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Journal of Group Theory

• Online ISSN: 1435-4446
• Print ISSN: 1433-5883
• Type: Journal
• Language: English
• Publisher: De Gruyter
• First published: January 1, 1998
• Publication Frequency: 6 Issues per Year
• Audience: Researchers interested in Group Theory

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On learning fundamental concepts of group theory

• Published: October 1994
• Volume 27 , pages 267–305, ( 1994 )

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• Ed Dubinsky 1 ,
• Jennie Dautermann 2 ,
• Uri Leron 3 &
• Rina Zazkis 4  

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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.

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Mathematics Department, Purdue University, 49707, West Lafayette, IN, USA

Ed Dubinsky

Miami University, USA

Jennie Dautermann

Israel Institute of Technology, Israel

Simon Fraser University, Canada

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Work on this project has been partially supported by the National Science Foundation.

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Dubinsky, E., Dautermann, J., Leron, U. et al. On learning fundamental concepts of group theory. Educ Stud Math 27 , 267–305 (1994). https://doi.org/10.1007/BF01273732

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The International Journal of Group Theory (IJGT) is a publication of the University of Isfahan in English. IJGT is an international mathematical journal founded in 2011. It carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges. IJGT is an international open access journal. There is no publication charge.  IJGT publishes 4 issues in each year.  The publication time of these issues are as follows: First issue at the end of March, second issue at the end of June, third issue at the end of September and  fourth issue at the end of  December. 

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• Published: 08 October 2008

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