Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

Bakker, Arthur; Hoffmann, Michael H. G.

doi:10.1007/s10649-005-5536-8

Cited by 78 publications

(39 citation statements)

References 25 publications

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“…I am proposing a semiotic approach as an intellectual foundation for a principled design framework (Abrahamson 2003(Abrahamson , 2004bAbrahamson & Wilensky 2007;Bakker & Hoffmann 2005;Fuson & Abrahamson 2005). Students perform semiotic acts with available media apropos of warranting intuitive inferences.…”

Section: Discussionmentioning

confidence: 99%

“…To begin with, a focus on media -the objects that formulate, store, convey, and mirror student expression -is closely aligned with design-based researchers' analytical and pragmatic objectives (Bakker & Hoffmann 2005): to better theorize the roles of mathematical objects in creating opportunities for mediated content learning and, so doing, to delineate principles for effective design. Methodologically, the approach improves calibration between, on the one hand, the sampling density of microgenetic analysis (Schoenfeld, Smith, & Arcavi 1991;Siegler & Crowley 1991) and, on the other hand, the apparent micro-intentions of the participant students.…”

Section: Background and Objectivesmentioning

confidence: 99%

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Embodied design: constructing means for constructing meaning

Abrahamson

2008

Educ Stud Math

108

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Design-based research studies are conducted as iterative implementationanalysis-modification cycles, in which emerging theoretical models and pedagogically plausible activities are reciprocally tuned toward each other as a means of investigating conjectures pertaining to mechanisms underlying content teaching and learning. Yet this approach, even when resulting in empirically effective educational products, remains underconceptualized as long as researchers cannot be explicit about their craft and specifically how data analyses inform design decisions. Consequentially, design decisions may appear arbitrary, design methodology is insufficiently documented for broad dissemination, and design practice is inadequately conversant with learning-sciences perspectives. One reason for this apparent under-theorizing, I propose, is that designers do not have appropriate constructs to formulate and reflect on their own intuitive responses to students' observed interactions with the media under development. Recent socio-cultural explication of epistemic artifacts as semiotic means for mathematical learners to objectify presymbolic notions (e.g., Radford, Mathematical Thinking and Learning 5(1): 37-70, 2003) may offer design-based researchers intellectual perspectives and analytic tools for theorizing design improvements as responses to participants' compromised attempts to build and communicate meaning with available media. By explaining these media as potential semiotic means for students to objectify their emerging understandings of mathematical ideas, designers, reciprocally, create semiotic means to objectify their own intuitive design decisions, as they build and improve these media. Examining three case studies of undergraduate students reasoning about a simple probability situation (binomial), I demonstrate how the semiotic approach illuminates the process and content of student reasoning and, so doing, explicates and possibly enhances design-based research methodology.

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Section: Discussionmentioning

confidence: 99%

Section: Background and Objectivesmentioning

confidence: 99%

Embodied design: constructing means for constructing meaning

Abrahamson

2008

Educ Stud Math

108

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“…Peirce distinguishes icons, indices and symbols, where icons are subdivided into metaphors, images and diagrams (see e.g., Bakker & Hoffmann, 2005;Stjernfelt, 2000). The main function of an index is to direct someone's attention to something (Peirce, 1976, Vol.…”

Section: Discussionmentioning

confidence: 99%

Situating graphs as workplace knowledge

et al. 2007

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We investigate the use and knowledge of graphs in the context of a large industrial factory. We are particularly interested in the question of "transparency", a question that has been extensively considered in the general literature on tool use and, more recently, by Michael Roth and his colleagues in the context of scientific work. Roth uses the notion of transparency to characterise instances of graph use by highly educated scientists in cases where the context was familiar: the scientists were able to read the situation "through" the graph. This paper explores the limits of the validity of the transparency metaphor. We present two vignettes of actual graph use by a factory worker, and contrast his actions and knowledge with that of a highly qualified process engineer working on the same production line. We note that in neither case the graphs were transparent. We argue that a fuller account that describes a spectrum of transparency is needed, and we seek to achieve this by adopting some elements of a semiotic approach that enhance a strictly activity-theoretical view.

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“…Na semiótica peirceana, diagramas são considerados importantes não apenas como meio de representar, mas, fundamentalmente, meios de pensar, compreender e raciocinar (BAKKER; HOFFMANN, 2005). Eles representam seus objetos através da similaridade nas relações, o que faz deles ícones.…”

Section: Diagramas: Signos Que Representam Relaçõesunclassified

“…O emprego de diagramas no Ensino de Ciências tem sido investigado nas últimas déca-das por uma diversidade de autores (BAKKER; HOFFMANN, 2005;CHITTLEBOROUGH;TREAGUST, 2008;GARCÍA;PERALES, 2006;KRAGTEN;ADMIRAAL;RIJLAARSDAM, 2013;LOMBARDI;CABALLERO, 2012;LOWE, 1987;SOLAZ-PORTOLÈS, 1996)chemicals. Em linhas gerais, tais autores compreendem que o papel dos diagramas é evidenciar relações entre conceitos, sendo, assim, ferramentas importantes para: tornar ideias abstratas mais concretas; integrar informações e facilitar o acesso a elas; pensar sobre ideias científicas e comunicá-las.…”

Section: Introductionunclassified

Diagramas de energia de orbitais em livros didáticos de Química Geral: uma análise sob o viés da semiótica Peirceana

Rozentalski

Porto²

2018

Ciênc. educ. (Bauru)

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Resumo: Neste artigo foi analisado o emprego de diagramas de energia de orbitais em livros didáticos de Química Geral, utilizados no ensino universitário brasileiro ao longo do século XX. Para isso, 16 livros publicados entre 1950 e 2001 foram selecionados, e a semiótica peirceana foi utilizada como referencial de análise para o entendimento sobre diagramas. A análise revelou que o uso de diagramas de energia de orbitais ocorre em diferentes contextos de aplicação e com diferentes objetivos. Do ponto de vista da semiótica, os significados dos signos que compõem os diagramas, e as regras que orientam sua construção e operação, são previamente convencionados, fornecendo, assim, bases mínimas a respeito de como interpretá-los. Todavia, aspectos mais sutis se afastam dessa base mínima e podem acarretar interpretações não pretendidas por seus autores. Tais concepções alternativas podem ser superadas através de compreensões mais elaboradas sobre a natureza e o papel das representações no ensino, fundamentadas na semiótica Peirceana.

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Diagrammatic Reasoning as the Basis for Developing Concepts: A Semiotic Analysis of Students' Learning about Statistical Distribution

Cited by 78 publications

References 25 publications

Embodied design: constructing means for constructing meaning

Embodied design: constructing means for constructing meaning

Situating graphs as workplace knowledge

Diagramas de energia de orbitais em livros didáticos de Química Geral: uma análise sob o viés da semiótica Peirceana

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