Reaching the unreachable: Technology and the semantics of asymptotes

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This work is part of a larger attempt to explore the nature of symbolic understanding involving graphic technology. This study describes learning advanced mathematics that occurs through constructing qualitative reasoning methods using graphic technology. Data was gathered from a precalculus class who, for a few weeks, investigated and explored asymptotic behavior of rational functions. The analysis is based on observations of group discussions and written works. Learning about asymptotes using software which serves as tool box for numerical evaluation and graphic representation amplifies epistemological complexities related to the infinity concept. Using the software to watch examples of rational functions, generated by symbolic and graphic operations between polynomial functions, enabled students to leave their own traces on the formalization of asymptotes - on its definition, its symbolic structure, and its computational procedures. The discrepancy between technology as a support for visual perception but a tool that cannot support the conception of approaching infinities, makes the study of asymptotes an intriguing domain for investigating what is being manipulated with software and how.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalInternational Journal of Computers for Mathematical Learning
Issue number1
StatePublished - 1997

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Engineering
  • Computer Science Applications
  • Computational Theory and Mathematics


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