| 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)
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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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| 11. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Designing example-generating tasks for a technology-rich mathematical environment
- 2023
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Ingår i: International Journal of Mathematical Education in Science and Technology. - : Taylor & Francis. - 0020-739X .- 1464-5211. ; , s. 1-17
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Tidskriftsartikel (refereegranskat)abstract
- This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students’ mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined use of a dynamic mathematics software environment and a computer-aided assessment system. In example-generating tasks, students are asked to generate examples that fulfil certain conditions. Based on data in terms of examples generated by 491 first-year engineering students, taking a first course in calculus, the paper examines patterns of student response to three example-generating tasks. As a theoretical lens, the notions of dimensions of possible variation and associated ranges of permissible change are used. In light of the observed patterns, the paper provides some guiding principles for designing example-generating tasks and associated formative feedback to foster students’ mathematical understanding by enriching their example spaces. For example, this paper illustrates occasions where it might be instructive to start by asking for two examples, followed by adapted feedback before requesting a third example.
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| 12. |
- Fahlgren, Maria, 1966-
(författare)
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Designing for the integration of dynamic software environments in the teaching of mathematics
- 2015
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis concerns the challenge of integrating dynamic software environments into the teaching of mathematics. It investigates particular aspects of the design of tasks which employ this type of computer-based system, with a focus on improvement, both of the tasks themselves and of the design process through which they are developed and refined.The thesis reports two research projects: a small initial one preceding a larger main project. The initial case study, involving two graduate students in mathematics, develops a task design model for geometrical locus problems. The main study constitutes the first iteration of a design-based study, conducted in collaboration with four upper-secondary school teachers and their classes. It seeks to identify task design characteristics that foster students’ mathematical reasoning and proficient use of software tools, and examines teachers’ organisation of ‘follow-up’ lessons.The findings concern three particular aspects: features of tasks and task environment relevant to developing a specific plan of action for a lesson; orchestration of a particular task environment to support the instrumental genesis of specific dynamic software tools; how to follow up students’ work on computer-based tasks in a whole-class discussion.
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| 13. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Designing tasks and feedback utilizing a combination of a dynamic mathematics software and a computer-aided assessment system
- 2022
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Ingår i: Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15). - Aarhus : Danish School of Education, Aarhus Unviersity. - 9788775075256 ; , s. 272-279
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Konferensbidrag (refereegranskat)abstract
- This paper reports on the planning of a design-based research (DBR) study, where the main aim is to develop principles in designing technology-enhanced learning environment utilizing a combination of a dynamic mathematics software (DMS) and a computer-aided assessment (CAA) system. The focus is on the design of tasks and automated feedback of high quality so as to enhance first year engineering students’ engagement in and conceptual understanding of mathematical contents. The paper outlines the rationale for the project and highlights theoretical aspects that will be considered in the study. Moreover, some findings from a pilot study that will inform the first cycle of the DBR study are presented.
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| 14. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Example-generating tasks in a computer-aided assessment system : Redesign based on student responses
- 2022
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Ingår i: Proceedings of the 13<sup>th</sup> ERME Topic Conference (ETC13). - : Constantine the Philosopher University in Nitra. - 9788055819129 ; , s. 141-144
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Based on the patterns of response to an example-generating task, this paper provides suggestions onhow the task could be redesigned to enrich students’ example spaces in relation to the key ideasaddressed by the task. The participants are 236 first-year engineering students
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| 15. |
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| 16. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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How the word 'mathematical' influences students’ responses to explanation tasks in a dynamic mathematics software environment
- 2018
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Ingår i: Proceedings of the Fifth ERME Topic Conference (ETC 5) on Mathematics Education in the Digital Age (MEDA). - Copenhagen, Denmark : University of Copenhagen. - 9788770787987 ; , s. 83-90
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Konferensbidrag (refereegranskat)abstract
- Task design is a central issue in mathematics education, not least in relation to digital technology. This paper reports how a smal lbut significant change in wording affects students’ explanatory responses. The study is comparative and involves 229 10th grade students working on tasks designed for a dynamic mathematics software environment. The findings indicate that inclusion of the word ‘mathematical’ prompted students to use algebraic symbols and algebraic arguments, to a higher degree.
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| 17. |
- Fahlgren, Maria, 1966-
(författare)
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Instrumental genesis concerning scales and scaling in a dynamic mathematics software environment
- 2015
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Ingår i: Proceedings of the Ninth Congress of European Research in Mathematics Education. - Prague : European Society for Research in Mathematics Education. ; , s. 2347-2353
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Konferensbidrag (refereegranskat)abstract
- It is recognized that the process in which an artefact becomes an instrument for a user, denoted as instrumental genesis, is a complex process. The aim of this paper is to identify elements of the process of instrumental genesis when students are dealing with scales and scaling issues in a dynamic mathematics software environment. This study involves four upper secondary school teachers and their classes. By observing the students’ instrumented techniques while working with tasks designed with a hypothetical instrumental genesis in mind, some key elements are identified.
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| 18. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Orchestrating whole-class discussions in mathematics using connected classroom technology
- 2019
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Ingår i: Proceedings of the 14<sup>th</sup> International Conference on Technology in Mathematics Teaching - ICTMT 14. ; , s. 173-182
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- This paper reports on the planning of a pilot study where the aim is to develop and investigate teaching practices, using connected classroom technology (CCT), to support formative classroom practices in mathematics. The focus is on the design of a teaching unit including a whole-class discussion drawing on students’ computer-based work. The paper outlines both generic and topicspecific theories underpinning the design. Moreover, findings from a previous study, in terms of student responses to a task developed for a dynamic mathematics software environment, are used in the planning. One important issue addressed in this paper is the sequencing of student responses to display and use as a basis for whole-class discussions.
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| 19. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Prospective teachers designing tasks for dynamic geometry environments
- 2022
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Ingår i: Proceedings of the Twelfth Congress of the European Society for Research in Mathematics Education (CERME 12). - Bozen-Bolzano : Free University of Bozen-Bolzano. - 9791221025378
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Konferensbidrag (refereegranskat)abstract
- The paper examines the quality of digitized tasks designed by 10 (small) groups of prospective upper secondary school teachers as part of a geometry course assignment. The results indicate that a small instructional intervention, addressing the planning and implementation of tasks in digitized task environments as well as how to stimulate students to make mathematical generalizations, led to a relatively high proportion (8 out of 10) of high-quality tasks designed by the prospective teachers.
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| 20. |
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| 21. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Student responses as a basis for whole class discussions in technology-rich environment
- 2020
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Ingår i: Proceedings of the Tenth ERME topic Conference (ETC 10). - Linz, Austria. - 9783950463057 ; , s. 183-190
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Konferensbidrag (refereegranskat)abstract
- This paper reports a study of four upper secondary school teachers’ use of Connected Classroom Technology to select student responses to computer-based activities, and to use these responses to launch successive stages of a planned whole-class discussion. Although the preparation for the class discussion was quite successful, it was a challenge for the teachers to conduct the whole-class discussion, particularly in posing specific questions based on appropriate student responses.
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| 22. |
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| 23. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Technology-rich assessment in mathematics
- 2021
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Ingår i: Mathematics Education in the Digital Age. - : Taylor & Francis. - 9781000390766 - 9780367684518 ; , s. 69-83
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Bokkapitel (övrigt vetenskapligt/konstnärligt)
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| 24. |
- Fahlgren, Maria, 1966-, et al.
(författare)
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Using slider tools to explore and validate
- 2015
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Ingår i: CERME9 Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education. - 9788072908448
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Konferensbidrag (refereegranskat)
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| 25. |
- Szabo, Attila, et al.
(författare)
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Surveying prospective teachers’ conceptions of GeoGebra when constructing mathematical activities for pupils
- 2020
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Ingår i: Proceedings of the 10th ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. - Linz : Johannes Kepler University. - 9783950463057
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Konferensbidrag (refereegranskat)abstract
- In this poster, we present an ongoing study about prospective mathematics teachers' conceptions about the relationship between mathematics, problem-solving and GeoGebra. The context of our study is a curriculum reform in Sweden that emphasizes the use of digital tools in mathematics education. In that respect, we will investigate prospective upper-secondary teachers´ conceptions when participating in a geometry course at the university level. During the course, participants will construct mathematical activities for pupils by using GeoGebra.
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| 26. |
- Vinerean-Bernhoff, Mirela, 1974-, et al.
(författare)
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Prospective teachers constructing dynamic geometry activities for gifted pupils : Connections between the frameworks of Krutetskii and van Hiele
- 2022
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Ingår i: Gifted Education International. - : Sage Publications. - 0261-4294 .- 2047-9077. ; 38:2, s. 273-294
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Tidskriftsartikel (refereegranskat)abstract
- The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.
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