| 1. |
- Borg, Andreas
(författare)
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Designing for the incorporation of programming in mathematical education : Programming as an instrument for mathematical problem solving
- 2021
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This study explored Swedish upper secondary school students’ use of programming for mathematical purposes. The aim of the study was to investigate the process through which students learn how to use a programming environment as a technical artefact during mathematical problem solving and how the orchestration of such learning situations could facilitate this process. In order to study the students’ use of the programming environment, design-based research was used as the main methodological approach. The design involved the development of specific mathematical tasks to be tried out with students, as well as the orchestration of the learning situation within the classroom e.g., by preparing scaffolding to be offered to the students. The subsequent implementation of the design was analysed so that, in accordance with the cyclic approach of design-based research, it could be revised ahead of the following design cycle. The study involved two complete design cycles. In the study, the Instrumental Approach was used as the theoretical framework and the instrumental genesis of the students in using a programming environment for mathematical purposes was thus of special interest. In order to analyse this process and the associated mental schemes developed by the students, Vergnaud’s concept of scheme served as an analytical framework. The findings revealed how the students, despite having basic knowledge in programming, experienced several difficulties when trying to use the programming environment as a technical mathematical artefact. These difficulties were related both to the fact that the mathematical affordances offered by the programming environment were unclear to many of the students, as well as to the handling of more specific computational concepts such as nested loops. The findings also revealed that the transformation of mathematical notations and ideas into programming code caused students difficulties.
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| 2. |
- Borg, Andreas, et al.
(författare)
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Analysing mathematical programming schemes using different lenses
- 2023
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Ingår i: Nordisk matematikkdidaktikk, NOMAD. - : University of Gothenburg, Sweden. - 1104-2176. ; 28:3–4, s. 199-219
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Tidskriftsartikel (refereegranskat)abstract
- The use of programming in mathematics education is undergoing a renaissanceand, in this paper, we analyse students’ handling of programming in mathematicsusing the Instrumental approach as a theoretical lens. We are especially interestedin analysing the development of mental schemes using two analytical frameworkswhich are compared and contrasted according the idea of networking theories. Thestudy illustrates that the frameworks’ detail of richness can have both advantagesand disadvantages and that one of the frameworks are more customed to be appliedwhen analysing students’ instrumental genesis concerning the use of a programmingenvironment as a mathematical artefact.
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| 3. |
- Borg, Andreas, et al.
(författare)
-
Programming as a mathematical instrument : the implementation of an analytic framework
- 2020
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Ingår i: Mathematics Education in the Digital Age (MEDA) PROCEEDINGS. - 9783950463057 ; , s. 435-442
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Konferensbidrag (refereegranskat)abstract
- This paper relates to an ongoing project using design-based research as a methodol- ogical approach in which students with no prior experiences of using programming as a mathematical tool are observed trying to solve mathematical problems with the help of programming. The Instrumental Approach is used as conceptual framework in which the concept of instrumental genesis describes the process where the programming environment as an artefact together with student-developed mental schemes forms an instrument in order to solve mathematical problems. The development of schemes is of special interest in this paper where Vergnaud’s components of a scheme provide a framework for analysing transcripts of talk between student pairs and the programming code that they generate.
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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 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. |
- 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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| 10. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Connected classroom technology to monitor, select and sequence student responses
- 2021
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Ingår i: Sustainable mathematics education in a digitalized world. - : Svensk förening för MatematikDidaktisk Forskning - SMDF. - 9789198402445 ; , s. 11-20
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Konferensbidrag (refereegranskat)abstract
- This paper reports a study of teachers’ use of Connected classroom technology to prepare for whole-class discussions building on students’ computer-based work in mathematics. The study investigates four upper secondary school teachers’ management of time and progression during the phase of the lesson where students are working in pairs. The findings highlight various didactical choices made by the teachers. These choices and some related challenges are discussed
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