| 1. |
- Brunström, Mats, 1960-
(författare)
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An Expanded Version of Toulmin’s Model to Analyze Students’ Mathematical Reasoning in a Dynamic Software Environment
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Toulmin’s model of argumentation has been used to analyse mathematical reasoning in a wide range of contexts. While conducting a recent case study of students’ mathematical reasoning in a dynamic software environment, it proved advantageous to develop an expanded version of this model to deepen the data analysis. Since this expanded model served well to discern and illustrate characteristic features in students’ reasoning, the question arose of whether it could also be useful in other cases. The present paper addresses this question, by considering further examples of students working in pairs in a dynamic software environment. The model was examined using data from two different studies, varying in the types of task and level of mathematics concerned. Transcribed data from these studies were interpreted in terms of the model to examine its applicability. Assessment of its use in all three studies shows that the expanded version of Toulmin’s model can enhance its capacity to analyse reasoning in this type of setting. At the same time, the operationalization of the model in concrete situations can sometimes be debatable, emphasising the importance of elucidating the interpretation principles used.
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| 2. |
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| 3. |
- Brunström, Mats, 1960-, et al.
(författare)
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Computer-aided assessment based on dynamic mathematics investigations
- 2020
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Ingår i: Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. - Linz, Austria.
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Konferensbidrag (refereegranskat)abstract
- In the poster, we will present a planned study focusing on the design of DMS tasks and elaborated feedback within a CAA system. The study will be conducted in a first year engineering mathematics course during autumn 2020.
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| 4. |
- Brunström, Mats, 1960-, et al.
(författare)
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Designing for a combined use of a dynamic mathematics software environment and a computer-aided assessment system
- 2022
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Ingår i: Proceedings of the Twelfth Congress of the European Research Society in Mathematics Education (CERME12). - : ERME.
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Konferensbidrag (refereegranskat)abstract
- This paper reports on a pilot study with the focus on (re)design of a digitized task environment utilizing two types of technology – a dynamic mathematics software and a computer-aided assessment system. The data consist of responses from 256 first year engineering students, taking their first Calculus course, on two different types of task. The results are discussed in relation to (re)design of tasks as well as possible feedback design options to enable a formative assessment approach.
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| 5. |
- Brunström, Mats, 1960-, et al.
(författare)
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Designing Prediction Tasks in a Mathematics Software Environment
- 2015
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Ingår i: The International Journal for Technology in Mathematics Education. - : RESEARCH INFORMATION LTD. - 1744-2710 .- 2045-2519. ; 22:1, s. 3-18
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Tidskriftsartikel (refereegranskat)abstract
- There is a recognized need in mathematics teaching for new kinds of task which exploit the affordances provided by new technology. This paper focuses on the design of prediction tasks to foster student reasoning about exponential functions in a mathematics software environment. It draws on the first iteration of a design based research study conducted by the authors in collaboration with four upper secondary school teachers. A task sequence was trailed with four 10th grade classes, involving a total of 85 students. The research process pinpointed key didactical variables that proved crucial in designing these tasks. As well as being useful in the task design process, the didactical variables were found to be valuable in the processes of analysis and revision. While the didactical variables identified a priori were informed by the research literature concerning reasoning and functions, those identified a posteriori deal mainly with scaffolding issues that emerged.
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| 6. |
- Brunström, Mats, 1960-, et al.
(författare)
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GeoGebra - A Tool to Create Favorable Learning Situations with Emphasize on Logical Reasoning and Communication
- 2009
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Konferensbidrag (populärvet., debatt m.m.)abstract
- Logic reasoning and communication are general competencies, important in all areas of mathematics. We think that one of the major advantages of GeoGebra is the possibility to create favorable learning situations for these competencies. We would like to investigate these possibilities. Our main interest is to find out how students use logic reasoning and how they communicate when they work in pairs with GeoGebra. We think that investigating the validity of certain geometrical statements is a kind of task appropriate for this purpose
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| 7. |
- Brunström, Mats, 1960-
(författare)
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Matematiska resonemang i en lärandemiljö med dynamiska matematikprogram
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The overall problem that formed the basis for this thesis is that students get limited opportunity to develop their mathematical reasoning ability while, at the same time, there are dynamic mathematics software available which can be used to foster this ability. The aim of this thesis is to contribute to knowledge in this area by focusing on task design in a dynamic software environment and by studying the reasoning that emerges when students work on tasks in such an environment. To analyze students’ mathematical reasoning, a new analytical tool was developed in the form of an expanded version of Toulmin’s model.Results from one of the studies in this thesis show that exploratory tasks in a dynamic software environment can promote mathematical reasoning in which claims are formulated, examined and refined in a cyclic process. However, this reasoning often displayed a lack of the more conceptual, analytic and explanatory reasoning normally associated with mathematics. This result was partly confirmed by another of the studies. Hence, one key question in the thesis has been how to design tasks that promote conceptual and explanatory reasoning. Two articles in the thesis deal with task design. One of them suggests a model for task design with a focus on exploration, explanation, and generalization. This model aims, first, to promote semantic proof production and then, after the proof has been constructed, to encourage further generalizations. The other article dealing with task design concerns the design of prediction tasks to foster student reasoning about exponential functions. The research process pinpointed key didactical variables that proved crucial in designing these tasks.
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| 8. |
- Brunström, Mats, 1960-, et al.
(författare)
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Orchestration of mathematical discussions drawing on students’ computer-based work
- 2017
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Ingår i: ICT in mathematics education: the future and the realities. - Göteborg : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402407 ; , s. 77-87
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Konferensbidrag (refereegranskat)abstract
- Research points out the importance of following up students’ work on computerbasedtasks with whole-class discussions in which students play a central role.However, at the same time, research highlights the challenge for teachers in orchestratingsuch follow-up discussions. This paper examines whether an establishedmodel developed as guidance for teachers to orchestrate mathematical whole-classdiscussions (Stein, Engle, Smith & Hughes, 2008) could be useful in this educationalsetting. Students’ written responses to two different tasks are the main data used toexamine the model. The results indicate that the model has great potential to guidethese follow-up discussions
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| 9. |
- Brunström, Mats, 1960-
(författare)
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Students’ Mathematical Reasoning in a Dynamic Software Environment
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- Mathematical reasoning has been identified as one of the key competencies needed to master mathematics. It is also well documented that dynamic mathematics software can be utilized to provide students with opportunities to practice different aspects of mathematical reasoning. In this study an expanded version of Toulmin’s model of argumentation was used to analyze the reasoning that emerged when three student pairs used GeoGebra to explore how the different parameters influence the graph of the function y = A sin (Bx + C) + D. Several characteristic features, both promising and cautionary, were discerned in the students’ reasoning.
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| 10. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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A Model for Task Design with Focus on Exploration,Explanation, and Generalization in a Dynamic GeometryEnvironment
- 2014
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Ingår i: Technology, Knowledge and Learning. - : Springer. - 2211-1662 .- 2211-1670. ; 19:3, s. 287-315
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Tidskriftsartikel (refereegranskat)abstract
- The increasing availability of new technologies in schools provides new possibilitiesfor the integration of technology in mathematics education. However, researchhas shown that there is a need for new kinds of task that utilize the affordances provided bynew technology. Numerous studies have demonstrated that dynamic geometry environmentsprovide opportunities for students to engage in mathematical activities such asexploration, conjecturing, explanation, and generalization. This paper presents a model fordesign of tasks that promote these kinds of mathematical activity, especially tasks thatfoster students to make generalizations. This model has been primarily developed to suitthe use of dynamic environments in tackling geometrical locus problems. The model wasinitially constructed in the light of previous literature. This initial model was used to designa concrete example of such a task situation which was tested in action through a case studywith two doctoral students. Findings from this case study were used to guide revision of theinitial model.
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