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Making explicit the analysis of students' mathematical discourses: Revisiting a newly developed methodological framework
Mälardalen University, Department of Mathematics and Physics.ORCID iD: 0000-0002-3329-0177
2006 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 62, no 2, 191-209 p.Article in journal (Refereed) Published
Abstract [en]

Sfard and Kieran [Kieran, C., Educational Studies in Mathematics 46, 2001, 187-228; Sfard, A., Educational Studies in Mathematics 46, 2001, 13-57; Sfard, A. and Kieran, C., Mind, Culture, and Activity 8, 2001, 42-76] have developed a methodological framework, which aims at characterizing the students' mathematical discourses while they are working in groups. In this study, I focus on an important aspect of this methodological framework, namely the interactive flowcharts. The aim of this study is to suggest two complementary analyses for the construction of the interactive flowcharts: an additional analysis by means of the analytical construct of contextualization as well as an analysis of types ofmathematical discourses. Based on data from a study of how four groups of Swedish engineering students collaboratively construct concept maps in linear algebra. I show that the two complementary analyses make the construction of the interactive flowcharts more coherent and transparent, and hence, more reliable. Furthermore, the two complementary analyses dramatically changed the picture as to whether the studied discourseswere to be seen as mathematically productive or not. In the end of the article, I discuss the possibilities of performing the suggested additionalanalyses within the original methodological framework.

Place, publisher, year, edition, pages
2006. Vol. 62, no 2, 191-209 p.
National Category
Didactics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-4000DOI: 10.1007/s10649-006-4834-0Scopus ID: 2-s2.0-33746694115OAI: oai:DiVA.org:mdh-4000DiVA: diva2:120508
Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2015-07-02Bibliographically approved
In thesis
1. Approaching Mathematical Discourse: Two analytical frameworks and their relation to problem solving interactions
Open this publication in new window or tab >>Approaching Mathematical Discourse: Two analytical frameworks and their relation to problem solving interactions
2006 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

The driving force of conducting the two studies presented in this thesis is to examine ways that conceptual understanding and problem solving could be part of mathematics teaching, and through that, part of students' mathematical knowledge. The specific aims of the thesis are: 1) to characterize the classroom discourse of two, apparently similar, problem solving courses in teacher education and 2) to discuss the possibilities of developing two analytical approaches - the communicational approach to cognition and the dialogical approach - used for studying mathematical discourse. The two aims are elaborated on by means of data collected through audiotaped recordings and field notes from observations of problem-solving activities in engineering and teacher education. In relation to the first aim, the analysis of the classroom discourse within the two courses makes it clear that both courses displayed different kinds of discourse that could be broadly categorized in terms of: subject-oriented, didactically oriented, and problem solving oriented discourses. However, the comparisons between the two courses reveal a marked difference in the distribution of these categories of discourse. It is suggested that the introduction of explicit conceptual frameworks in teaching is of crucial importance for the topical focus of the classroom discourse, and for prospective teachers' opportunity to engage in mathematical productive discourse. The analyses of the two approaches for studying mathematical discourse reveal that the two frameworks can be further developed and the study also indicates ways in which such development can be achieved using a theory of contextualization and theories of mathematical learning. Finally, the thesis discusses theoretical and practical implications of the results, foregrounding issues of importance for the research on mathematical discourse, and for teachers and teacher educators involved in designing instructions for mathematical problem solving.

Place, publisher, year, edition, pages
Västerås: Mälardalens högskola, 2006
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 30
Keyword
Didactics of Mathematics, Mathematics Education, Analytical approaches, Communication, Concept maps, Contextualization, Discourse, Engineering students, Higher Education, Intentional analysis, Methodological framworks, Problem solving, Prospective teachers, Student teachers, Teacher education, Theoretical frameworks
National Category
Mathematics
Research subject
Matematik/tillämpad matematik
Identifiers
urn:nbn:se:mdh:diva-137 (URN)91-85485-13-6 (ISBN)
Public defence
2006-06-28, Kappa, Västerås, 13:15
Opponent
Supervisors
Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2013-12-04

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