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Educational Studies in Mathematics

, Volume 29, Issue 2, pp 153–174 | Cite as

Learning group isomorphism: A crossroads of many concepts

  • Uri Leron
  • Orit Hazzan
  • Rina Zazkis
Article

Abstract

This article is concerned with how undergraduate students in their first abstract algebra course learn the concept of group isomorphism. To probe the students' thinking, we interviewed them while they were working on tasks involving various aspects of isomorphism. Here are some of the observations that emerged from analysis of the interviews. First, students show a strong need for “canonical”, unique, step-by-step procedures and tend to get stuck of having to deal with some degrees of freedom in their choices. Second, students exhibit various degrees of personification and localization in their language, as in “I can find a function that takes every element of G to every element of G′” vs. “there exists a function from G to G′”. Third, when having to deal with a list of properties, students choose first the properties they perceive as simpler; however, it turns out that their choice depends on the type of the task and the type of complexity involved. That is, in tasks involving groups in general, students mostly prefer to work with properties which aresyntactically simple, whereas in tasks involving specific groups, students prefer properties which arecomputationally simpler.

Keywords

Undergraduate Student Specific Group Learn Group Group Isomorphism Abstract Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Uri Leron
    • 1
  • Orit Hazzan
    • 1
  • Rina Zazkis
    • 2
  1. 1.Department of Science Education, TechnionIsrael Institute of TechnologyHaifaIsrael
  2. 2.School of EducationSimon Fraser UniversityBurnabyCanda

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