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
The Ecology of Mary’s Mathematics Teaching: Tracing Co-determination within School Mathematics Practices
Stockholm University, Faculty of Science, Department of Mathematics and Science Education.ORCID iD: 0000-0003-2896-0890
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Teachers’ mathematics teaching has been studied in many different ways. Such studies not often include more contexts than the teacher’s teaching practice. An assumption in this thesis is that in order to create a deeper understanding of mathematics teachers’ teaching we also need to study the contexts around mathematics teachers, and in relation to each other. Together such contexts create an environment for teachers’ teaching. The determination of how mathematics is taught is not decided in any of the contexts alone. Rather, all contexts participate in the determination of how mathematics is taught and teachers need to negotiate how different contexts privilege both mathematics and mathematics education. In this study, I have studied one teacher’s, Mary’s, teaching practice as well as three contexts from her close environment, the teacher group she participated in, the textbooks she used, and the national curriculum she was bound to follow. To study how mathematics and mathematics teaching was privileged in the four studied contexts became a way to trace how the contexts participate in the determination, in short, their co-determination of how mathematics is taught.

With an aim to deepen the understanding of how the environment of a teacher’s teaching enables and constrains mathematics teaching, the four contexts were studied in relation to each other in different ways, in four studies. First, the context of Mary’s mathematics teaching was studied in relation to the teacher group in how the justifications of Mary’s mathematics teaching was constituted in relation to a teacher group discussion. Second, Mary’s teaching of problem-solving was studied in relation to how problem-solving was privileged in both mathematics textbook and national curriculum. Third, praxeology was explored as an analytical tool to understand how mathematics was privileged in teaching practice in relation to the privileging of mathematics in textbooks. Fourth, all four contexts were studied to trace arguments and principles for teaching rational numbers and how these enable and constrain the teaching of rational numbers.

To address these different contexts, ATD as described by Chevallard was adopted. In ATD, the environment of contexts with influence of teachers’ practices, is described as an ecology with levels that co-determine each other. The studied contexts represented some of these levels of co-determination. The privileging of mathematics and mathematics teaching was studied from a varied data material. Data from Mary’s teaching practice was transcripts of classroom observations and interviews. Data from the teacher group was transcripts of teacher meetings. Data from the textbook context was the textbooks and teacher guides Mary used. Data from the context of the national curriculum was the mathematics syllabus accompanied with clarifying and explanatory comments.

The analyses revealed a strong resemblance of the mathematical communication between the different contexts. They all emphasised similar approaches to problem-solving, aspects of rational numbers, mathematical values, or explanations of angles. Mary, however, anchored her arguments for mathematics teaching in partially different theoretical principles than those privileged in the ecology. Theoretical principles were not explicitly communicated in any context. They were inferred from the communication. An implication generated by these findings is the importance for teachers to engage in the principles behind the privileging expressed in contexts they need to negotiate. These principles need to be discussed and challenged. Another implication is the relevance of allowing for teachers to engage in research literature, and to have influences from other sources than their immediate contexts. The thesis also point to the need to study textbooks and national curriculum, not in terms of how they are enacted by teachers, but what they privilege. By doing so teachers practices may be understood in the sense of what teachers have to negotiate, where the consequence is a deeper understanding of constraints and affordances for teachers’ teaching practices.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics and Science Education, Stockholm University , 2018. , p. 115
Series
Doctoral thesis from the department of mathematics and science education ; 19
Keywords [en]
Mathematics teaching, Mathematics teachers, ATD, Co-determination, Praxeology
National Category
Didactics
Research subject
Mathematics Education
Identifiers
URN: urn:nbn:se:su:diva-160693ISBN: 978-91-7797-450-5 (print)ISBN: 978-91-7797-451-2 (electronic)OAI: oai:DiVA.org:su-160693DiVA, id: diva2:1252585
Public defence
2018-11-23, Vivi Täckholmsalen (Q-salen), NPQ-huset, Svante Arrhenius väg 20, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.

Available from: 2018-10-29 Created: 2018-10-02 Last updated: 2018-10-29Bibliographically approved
List of papers
1. Justifications for mathematics teaching: A case study of a mathematics teacher in collegial collaboration
Open this publication in new window or tab >>Justifications for mathematics teaching: A case study of a mathematics teacher in collegial collaboration
2015 (English)In: Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education / [ed] Konrad Krainer, Naďa Vondrová, European Socitey for Research in Mathematics Education , 2015, p. 1637-1643Conference paper, Published paper (Refereed)
Abstract [en]

The broad interest of this paper lies in how a mathematics teacher, Mary, justifies her professional decision making. The reported study draws on aspects of a PhD project and analyses Mary's communications within a collaborative teacher meeting focused on the teaching of mathematics to grade five students. The analysis, drawing on social semiotics, highlighted the significance of artefacts, such as multiplication tests, in Mary's articulated decision making. We also give account for what is addressed in a teacher's justifications and how the teacher relates to her students in the justifications. Finally, we discuss the wider social and political context in which the teacher is working.

Place, publisher, year, edition, pages
European Socitey for Research in Mathematics Education, 2015
Keywords
Mathematics teacher, mathematics teaching, teacher collaboration, case study, social semiotics
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-129749 (URN)
Conference
CERME 9 - Ninth Congress of the European Society for Research in Mathematics Education, February 2015, Prague, Czech Republic
Available from: 2016-04-28 Created: 2016-04-28 Last updated: 2018-10-02Bibliographically approved
2. The teaching of mathematical problem-solving in Swedish classrooms: a case study of one grade five teachers practice
Open this publication in new window or tab >>The teaching of mathematical problem-solving in Swedish classrooms: a case study of one grade five teachers practice
2017 (English)In: Nordisk matematikkdidaktikk, NOMAD: [Nordic Studies in Mathematics Education], ISSN 1104-2176, Vol. 22, no 1, p. 65-84Article in journal (Refereed) Published
Abstract [en]

In this paper we examine the teaching of mathematical problem-solving to grade five students of one well-regarded and experienced Swedish teacher, whom we call Mary. Working within a decentralised curriculum in which problem-solving is centrally placed, Mary is offered little systemic support in her professional decision making with respect to problem-solving instruction. Drawing on Lester’s and Schroeder’s descriptions of teaching for, about and through problem-solving, we draw on multiple sources of data, derived from interviews and videotaped lessons, to examine how Mary’s problem-solving-related teaching is constituted in relation to the weaklyframed curriculum and the unregulated textbooks that on which she draws. The analyses indicate that Mary’s emphases are on teaching for and about problem-solving rather than through, although the ambiguities that can be identified throughout her practice with respect to goals, curricular aims and the means of their achievement can also be identified in the curricular documents from which she draws.

National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-160672 (URN)
Available from: 2018-10-01 Created: 2018-10-01 Last updated: 2018-10-02Bibliographically approved
3. Mathematics Teachers’ Teaching Practices in Relation to Textbooks: Exploring Praxeologies
Open this publication in new window or tab >>Mathematics Teachers’ Teaching Practices in Relation to Textbooks: Exploring Praxeologies
2018 (English)In: The Montana Mathematics Enthusiast, ISSN 1551-3440, E-ISSN 1551-3440, Vol. 15, no 3, article id 13Article in journal (Refereed) Published
Abstract [en]

In this article, we explore affordances of adopting the framework of praxeology by Chevallard in the analysis of mathematics classroom communication in relation to the communication in a textbook. While adopting praxeology, we carried out detailed analysis of communication in both classroom data and textbooks. The construed praxeologies describe the organisation of knowledge expressed for the same type of task in both classroom and textbook. The praxeologies were compared, with specific attention to the teacher’s practice. This analysis illuminates how teachers’ practices, realised in classroom communication, may be compared to other texts describing the same topics, with a focus on procedures, explanations, theoretical aspects, et cetera. Hence, praxeology as a framework enabled an analytical structuring of classroom and textbook communication, and consequently a systematic comparison. In other studies about the use of mathematics textbooks the teaching frequently is categorised as regulated by the textbook, and in this article, we problematize this. The teaching practice was, in fact,closely related to the textbook when comparing exercises and procedures, but when specifically examining the explanations of concepts, it became possible to discern how the teaching practice differed from the textbook.

Keywords
Mathematics teacher education, textbooks, teaching practices, praxeology
National Category
Educational Sciences
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-156844 (URN)000436178100013 ()
Available from: 2018-05-31 Created: 2018-05-31 Last updated: 2018-10-02Bibliographically approved
4. Principles and arguments for the teaching of rational numbers in different contexts
Open this publication in new window or tab >>Principles and arguments for the teaching of rational numbers in different contexts
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Teachers do not solely determine how a mathematics content matter is taught. Rather, this determination takes place within different contexts, which teachers need to negotiate. To understand how a teacher’s teaching of rational numbers was enabled and constrained by surrounding contexts I studied four contexts, where a teacher group, textbooks and the national curriculum constituted parts of an ecology of a teacher’s teaching practice. I drew on Chevallard and ATD to analyse the technology of didactic praxeologies. In this analysis, inferred arguments for how rational numbers should be taught in terms of how sub-constructs of rational numbers were distributed within the different contexts. To analyse the theory of didactic praxeologies, traces of principles were inferred, using Bishop’s mathematical values as a framework. These analyses showed a very homogenous ecology, where the four contexts privileged the similar aspects of rational numbers and the same mathematical values. Seeing how aspects of rational numbers were expressed in relation to teaching activities, it was possible to discuss how the privileged mathematical values may have affected how rational numbers were presented and dealt with. If the principles and arguments that generate teaching activities are privileged the same way in several contexts, we need to include a broader context than teachers’ classrooms in professional development strategies. Teachers need to engage in other sources than textbooks and official curricula and to have the opportunities to discuss the political dimension of their teaching practice as well as how other contexts influence the teaching of specific content matter.

Keywords
Teachers, Teaching, ATD, Praxeology
National Category
Didactics
Research subject
Mathematics Education
Identifiers
urn:nbn:se:su:diva-160663 (URN)
Available from: 2018-10-01 Created: 2018-10-01 Last updated: 2018-10-22Bibliographically approved

Open Access in DiVA

The Ecology of Mary’s Mathematics Teaching(2616 kB)230 downloads
File information
File name FULLTEXT02.pdfFile size 2616 kBChecksum SHA-512
2a0c20889bfbe8481f462aa50cc676cdaf36a7e8bda64682d1d488d68edbebc8330b5ae801d08935063bda4e47c22780f57b8fa88f68030c8a04abdb2259aa56
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Pansell, Anna
By organisation
Department of Mathematics and Science Education
Didactics

Search outside of DiVA

GoogleGoogle Scholar
Total: 231 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: 1283 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