| 1. |
- Ryve, Andreas, et al.
(author)
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Analyzing effective communication in mathematics group work : The role of visual mediators and technical terms
- 2013
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In: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 82:3, s. 497-514
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Journal article (peer-reviewed)abstract
- Analyzing and designing productive group work and effective communication constitute ongoing research interests in mathematics education. In this article we contribute to this research by using and developing a newly introduced analytical approach for examining effective communication within group work in mathematics education. By using data from 12 to 13-year old students playing a dice game as well as from a group of university students working with a proof by induction, the article shows how the link between visual mediators and technical terms is crucial in students' attempts to communicate effectively. The critical evaluation of visual mediators and technical terms, and of links between them, is useful for researchers interested in analyzing effective communication and designing environments providing opportunities for students to learn mathematics.
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| 2. |
- Nilsson, Per, 1967-, et al.
(author)
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Focal event, contextualization, and effective communication in the mathematics classroom
- 2010
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In: Educational Studies in Mathematics. - : Springer Science and Business Media LLC. - 0013-1954 .- 1573-0816. ; 74:3, s. 241-258
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Journal article (peer-reviewed)abstract
- The aim of this article is to develop analytical tools for studying mathematical communication in collaborative activities. The theoretical construct of contextualization is elaborated methodologically in order to study diversity in individual thinking in relation to effective communication. The construct of contextualization highlights issues of diversity in collaborative activities as it emphasizes how students may struggle differently with a learning activity. The interaction of students (12 to 13 years old), playing a specifically designed dice game, is used as an example for illustration. The article shows how accounting for the focal events of the interlocutors, and the contexts in which they contextualize these events, help in organizing our thinking about mathematically effective communication in collaborative activities.
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| 3. |
- Ryve, Andreas, et al.
(author)
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Establishing mathematics for teaching within classroom interactions in teacher education
- 2012
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In: Educational Studies in Mathematics. - : Springer Netherlands. - 0013-1954 .- 1573-0816. ; 81:1, s. 1-14
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Journal article (peer-reviewed)abstract
- Teacher educators’ processes of establishing ‘mathematics for teaching’ in teacher education programs have been recognized as an important area for further research. In this study we examine how two teacher educators establish and make explicit features of mathematics for teaching within classroom interactions. The study shows how the establishment of mathematics for teaching is dependent on the use of keywords from the mathematics education domain, the introduction of variation, and the use of generic communicative strategies. As such, the study could be seen as a contribution to ongoing research on how mathematics teacher educators interactively deal with mathematics for teaching.
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| 4. |
- Nilsson, Per, 1967-, et al.
(author)
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Characterizing theories aimed at supporting teachers' mathematical classroom practices
- 2017
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In: PROCEEDINGS OF THE TENTH CONGRESS OF THE EUROPEAN SOCIETY FOR RESEARCH IN MATHEMATICS EDUCATION (CERME10). - : DUBLIN CITY UNIV GLASNEVIN CAMPUS, INST EDUCATION. ; , s. 3865-3872
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Conference paper (peer-reviewed)abstract
- In this paper we draw upon examples from a recently published systematic literature review (Ryve et al., 2015) on productive classroom practice to contribute to the research on the nature of theories for action in mathematics education. By relating the results from the review to theories and literature on educational policy research, professional development research and implementation research we construct a framework for categorizing theories aiming at supporting teachers' actions in mathematical classroom practices.
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| 5. |
- Nilsson, Per, 1967-, et al.
(author)
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The nature and role of common ground in the learning of mathematics in small-group discussions
- 2014
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In: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 58:5, s. 609-623
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Journal article (peer-reviewed)abstract
- This study investigates the nature and role of common ground in group learning of mathematics by means of the analytical construct of focal projects and contextualization. The analysis investigates two students (12-13 years old) playing a dice game, where they are to distribute a set of markers based on the totals of two dice. The analysis shows how the consistency between the students’ focal projects became critical to their progression from a uniform to a non-uniform distribution of the markers. The task system and concrete manipulatives became crucial in furthering the students’ explorations. In the frame of a frequency context, we also discuss how a contextualization may restrict certain aspects of probability from coming into play during such explorations.
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| 6. |
- Ryve, Andreas, 1973-, et al.
(author)
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Analyzing content and participation in classroom discourse : dimensions of variation, mediating tools, and conceptual accountability
- 2013
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In: Scandinavian Journal of Educational Research. - : Informa UK Limited. - 0031-3831 .- 1470-1170. ; 57:1, s. 101-114
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Journal article (peer-reviewed)abstract
- 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.
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| 7. |
- Bergwall, Andreas, 1972-
(author)
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Proof-related reasoning in upper secondary mathematics textbooks : Characteristics, comparisons, and conceptualizations
- 2021
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Doctoral thesis (other academic/artistic)abstract
- Proofs and proving are difficult to learn and difficult to teach. A common problem is that many students use specific examples as evidence for general statements. Difficulties with proofs are also part of the transition problems that exist between secondary and tertiary schooling in mathematics. As mathematics teaching often follows a textbook, the design of textbooks has been pointed out as one possible cause of the problems, and international textbook research suggests that proofs often have only a marginal place in textbooks.This thesis focuses on proofs and proving in upper secondary mathematics textbooks. It also addresses theoretical and methodological questions about what marks an opportunity to develop proving competence, and which properties of such opportunities are relevant to investigate and characterize. The thesis is based on data from four Swedish and Finnish textbook series for upper secondary school, and focuses on sections on logarithms, primitive functions, definite integrals, and combinatorics. It examines how addressed mathematical principles are justified, and whether the textbooks’ exercises offer opportunities to develop proof-related skills such as formulating and investigating hypotheses, developing and evaluating arguments, identifying and correcting errors, and finding counterexamples.The results show that just over half of the mathematical principles addressed in the analyzed textbook material are justified, and that only half of the justifications are general proofs. Few exercises are proof-related (10%), and those that include reasoning about general cases even fewer. General proofs are more common in the Finnish books, but proof-related tasks are more common and of a more varied nature in the Swedish ones. The most common form of proofs are direct derivations of calculation formulas, while reasoning about existence and uniqueness is unusual, as are contrapositive proofs and proofs by contradiction.Based on the results, explicit suggestions are offered as to what teaching can pay more attention to. For the analysis and design of proof-related activities, a framework consisting of four main categories is proposed: develop a statement, investigate a statement, develop an argument, and investigate an argument. Several properties that such activities may have, regardless of which category they belong to, are discussed. Finally, three areas for future research are suggested: how worked examples can support students’ learning of proof, how textbooks can be designed to stimulate formulation as well as the formal proving of hypotheses, and mapping of differences regarding proof between upper secondary and university textbooks.
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| 8. |
- Knutsson, Malin, 1978-, et al.
(author)
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School-based mathematics teacher education in Sweden and Finland : characterizing mentor – prospective teacher discourse
- 2013
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In: The Eighth Congress of the European Society for Research in Mathematics Education. Feb 6th - Feb 10th, 2013. - Antalya, Turkey. - 9789754293159
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Conference paper (peer-reviewed)abstract
- Despite many similarities between the neighbouring countries Sweden and Finland, prior studies indicate that conceptualizations and discourses about school-based teacher education are very different. In this paper we add to this picture of differences, and contribute to the research discourse about school-based teacher education, by identifying and characterizing aspects of mathematics teaching made relevant in review meetings between mentors and prospective primary teachers. While the Swedish discourse typically focuses on the students’ individual work with textbooks, connections to everyday experiences and teaching as individual supervision, the Finnish discourse emphasizes lesson aims, learning and progression in mathematics through formative assessment and differentiation according to pupils’ abilities
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