On learning fundamental concepts of group theory View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1994-10

AUTHORS

Ed Dubinsky, Jennie Dautermann, Uri Leron, Rina Zazkis

ABSTRACT

The research reported in this paper explores the nature of student knowledge about group theory, and how an individual may develop an understanding of certain topics in this domain. As part of a long-term research and development project in learning and teaching undergraduate mathematics, this report is one of a series of papers on the abstract algebra component of that project. The observations discussed here were collected during a six-week summer workshop where 24 high school teachers took a course in Abstract Algebra as part of their work. By comparing written samples, and student interviews with our own theoretical analysis, we attempt to describe ways in which these individuals seemed to be approaching the concepts of group, subgroup, coset, normality, and quotient group. The general pattern of learning that we infer here illustrates an action-process-object-schema framework for addressing these specific group theory issues. We make here only some quite general observations about learning these specific topics, the complex nature of “understanding”, and the role of errors and misconceptions in light of an action-process-schema framework. Seen as research questions for further exploration, we expect these observations to inform our continuing investigations and those of other researchers. We end the paper with a brief discussion of some pedagogical suggestions arising out of our considerations. We defer, however, a full consideration of instructional strategies and their effects on learning these topics to some future time when more extensive research can provide a more solid foundation for the design of specific pedagogies. More... »

PAGES

267-305

References to SciGraph publications

  • 1976. Piaget’s Theory in PIAGET AND HIS SCHOOL
  • 1991. Constructive Aspects of Reflective Abstraction in Advanced Mathematics in EPISTEMOLOGICAL FOUNDATIONS OF MATHEMATICAL EXPERIENCE
  • 1977. Epistemology and Psychology of Functions in NONE
  • 1992-06. Development of the process conception of function in EDUCATIONAL STUDIES IN MATHEMATICS
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/bf01273732

    DOI

    http://dx.doi.org/10.1007/bf01273732

    DIMENSIONS

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