Investigating Plane Geometry Problem-Solving Strategies of Prospective Mathematics Teachers in Technology and Paper-and-Pencil Environments

Koyuncu, İlhan; Akyüz, Didem; Çakıroğlu, Erdinç

doi:10.1007/s10763-014-9510-8

Cited by 23 publications

(18 citation statements)

References 9 publications

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“…However, as Gawlick (2002) pointed out, to profit from such an environment, students-especially low achievers-need some time to get accustomed to handling the software. Comparing DGS and paper-and-pencil environments, Koyuncu et al (2015) observed that in a study with two pre-service teachers, " [b] oth participants had a tendency toward using algebraic solutions in the [paper-and-pencil based] environment, whereas they used geometric solutions in the [DGS based] environment." (p. 857 f.).…”

Section: Problem Solving In Geometry and Dynamic Geometry Softwarementioning

confidence: 99%

A descriptive phase model of problem-solving processes

Rott

Specht

Knipping

2021

ZDM Mathematics Education

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Complementary to existing normative models, in this paper we suggest a descriptive phase model of problem solving. Real, not ideal, problem-solving processes contain errors, detours, and cycles, and they do not follow a predetermined sequence, as is presumed in normative models. To represent and emphasize the non-linearity of empirical processes, a descriptive model seemed essential. The juxtaposition of models from the literature and our empirical analyses enabled us to generate such a descriptive model of problem-solving processes. For the generation of our model, we reflected on the following questions: (1) Which elements of existing models for problem-solving processes can be used for a descriptive model? (2) Can the model be used to describe and discriminate different types of processes? Our descriptive model allows one not only to capture the idiosyncratic sequencing of real problem-solving processes, but simultaneously to compare different processes, by means of accumulation. In particular, our model allows discrimination between problem-solving and routine processes. Also, successful and unsuccessful problem-solving processes as well as processes in paper-and-pencil versus dynamic-geometry environments can be characterised and compared with our model.

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Section: Problem Solving In Geometry and Dynamic Geometry Softwarementioning

confidence: 99%

A descriptive phase model of problem-solving processes

Rott

Specht

Knipping

2021

ZDM Mathematics Education

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“…Barrera-Mora and Reyes-Rodriguez (2013) concluded that DGEs act as reorganizers of mathematical thinking, allowing cognitive activities only possible due to the dynamism embedded in the tool, leading to explore variation and covariation, and to different forms of justifying a conjecture and expressing it with the tool. Other studies point that the mathematics used by students working on a paper-and-pencil task is different from the one they apply when using a touchscreen device (Bairral, Arzarelo, & Assis, 2017); students use similar strategies both with paper-and-pencil and an applet in solving equations (Jupri, Drijvers, & van den Heuvel-Panhuizen, 2016); there are benefits in both environments (Koyuncu, Akyuz, & Cakiroglu, 2015), or the two environments play a complementary role in mathematical learning, particularly in conjecturing and proving activities (Komatsu & Jones, 2020). Some researchers call for a "partnership of paper and digital settings" (Usiskin, 2018, p. 861), since the 'electronic partner' provides new affordances for real-world problemsolving, such as dynamic representations of variation.…”

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confidence: 99%

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Jacinto

Carreira

2021

J. Math. Educ.

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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

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“…A case study by Prusak et al (2012) showed that a pair of preservice teachers engaged in productive argumentation through an iterative combination of DGE use and paper-and-pencil work accompanied with paper folding. Meanwhile, Koyuncu et al (2015) showed differences between prospective teachers' problemsolving strategies in a DGE and in a paper-and-pencil environment.…”

mentioning

confidence: 99%

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

Komatsu

Jones

2020

Digit Exp Math Educ

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Digital tools have a potential to change significantly the form of mathematical learning taking place in classrooms, with research pointing to various affordances in comparison with physical tools such as paper-and-pencil environments. Nevertheless, there is a scarcity of research that has examined in-depth the interrelated roles these two types of tools fulfil in mathematics learning. This issue of interrelated roles is important because, when digital tools are incorporated into classrooms, students usually also have notebooks and worksheets within which they carry out actions complementary to their use of digital tools. In this article, we focus on the use of dynamic geometry environments (DGEs) in conjecturing and proving, and, in particular, we examine the interplay between students' paper-and-pencil activity and their use of a DGE during the producing and proving of a generalisation of a statement. We analyse a series of lessons involving secondary school students (aged 14-15, Grade 9) and show that, while DGE use supported the students in generalising a statement, they were initially unable to prove the generalisation while using the DGE, but subsequently succeeded through their paper-and-pencil activity. Our research illustrates the affordance of paper-andpencil environments to support students in working on different representations, and thus highlights how the interplay between paper-and-pencil activity and DGE use can be important for the progress of conjecturing and proving. We also show the roles taken by the teacher in supporting the students' work, and point to the need for further research into the back-and-forth use of digital and physical tools. Keywords Digital tool. Physical tool. Dynamic geometry environment. Paper-and-pencil activity. Generalisation and proof. Teacher role It is now well known that digital tools provide relative affordances in comparison with those provided by physical tools, such as paper-and-pencil environments and concrete

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Investigating Plane Geometry Problem-Solving Strategies of Prospective Mathematics Teachers in Technology and Paper-and-Pencil Environments

Cited by 23 publications

References 9 publications

A descriptive phase model of problem-solving processes

A descriptive phase model of problem-solving processes

Digital Tools and Paper-and-Pencil in Solving-and-Expressing: How Technology Expands a Student’s Conceptual Model of a Covariation Problem

Interplay between Paper-and-Pencil Activity and Dynamic-Geometry-Environment Use during Generalisation and Proving

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