A Model for Task Design with Focus on Exploration, Explanation, and Generalization in a Dynamic Geometry Environment

Fahlgren, Maria; Brunström, Mats

doi:10.1007/s10758-014-9213-9

Cited by 21 publications

(11 citation statements)

References 33 publications

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“…In this article, the mathematics tasks designed by teachers were analyzed through the lens of Dynamic Geometry Tasks Analysis Framework (Trocki & Hollebrands, 2018). There are other frameworks proposed by mathematics education researchers (e.g., Fahlgren & Brunström, 2014;Gustafsson, 2016;Leung, 2017) to examine the quality of DigiTech mathematics tasks. We decided to use the framework from Trocki and Hollebrands (2018) since it is specific to the tasks created from dynamic geometry software such as GeoGebra and relating mathematical dept with technological actions.…”

Section: Digitech Tpdmentioning

confidence: 99%

“…In this article, we present the theories which relate to design of the task and classroom orchestration. For the first case, there are three proposed frameworks: (1) epsitemic model of task design in dynamic geometry environment (Leung, 2011) which he revised to Mathematics Digital Task Design Knowledge (Leung, 2017); (2) a model of task design which focus on exploration, explanation and generalization (Fahlgren & Brunström, 2014); and (3) Dynamic Geometry Tasks Analysis Framework (Trocki & Hollebrands, 2018). For the second case, instrumental orchestration and structuring features of classroom practices (Bozkurt & Ruthven, 2015;Ruthven, 2009) have used to examine how mathematics teachers orchestrate technology-rich mathematics teachings.…”

Section: Table 2 Coding Summary Of Group Digitech Mathematics Tasksmentioning

confidence: 99%

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Mathematics Teachers and Digital Technology: A Quest for Teachers’ Professional Development in Indonesia

Wahyu¹,

Ratnasari²,

Mahfudy³

et al. 2019

J. Res. Adv. Math. Educ

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This article aims to explore a possible criterion of digital technology mathematics teachers’ professional development[1]. The criterion was canvassed through qualitative exploratory study which involve a hybrid model of DigiTech TPD, online published articles of related TPD, and theoretical perspective which relate to digital technology in mathematics education. Related frameworks (Drijverset al, 2010; Trocki & Hollebrands, 2018) and content analysis were utilized to analyze the first two data. Theoretical perspectives of digital technology in mathematics education were accounted to reflect prior data and explore the criterion. We found that the current TPD[2]has not developed the knowledge of task design and supported teachers' roles in orchestrating technology-rich mathematics teaching as seen in the low level of tasks and teachers' orchestration in the classroom. Related articles on TPD in Indonesia show that the programs have not touched decisive factors of successfully implementing digital technology. An alternative criterion for DigiTech TPD is explored which includes three aspects namely theoretical approach, model and content. It could be alternative point of departure for designing and conducting DigiTech TPD in Indonesia.

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Section: Digitech Tpdmentioning

confidence: 99%

Section: Table 2 Coding Summary Of Group Digitech Mathematics Tasksmentioning

confidence: 99%

Mathematics Teachers and Digital Technology: A Quest for Teachers’ Professional Development in Indonesia

Wahyu¹,

Ratnasari²,

Mahfudy³

et al. 2019

J. Res. Adv. Math. Educ

View full text Add to dashboard Cite

show abstract

“…Indeed, a few researchers have explicated task design principles/models for particular aspects of proof-related activity (e.g. Fahlgren & Brunström, 2014;Leung, 2011). For example, Prusak, Hershkowitz and Schwarz (2012), in aiming at leading pre-service teachers to engage in productive peer argumentation, proposed three principles for task design: creating a situation of conflict, creating a collaborative situation, and providing tools for raising and checking hypotheses.…”

Section: Task Design With Dgementioning

confidence: 99%

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Komatsu

Jones

2018

Int J of Sci and Math Educ

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Task design is increasingly recognised as crucial for enhancing student learning of mathematics. Even so, and despite the significance of mathematical activity related to proofs and counterexamples in school mathematics, the task design principles underpinning students' success in proof-related activity remains under-explored in mathematics education research. What is more, although the affordances of using dynamic geometry environments (DGEs) have been established in the literature, task design in DGEs remains somewhat under-studied. In this paper, we address both these issues by theoretically developing, and empirically testing, task design principles for supporting students' heuristic refutation (revising conjectures/proofs through addressing counterexamples) in DGEs. We use the existing literature to elaborate three design principles: using tasks whose conditions are purposefully implicit, providing tools that enhance the production of counterexamples, and increasing students' recognition of contradictions. To test these principles empirically, we analyse two sets of task-based interviews, one with a triad of secondary school students and the other with a pair of undergraduates, where tasks designed according to the principles were implemented. Our analysis shows that using the tasks enabled the students to engage successfully in heuristic refutation. The matter of examining mathematical definitions when handling counterexamples emerged as an issue for further research.

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“…Both Fahlgren and Brunström (2014) and Leung (2011) propose models for the design of tasks that foster students to make generalizations by capitalising on the drag-mode within DGEs. Meanwhile, Trgalova et al (2011) showed how the idea of involving teachers in evaluating the quality of tasks is a "promising way of stimulating the use of dynamic geometry in classrooms" provided that teachers "benefit from support to make the quality pro-cess their own" (p. 337).…”

Section: Task Design With Technologiesmentioning

confidence: 99%

Recent research on geometry education: an ICME-13 survey team report

Sinclair

Bartolini

Villiers

et al. 2016

ZDM Mathematics Education

130

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This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.

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A Model for Task Design with Focus on Exploration, Explanation, and Generalization in a Dynamic Geometry Environment

Cited by 21 publications

References 33 publications

Mathematics Teachers and Digital Technology: A Quest for Teachers’ Professional Development in Indonesia

Mathematics Teachers and Digital Technology: A Quest for Teachers’ Professional Development in Indonesia

Task Design Principles for Heuristic Refutation in Dynamic Geometry Environments

Recent research on geometry education: an ICME-13 survey team report

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