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.
- RT @shankerinst: We are devastated to report the death of David K. Cohen, a founding member of the Albert Shanker Institute’s board of dire… 3 months ago
- Check this out! twitter.com/SLSingh/status… 4 months ago
- I really appreciated the keynote by @deborah_ball #TWSummerInstitute To quote some of her closing words: "It's coll… twitter.com/i/web/status/1… 6 months ago
- RT @TeachingWorks: Today is the day! If you signed up to join us, the link to view our #TWSummerInstitute keynote address today is waiting… 6 months ago
- Looking forward to the lecture by @deborah_ball at #TWSummerInstitute 6 months ago