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Balancing on the edge of competency-oriented versus procedural-oriented practices: orchestrating whole-class discussions of complex mathematical problems
Mälardalen University, School of Education, Culture and Communication. (M-TERM)ORCID iD: 0000-0002-6518-1418
Mälardalen University, School of Education, Culture and Communication. (M-TERM)ORCID iD: 0000-0002-3329-0177
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.

Place, publisher, year, edition, pages
2012. Vol. 24, no 4, 447-465 p.
National Category
Educational Sciences
Research subject
Mathematics/Applied Mathematics; Didactics
Identifiers
URN: urn:nbn:se:mdh:diva-15674DOI: 10.1007/s13394-012-0049-0Scopus ID: 2-s2.0-84869118757OAI: oai:DiVA.org:mdh-15674DiVA: diva2:561600
Available from: 2012-10-19 Created: 2012-10-19 Last updated: 2016-07-05Bibliographically approved
In thesis
1. Orchestrating mathematical whole-class discussions in the problem-solving classroom: Theorizing challenges and support for teachers
Open this publication in new window or tab >>Orchestrating mathematical whole-class discussions in the problem-solving classroom: Theorizing challenges and support for teachers
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
whole-class discussion, problem solving, five practices model, mathematical connection, argumentation, inquiry/argument, supportive tool
National Category
Didactics
Research subject
Didactics
Identifiers
urn:nbn:se:mdh:diva-29409 (URN)978-91-7485-242-4 (ISBN)
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

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