Problem solving and the use of digital technologies within the Mathematical Working Space framework

Santos‐Trigo, Manuel; Moreno–Armella, Luis; Camacho-Machín, Matías

doi:10.1007/s11858-016-0757-0

Cited by 29 publications

(13 citation statements)

References 14 publications

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“…The U.S. National Council of Teachers of Mathematics (NCTM 2009) suggests that using technology to link multiple representations of mathematical objects dynamically provides students with opportunities to engage in mathematical sense-making. Such tasks should engage students in problem solving (Santos-Trigo et al 2016) and invite students to visualize objects and explore dynamic variations, by investigating, for example, the areas of triangles with different shapes and a given perimeter. Leung (2011) argues that for students to benefit from dynamic software, the given tasks should invite them to explore, reconstruct and explain mathematical concepts and relations.…”

Section: Designing Tasks For Problem Solving and Reasoningmentioning

confidence: 99%

“…GeoGebra has the potential to provide students with dynamic, algebraic and graphical representations of mathematical objects. It has been found that students use GeoGebra tools to explore and investigate these objects' relations and properties (Preiner 2008;Bu and Schoen 2011;Santos-Trigo et al 2016). Based on our experiences and literature, in the context of this study (presented below in the BMethod^Section), GeoGebra's potential to support problem solving and reasoning is specified in terms of:…”

Section: The Potential Of Geogebra To Support Problem Solving and Reamentioning

confidence: 99%

“…Task 2 in this study provided the students with multiple examples of successfully constructed objects and perpendicular graphs, and invited them to explore the relationships between the graphical and algebraic representations of linear functions. Such circumstances have been suggested as beneficial for reasoning (Falcade et al 2007), problem solving (Santos-Trigo et al 2016) and developing an understanding of functions (Vinner and Dreyfus 1989).…”

Section: Intention and Outcome Of Taskmentioning

confidence: 99%

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Relations Between Task Design and Students’ Utilization of GeoGebra

Olsson

2019

Digit Exp Math Educ

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This study contributes insights into how task design with different elements of guidance may influence students' utilization of dynamic software for problem solving and reasoning. It compared students' solving of two tasks with different designs supported by the dynamic software GeoGebra. Data analysed examined students' approaches to utilizing GeoGebra, the characteristics of their reasoning and their ability to prove the validity of their solutions after solving the problems. The results showed that students who solved the task with less guidance (without instructions about a specific solving method) were better able to utilize GeoGebra's potential to support their reasoning and problem solving. These students reasoned more creatively and presented more advanced proofs for their solutions than the more guided ones. Keywords GeoGebra. Creative reasoning. Task design. Non-routine tasks A recurrent question in educational research is whether and how technology may support students' learning mathematics. Dynamic software, in this case GeoGebra, invites students to create and manipulate geometric and algebraic representationsfeatures that are considered to have the potential to support problem solving and reasoning (Falcade et al. 2007; Preiner 2008). In situations where students make use of these potentials, they create mathematical objects based on questions or hypotheses. They then interpret, assess and transform the outcomes to proceed in their problem solving. The results, however, are assumed to come from the students' engaging in problem solving and reasoning, and their use of the features of the software to do so. However, it is important to know, rather than simply to assume, what students do when they use dynamic software such as GeoGebra and what guides them in using the

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Section: Designing Tasks For Problem Solving and Reasoningmentioning

confidence: 99%

Section: The Potential Of Geogebra To Support Problem Solving and Reamentioning

confidence: 99%

Section: Intention and Outcome Of Taskmentioning

confidence: 99%

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Relations Between Task Design and Students’ Utilization of GeoGebra

Olsson

2019

Digit Exp Math Educ

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“…Problem solving is an important aspect of mathematics teaching and learning, it occurs in all mathematical curricula [2]. In recent years the use of digital technologies in problem solving activities has allowed a precious variety of representation and exploration of mathematical tasks [3] extending the ways of thinking about the strategies involved in problem solving [4]. One of the technologies used for problem solving activities is Maple, which allows numerical and symbolic calculations, static and animated graphical representations in 2 and 3 dimensions, writing procedures in simple language, programming and connecting all these different registers representation in a single worksheet using verbal language, too [5].…”

Section: Introductionmentioning

confidence: 99%

The Creation of Animated Graphs to Develop Computational Thinking and Support STEM Education

Barana

Conte

Floris

et al. 2020

Communications in Computer and Information Science

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Problem solving and computational thinking are the key competences that all individuals need for professional fulfillment, personal development, active citizenship, social inclusion and employment. In mathematics, during contextualized problem solving using Maple, the differences between these two skills become thinner. A very important feature of Maple for problem solving is the programming of animated graphs: an animation obtained by generalizing a static graph, choosing the parameter to be varied and its interval of variation. The first objective of this research is to analyze the computational thinking processes behind the creation of animated graphs for the resolution of a contextualized problem. To this end, we selected and analyzed some resolutions of problems carried out by fourth-grade students of upper secondary schools in Italy (grade 12). The paper shows some examples in which different processes of computational thinking have emerged, which reflect resolutive strategies and different generalization processes. From the analysis it emerged that all the processes underlying the mental strategies of the computational thinking useful for solving problems are activated in the creation of animated graphs. In the second part of the article we discuss examples of animations created during training activities with secondary school teachers, and how animations can support the learning of scientific concepts. It is very important to train the teachers in this regard, both to understand the processes that the students would activate during the creation of animated graphics and to enrich the theoretical or practical explanations with animated representations.

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“…In the resolution of a problem, they enable to visualize how the results change when the input parameters are changed and therefore they allow to generalize the solving process of a problem. In the problem solving process, generalizing is an important process by which the specifics of a solution are examined and questions such as why it worked are investigated [6,7]. This process is analogue to the verification and elaboration stages of invention and creativity [8].…”

Section: Introductionmentioning

confidence: 99%