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Orchestrating mathematical whole-class discussions in the problem-solving classroom: Theorizing challenges and support for teachers
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (M-TERM)ORCID iD: 0000-0002-6518-1418
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Promising teaching approaches for developing students’ mathematical competencies include the approach of teaching mathematics through problem solving. Orchestrating a whole-class discussion of students’ ideas is an important aspect of teaching through problem solving. There is a wide consensus within the field that it is very challenging for the teacher to conduct class discussions that both build on student ideas and highlight key mathematical ideas and relationships. Further, fostering argumentation in the class, which is important for students’ participation, is also a grand challenge. Teachers need support in these challenges. The aim of the thesis is to characterize challenges and support for mathematics teachers in orchestrating productive problem-solving whole-class discussions that focus on both mathematical connection-making and argumentation. In particular, it is investigated how Stein et al.’s (2008) model with five practices – anticipating, monitoring, selecting, sequencing and connecting student solutions – can support teachers to handle the challenges and what constitutes the limitations of the research-based and widely-used model. This thesis builds on six papers. The papers are based on three intervention studies and on one study of a mathematics teacher proficient in conducting problem-solving class discussions. Video recordings of observed whole-class discussions as well as audio-recorded teacher interviews and teacher meetings constitute the data that are analyzed. It is concluded in the thesis that the five practices model supports teachers’ preparation before the lesson by the practice of anticipating. However, making detailed anticipations, which is shown to be both challenging and important to foster argumentation in the class, is not explicitly supported by the model. Further, the practice of monitoring supports teachers in using the variety of student solutions to highlight key mathematical ideas and connections. Challenging aspects not supported by the monitoring practice are, however, how to interact with students during their exploration to actually get a variety of different solutions as a basis for argumentation. The challenge of selecting and sequencing student solutions is supported for the purpose of connection-making, but not for the purpose of argumentation. Making mathematical connections can be facilitated by the last practice of connecting, with the help of the previous practices. However, support for distinguishing between different kinds of connections is lacking, as well as support for creating an argumentative classroom culture. Since it is a great challenge to promote argumentation among students, support is needed for this throughout the model. Lastly, despite the importance and challenge of launching a problem productively, it is not supported by the model. Based on the conclusions on challenges and support, developments to the five practices model are suggested. The thesis contributes to research on the theoretical development of tools that support teachers in the challenges of orchestrating productive problem-solving whole-class discussions.

Place, publisher, year, edition, pages
Västerås: Mälardalen University , 2015.
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 193
Keyword [en]
whole-class discussion, problem solving, five practices model, mathematical connection, argumentation, inquiry/argument, supportive tool
National Category
Didactics
Research subject
Didactics
Identifiers
URN: urn:nbn:se:mdh:diva-29409ISBN: 978-91-7485-242-4 (print)OAI: oai:DiVA.org:mdh-29409DiVA: diva2:865533
Public defence
2015-12-11, Kappa, Mälardalens högskola, Västerås, 13:00 (English)
Opponent
Supervisors
Available from: 2015-10-28 Created: 2015-10-28 Last updated: 2015-11-24Bibliographically approved
List of papers
1. Analyzing Content and Participation in Classroom Discourse: Dimensions of Variation, Mediating Tools, and Conceptual Accountability
Open this publication in new window or tab >>Analyzing Content and Participation in Classroom Discourse: Dimensions of Variation, Mediating Tools, and Conceptual Accountability
2013 (English)In: Scandinavian Journal of Educational Research, ISSN 0031-3831, E-ISSN 1470-1170, Vol. 57, no 1, 101-114 p.Article in journal (Refereed) Published
Abstract [en]

Balancing content and students' participation in the mathematics classroom is an area of both practical and theoretical interest. In this article we relate and contribute to these two interests by analyzing classroom data from an intervention project aiming at teaching mathematics through problem solving. The study shows that several aspects such as mediating tools, the teacher's conceptual accountability and interactional moves play important roles in the nature of the co-construction of critical dimensions of variation. We therefore suggest that an analysis of content and participation in the mathematics classroom would benefit from drawing on several theoretical sources. As such, the study could be seen as a contribution to recent elaborations on developing variation theory for analyzing the enacted object of learning.

Keyword
Content, discourse, mathematics, participation
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-13149 (URN)10.1080/00313831.2011.628689 (DOI)000313671900007 ()2-s2.0-84872576446 (Scopus ID)
Available from: 2011-10-19 Created: 2011-10-19 Last updated: 2016-07-05Bibliographically approved
2. Balancing on the edge of competency-oriented versus procedural-oriented practices: orchestrating whole-class discussions of complex mathematical problems
Open this publication in new window or tab >>Balancing on the edge of competency-oriented versus procedural-oriented practices: orchestrating whole-class discussions of complex mathematical problems
2012 (English)In: Mathematics Education Research Journal, ISSN 1033-2170, Vol. 24, no 4, 447-465 p.Article in journal (Refereed) Published
Abstract [en]

Establishing and maintaining key mathematical practices in wholeclass discussions, such as justifying claims, representing mathematical objects and making connections between the representations, is crucial to the development of students' mathematical competencies. The aim of this article is to investigate how and why the establishment of key mathematical practices in whole-class discussions varies in a teaching mathematics through problemsolving project. Analyses of transcribed video-recorded whole-class discussions result in the suggestion that the complexity of the mathematical problem itself as well as the complexity related to teaching the problem may contribute to more procedure-oriented practices instead of competency-oriented practices that create opportunities for the students to develop their mathematical competencies on a broad front. However, the results also suggest that the teaching of complex mathematical problems might develop the teacher's establishment and maintenance of key mathematical practices. Researchers initiating an intervention project hence have to consider both the students' and the teacher's learning trajectories, which might not always coincide. Other important aspects for the researcher to consider are discussed and pointed out as important areas for future research, such as how explicit introduction of appropriate frameworks may support teachers in learning to teach mathematics through problem solving.

National Category
Educational Sciences
Research subject
Mathematics/Applied Mathematics; Didactics
Identifiers
urn:nbn:se:mdh:diva-15674 (URN)10.1007/s13394-012-0049-0 (DOI)2-s2.0-84869118757 (Scopus ID)
Available from: 2012-10-19 Created: 2012-10-19 Last updated: 2016-07-05Bibliographically approved
3. EFFECTIVE TEACHING THROUGH PROBLEM-SOLVING BY SEQUENCING AND CONNECTING STUDENT SOLUTIONS
Open this publication in new window or tab >>EFFECTIVE TEACHING THROUGH PROBLEM-SOLVING BY SEQUENCING AND CONNECTING STUDENT SOLUTIONS
2011 (English)In: Proceedings of NORMA11: The sixth Nordic conference on mathematics education in Reykjavik, May 11-14 2011 / [ed] G. H. Gunnarsdóttir, F. Hreinsdóttir, G. Pálsdóttir, M. Hannula, M. Hannula-Sormunen, E. Jablonka, U. T. Jankvist, A. Ryve, P. Valero, & K. Waege, Reykjavik: University of Iceland Press , 2011, 425-434 p.Conference paper, Published paper (Refereed)
Abstract [en]

How can researchers support teachers in the complexity of orchestrating productive mathematical whole-class discussions based on students’ solutions to challenging problems? This study has two aims: Firstly, to study how the teacher can select, sequence and connect different student solutions in order to effectively orchestrate mathematical whole-class discussions. Secondly, to critically reflect on the role of the researchers in this intervention project. Analyses of audio recorded interviews and video recorded whole-class discussions result in suggestions for how student solutions can be sequenced in this particular case to set the scene for connecting them with each other and with key mathematical ideas. We further critically reflect on how we as researchers can improve our work in supporting practicing teachers.

Place, publisher, year, edition, pages
Reykjavik: University of Iceland Press, 2011
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-15704 (URN)978-9979-54-965-9 (ISBN)
Conference
NORMA11
Available from: 2012-10-24 Created: 2012-10-24 Last updated: 2016-07-05Bibliographically approved
4. Incorporating the practice of arguing in Stein et al.'s model for helping teachers plan and conduct productive whole-class discussions
Open this publication in new window or tab >>Incorporating the practice of arguing in Stein et al.'s model for helping teachers plan and conduct productive whole-class discussions
2015 (English)In: Development of Mathematics Teaching: Design, Scale, Effects: Proceedings from MADIF9: The Ninth Swedish Mathematics Education Research Seminar, Umeå, February, 4-5, 2014 / [ed] O. Helenius, A. Engström, T. Meaney, P. Nilsson, E. Norén, J. Sayers, & M. Österholm, Linköping: SMDF , 2015, 97-106 p.Conference paper, Published paper (Refereed)
Abstract [en]

How can pedagogical models support in-service and pre-service teachers in the complexity of orchestrating productive mathematical whole-class discussions? The overarching aim of this paper is to elaborate on a newly developed model to make it an even more useful tool for teachers to manage the challenging task of conducting productive whole-class discussions. Analyses of audio-recorded interviews and video-recorded whole-class discussions with a proficient mathematics teacher result in principles for how student solutions can be sequenced in order to take into account argumentation as well as connection-making in whole-class discussions. The findings suggest broadening the last practice in the five practices model to also incorporate the practice of arguing.

Place, publisher, year, edition, pages
Linköping: SMDF, 2015
Keyword
problem solving, whole-class discussion, argumentation, connection-making, five practices model
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-29401 (URN)
Conference
MADIF9
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2015-10-28Bibliographically approved
5. Exploring a framework for classroom culture: A case study of the interaction patterns in mathematical whole-class discussions
Open this publication in new window or tab >>Exploring a framework for classroom culture: A case study of the interaction patterns in mathematical whole-class discussions
2015 (English)In: Proceedings of CERME9: 9th Congress of European Research in Mathematics Education, Prague, February, 4-8, 2015 / [ed] K. Krainer & N. Vondrová, Prague: PedF UK v Praze and ERME , 2015Conference paper, Published paper (Refereed)
Abstract [en]

Research is needed on frameworks that support teachers in the important and challenging work of orchestrating productive problem-solving whole-class discussions. The aim of this paper is to explore a framework for classroom culture with the overarching goal of supporting teachers in conducting class discussions focused on argumentation as well as connection making. Analyses of video-recorded whole-class discussions result in the articulation of some difficulties in clearly distinguishing between certain interaction patterns within different classroom cultures. The overall findings, however, suggest that the framework can be useful for characterizing interaction in terms of an inquiry/argument classroom culture.

Place, publisher, year, edition, pages
Prague: PedF UK v Praze and ERME, 2015
Keyword
interaction pattern, whole-class discussion, classroom culture, inquiry/argument, instructional practice
National Category
Didactics
Identifiers
urn:nbn:se:mdh:diva-29402 (URN)
Conference
CERME9
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2015-10-28Bibliographically approved
6. Sensitizing Stein et al.'s five practices model to challenges crucial for argumentation in mathematical whole-class discussions
Open this publication in new window or tab >>Sensitizing Stein et al.'s five practices model to challenges crucial for argumentation in mathematical whole-class discussions
(English)Manuscript (preprint) (Other academic)
Keyword
whole-class discussion, problem solving, five practices model, argumentation, inquiry/argument, connection-making
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-29404 (URN)
Available from: 2015-10-27 Created: 2015-10-27 Last updated: 2016-02-25Bibliographically approved

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