correspondence to Rina Zazkis.

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Zazkis, R., Marmur, O. Scripting Tasks as a Springboard for Extending Prospective Teachers’ Example Spaces: a Case of Generating Functions. Can. J. Sci. Math. Techn. Educ. 18, 291–312 (2018). https://doi.org/10.1007/s42330-018-0019-y

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