Encrypted objects and decryption processes: problem-solving with functions in a learning environment based on cryptography |
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| Authors: | Tobin White |
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| Institution: | (1) School of Education, University of California, Davis, 2043 Academic Surge Building, One Shields Avenue, Davis, CA 95616, USA |
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| Abstract: | This paper introduces an applied problem-solving task, set in the context of cryptography and embedded in a network of computer-based
tools. This designed learning environment engaged students in a series of collaborative problem-solving activities intended
to introduce the topic of functions through a set of linked representations. In a classroom-based study, students were asked
to imagine themselves as cryptanalysts, and to collaborate with the other members of their small group on a series of increasingly
difficult problem-solving tasks over several sessions. These tasks involved decrypting text messages that had been encrypted
using polynomial functions as substitution ciphers. Drawing on the distinction between viewing functions as processes and
as objects, the paper presents a detailed analysis of two groups’ developing fluency with regard to these tasks, and of the
aspects of the function concept underlying their problem-solving approaches. Results of this study indicated that different
levels of expertise with regard to the task environment reflected and required different aspects of functions, and thus represented
distinct opportunities to engage those different aspects of the function concept. |
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| Keywords: | Functions Multiple representations Problem solving Technology Context |
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