Computational Construction as a Means to Coordinate Representations of Infinity

Sacristán, Ana Isabel; Noss, Richard

doi:10.1007/s10758-008-9127-5

Cited by 13 publications

(6 citation statements)

References 17 publications

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“…From this contemporary hermeneutic viewpoint, mathematical thinking emerges from a process of interpretation, with understanding and concepts perceived as temporary fixes of ongoing development, rather than permanent realities. This resonates with the notion of the hermeneutic circle, with learning and understanding always in transition (Ricoeur, 1981). Our understanding of mathematical ideas emerges through cyclical engagements with the phenomena and the continual drawing forward of previous encounters and understandings.…”

Section: Methodsmentioning

confidence: 68%

Using Scratch to facilitate mathematical thinking

Calder¹

2019

WJE

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This article reports on a research project that examined the ways that 10-year-old students, who were using Scratch for coding, engaged with mathematical ideas. Interactive software is emerging that has cross-curricula implications and facilitates thinking in rich, problem-solving environments. Scratch, a free-to-use graphical programming environment provides opportunities for creative problem solving. When students process mathematics through digital technologies, the digital pedagogical media influences the learning process and students’ understanding emerges in distinctive ways. The children used Scratch to create mathematical digital learning objects, including games. An interpretive approach was undertaken, with the data collected over a two-week research period. The students wrote daily blogs articulating their progress and reflections. Students and the teacher were interviewed, and classroom observations (both written and photographic) were recorded. The findings suggest that mathematical thinking, including geometry and problem-solving processes, was facilitated through this process. Together, these findings indicate that teachers should not only use Scratch in primary school classroom programmes to develop coding skills but also be aware of its potential to facilitate thinking in other related areas.

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Section: Methodsmentioning

confidence: 68%

Using Scratch to facilitate mathematical thinking

Calder¹

2019

WJE

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“…Several studies focus on the various integrations of technologies into current educational settings and some on the future potentials of new emerging technologies [4]. These experiences have deepened students' understanding and boosted their Sustainability 2022, 14, 7237 2 of 15 confidence and enjoyment of engaging with mathematics and other science subjects [5][6][7][8][9]. Increasing students' confidence and enjoyment in engaging with mathematics and other science subjects should contribute to sustainable learning, according to [10].…”

Section: Introductionmentioning

confidence: 99%

Developing and Evaluating Educational Innovations for STEAM Education in Rapidly Changing Digital Technology Environments

et al. 2022

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In this paper, we offer three examples from our research projects on both technological and pedagogical innovations to illustrate the impact of rapid technology changes on research. Members of our research team both developed and used technology applications in their research projects, utilizing design-based research (DBR). During the experiments, we encountered new challenges by the end of the research cycle due to updates in technologies. Although we had an idea of how to redesign the project for the next cycle based on the analyses of data, we noticed that we needed to not only redesign our approaches based on the research results but the changes in technologies were so rapid that materials and pedagogies needed to be altered as well. In our article, we propose an additional aspect to be considered in DBR while researching technology integration or innovative technologies. Moreover, the rapid change in technology raises further challenges to teachers’ professional development and the integration of those innovative technologies in classrooms. We anticipate our work to contribute to the development of technology resources and related pedagogies as well as the refinement of research methodologies in technology environments. Our contributions for the development of technology resources and refinement of research methods in technology-supported learning environments should, among other things, contribute to a less complex and at the same time more sustainable integration of pedagogical innovations into scientific and school practices.

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“…Beyond translating, some mathematics educators have already mentioned the need to make the connections between representations more explicit (Duval, 2006;Kaput, 1989;Marshall et al, 2010;Prediger & Wessel, 2013;Sacristán & Noss, 2008). The teaching practice is therefore now often referred to as connecting multiple representations: for example, the practical paper by Marshall et al (2010) suggested the instructional strategy that teachers engage students in dialog to make explicit the connections among representations (similarly NCTM, 2014).…”

Section: Connecting Rather Than Translating As a Relevant Student Pro...mentioning

confidence: 99%

Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information

Post

Prediger

2022

Math Ed Res J

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Multiple representations can enhance students’ understanding of mathematical concepts and complex information but can also pose well-documented challenges for students. Whereas instructional designs have been optimized to support students’ learning with multiple representations, little is known about supportive teaching practices for dealing with multiple representations in whole-class discussions. In this article, we qualitatively investigate two cases of teacher-student interaction in whole-class discussions in grades 10–12 (about the mathematical topic of complex conditional probability information). The analysis aims at decomposing the teaching practices into those actions that can support or hinder students’ understanding. The comparison of cases reveals that teaching practices can vary greatly: simply translating compacted concepts of a given text into other representations (visual area model, symbolic representation of fractions, and three language varieties) seems to be sufficient for students with advanced understanding. Other students need teachers’ supportive actions for unfolding the highly compacted concepts (such as part-of-part) into several concept elements (part, whole, and part-whole relationship) and explicitly connecting (rather than only translating) the concept elements in multiple representations for the different concept elements. The findings can inform both theory building on teaching practices with multiple representations and professional development.

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Computational Construction as a Means to Coordinate Representations of Infinity

Cited by 13 publications

References 17 publications

Using Scratch to facilitate mathematical thinking

Using Scratch to facilitate mathematical thinking

Developing and Evaluating Educational Innovations for STEAM Education in Rapidly Changing Digital Technology Environments

Teaching practices for unfolding information and connecting multiple representations: the case of conditional probability information

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