A Reaction to Burn ' s \ What Are The Fundemental Concepts of Group Theory ?

In his abstract, Burn calls his paper is a \: : :critical analysis of Dubinsky et al (1994): : :" and we are profoundly puzzled over what appears to be an interesting discussion, but which certainly does not seem to be about our paper. Consider for example, the following two quotes, rst from the rst paragraph in Burn and then from the rst page of Dubinsky et al (op cit). Burn: \It (Dubinsky et al) is a report of a novel teaching procedure using the computer software ISETL in the teaching of group theory." Dubinsky et al: \In this paper we hope to open a discussion concerning the nature of knowledge about abstract algebra, in particular group theory, and how an individual may develop an understanding of various topics in this domain: : : We include, at the end, a brief discussion of some pedagogical suggestions arising out of our observations, but a full consideration of instructional strategies and their eeect on learning this subject must await future investigations yet to be conducted." The paper is not about teaching abstract algebra, with ISETL or otherwise. ISETL itself is not mentioned at all in the body of the paper, nor are there any examples of computer activities, or indeed any speciics of the pedagogy. The teaching method used in the course under discussion was mentioned only incidentally (in a single paragraph), as part of the background for the research. In fact we make no claims whatever in this paper on the teaching of abstract algebra. Rather, this paper presents research that attempts to contribute to knowledge of how stu-dents' understanding of certain group concepts (group, subgroup, coset, normality, quotient group) may develop. As such, it has a clearly stated research methodology and a theoretical framework within which it analyzes the data. Most of the discussion is devoted to excerpts from in-depth interviews of students and interpretations that try to relate students' responses 1