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Exploring the potential role of visual reasoning tasks among inexperienced solvers

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Abstract

The collective case study described herein explores solution approaches to a task requiring visual reasoning by students and teachers unfamiliar with such tasks. The context of this study is the teaching and learning of calculus in the Palestinian educational system. In the Palestinian mathematics curriculum the roles of visual displays rarely go beyond the illustrative and supplementary, while tasks which demand visual reasoning are absent. In the study, ten teachers and twelve secondary and first year university students were presented with a calculus problem, selected in an attempt to explore visual reasoning on the notions of function and its derivative and how it interrelates with conceptual reasoning. A construct named “visual inferential conceptual reasoning” was developed and implemented in order to analyze the responses. In addition, subjects’ reflections on the task, as well as their attitudes about possible uses of visual reasoning tasks in general, were collected and analyzed. Most participants faced initial difficulties of different kinds while solving the problem; however, in their solution processes various approaches were developed. Reflecting on these processes, subjects tended to agree that such tasks can promote and enhance conceptual understanding, and thus their incorporation in the curriculum would be beneficial.

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Acknowledgments

We deeply thank Abraham Arcavi for sharing with us his wisdom and for his helpful and instructive comments on earlier versions of this manuscript.

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Authors and Affiliations

  1. Abdallah Iben Al-Husein High School, Jerusalem, Israel

    Intisar Natsheh

  2. Weizmann Institute of Science, Rehovot, Israel

    Ronnie Karsenty

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  1. Intisar Natsheh
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Correspondence to Ronnie Karsenty.

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Natsheh, I., Karsenty, R. Exploring the potential role of visual reasoning tasks among inexperienced solvers. ZDM Mathematics Education 46, 109–122 (2014). https://doi.org/10.1007/s11858-013-0551-1

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