mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Approaching Mathematical Discourse: Two analytical frameworks and their relation to problem solving interactions
Mälardalen University, Department of Mathematics and Physics.ORCID iD: 0000-0002-3329-0177
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
Keywords [en]
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: urn:nbn:se:mdh:diva-137ISBN: 91-85485-13-6 (print)OAI: oai:DiVA.org:mdh-137DiVA, id: diva2:120510
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
List of papers
1. Can collaborative concept mapping create mathematically productive discourses?
Open this publication in new window or tab >>Can collaborative concept mapping create mathematically productive discourses?
2004 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, Vol. 56, no 2-3, p. 157-177Article in journal (Refereed) Published
Abstract [en]

Four groups (three engineering students in each group) were videotaped while constructing concept maps in Linear Algebra. There are two aims of this study. The first is to characterize the discourse in the groups by addressing the following research questions: Do the students communicate in an effective way? Do the students' communications contain the elements typical for a mathematically productive discourse? The analysis indicates that the communication among the students is effective and contains the elements that are characteristic for a mathematicallyproductive interaction. The two types of methods used to analyze the data were focal and preoccupational analysis. The mathematical content and the coherence of the conversations were examined through focal analysis. The participants' engagement in the discourse was examined by preoccupational analysis, carried out by means of interactive flowchart. The second aim of this study is to evaluate the newly developed methodological framework used to characterize the discourses. The study shows that several aspects of the methodological framework need to be developed.

National Category
Didactics
Identifiers
urn:nbn:se:mdh:diva-3999 (URN)10.1023/B:EDUC.0000040395.17555.c2 (DOI)2-s2.0-4544292839 (Scopus ID)
Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2015-06-29Bibliographically approved
2. Making explicit the analysis of students' mathematical discourses: Revisiting a newly developed methodological framework
Open this publication in new window or tab >>Making explicit the analysis of students' mathematical discourses: Revisiting a newly developed methodological framework
2006 (English)In: Educational Studies in Mathematics, ISSN 0013-1954, E-ISSN 1573-0816, Vol. 62, no 2, p. 191-209Article 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.

National Category
Didactics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-4000 (URN)10.1007/s10649-006-4834-0 (DOI)2-s2.0-33746694115 (Scopus ID)
Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2017-12-14Bibliographically approved
3. What is actually discussed in problem solving courses for prospecitve teachers
Open this publication in new window or tab >>What is actually discussed in problem solving courses for prospecitve teachers
2007 (English)In: Journal of Mathematics Teacher Education, ISSN 1386-4416, E-ISSN 1573-1820, Vol. 10, no 1, p. 41-63Article in journal (Refereed) Published
Abstract [en]

The aim of this study is to characterize the discourse of two problem-solving courses for prospective teachers. The data, consisting of audio recordings and field notes, were examined from a dialogical approach combined with the theory of contextualization. I show not only the substantial differences between the two classroom discourses but also elaborate on plausible reasons for the divergency found. The findings then serve as a basis for a discussion of how to develop a problem-solving course within the mathematics teacher program.

Place, publisher, year, edition, pages
Kluwer Academic Publishers, 2007
Keywords
Contextualization; Dialogical approach; Discourse; Problem solving; Prospective teachers; Student teachers
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-4001 (URN)10.1007/s10857-007-9027-y (DOI)2-s2.0-33947715047 (Scopus ID)
Available from: 2006-04-27 Created: 2006-04-27 Last updated: 2017-12-14Bibliographically approved

Open Access in DiVA

fulltext(573 kB)4058 downloads
File information
File name FULLTEXT01.pdfFile size 573 kBChecksum MD5
003cbe17728b2b4379f178ac791878e1005d42e7ee2c4785162eefb19d6d3e20d281bb22
Type fulltextMimetype application/pdf

Authority records BETA

Ryve, Andreas

Search in DiVA

By author/editor
Ryve, Andreas
By organisation
Department of Mathematics and Physics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 4058 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 4920 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf