Diagrammatic Thinking

Dörfler, Willibald

doi:10.1007/0-387-24270-8_6

Cited by 20 publications

(5 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Neste sentido, sob um "ponto de vista epistemológico, a essência do raciocínio diagramático pode ser vista no fato de que ele oferece a base para abstrações hipostáticas -meios cognitivos que podem ser usados e desenvolvidos em um raciocínio diagramático posterior" (BAKKER; HOFFMAN, 2005, p. 353, tradução nossa), visto que possui um aspecto genérico e podem ser interpretados em um sentido relacional (DÖRFLER, 2005).…”

Section: Sobre Raciocínio Diagramático Na Semiótica Peirceanaunclassified

Raciocínio Diagramático Em Atividades De Modelagem Matemática No Ensino Fundamental

Silva,

Martins

2023

Vidya

View full text Add to dashboard Cite

Neste artigo, buscamos inferir sobre os conhecimentos dos alunos de uma turma do 9 o ano do Ensino Fundamental no desenvolvimento de atividades de modelagem matemática. Entendemos que a modelagem matemática é uma abordagem didático-pedagógica e que a construção do conhecimento pode ser evidenciada no raciocínio diagramático, assim nos respaldamos na semiótica peirceana, mais especificamente nos diagramas produzidos pelos alunos. A análise qualitativa subsidiada no processo de triangulação levou em consideração como sujeitos oito alunos do 9 o ano do Ensino Fundamental de uma escola particular do norte do Paraná, como objeto os diagramas construídos no desenvolvimento de duas atividades de modelagem e como fenômeno o raciocínio diagramático que emergiu das atividades. Os resultados nos permitiram inferir que o raciocínio diagramático mobilizado nos diagramas produzidos para as situações em estudo, seja para realizar simplificações ou simulações, revelou que os alunos buscaram implementar conhecimentos matemáticos já estudados ao longo do ano letivo.

show abstract

Section: Sobre Raciocínio Diagramático Na Semiótica Peirceanaunclassified

Raciocínio Diagramático Em Atividades De Modelagem Matemática No Ensino Fundamental

Silva,

Martins

2023

Vidya

View full text Add to dashboard Cite

show abstract

“…Different conceptions are proposed about the use of diagrams in the works of research analysed in the field of mathematics education. Arcavi includes them as just another visual resource which coordinates with visualization; however according to the literature about diagrammatic reasoning, the diagrams, understood in the framework of Peircean semiotics (Dörfler, 2005;Bakker & Hoffmann, 2005;Rivera, 2011), form an essential resource of mathematics reasoning in addition to other fields and scientific disciplines (Bechtel, 2017;Giardino, 2017;Shin & Lemon, 2008).…”

Section: The Role Of Diagrams In Mathematical Workmentioning

confidence: 99%

“…Unlike the other areas of scientific knowledge, signs and semiotic representation transformation are at the heart of mathematics activity. (Duval, 2006, p. 107) Dörfler (2005) recognises that the diagrams can make up a register of autonomous representation to represent and produce mathematics knowledge in certain specific fields, however it is not complete. It requires to be complemented by conceptual-verbal language to express notions like continuity and differentiability; impossibility that specific objects exist; or situations of the use of quantifiers for all, each one and there are.…”

Section: Registers Of Representation and Diagramsmentioning

confidence: 99%

Onto-semiotic Analysis of Diagrammatic Reasoning

Giacomone

Godino

Blanco

et al. 2022

Int J of Sci and Math Educ

View full text Add to dashboard Cite

Diagrams and in general the use of visualization and manipulative material, play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an epistemological point of view as well as an educational one. In this paper we apply theoretical tools of the ontosemiotic approach of mathematics knowledge to analyze the diversity of objects and processes implied in mathematics activity, which is carried out with diagrammatic representations. This enables us to appreciate the synergic relations between ostensive (visual and sequential languages) and non-ostensive objects (abstract and mental entities) overlapping in mathematics practices. The analysis of the characteristics of diagrammatic reasoning and its interpretation in onto-semiotic terms is contextualised by means of the analysis of solving a problem about fractions by applying three procedures that involve diagrams.

show abstract

“…Graphs have the potential to provide deeper insight through their Downloaded by [New York University] at 02:07 16 May 2015 symbolic nature and geometrical formation of points, lines, arrows, curves and axes. We therefore include graphical representations within Dörfler's (2005) observation that diagrams are not passive symbols, but rather objects for mental operations. Functional relationships are regarded as the most influential and valuable notation in mathematics.…”

Section: Introductionmentioning

confidence: 99%

The role of visualisation in learners' conceptual understanding of graphical functional relationships

Mudaly¹,

Rampersad²

2010

African Journal of Research in Mathematics, Science and Technol

View full text Add to dashboard Cite

This paper is based on a study which explored the conceptual understanding of Grade 11 mathematics learners of graphical functional relationships, in particular their understanding of the Cartesian plane, notation, symbols and graphical terminology. The National Curriculum Statement (NCS) for Grades 10-12 in mathematics stipulates functional relationships as a key learning outcome, emphasising a variety of graphical skills. The study highlights visualisation skills in graphical interpretation, and explores the relationship between the way graphs are presented and learners' understanding of graphs. Learners' understanding of graphical representations is analysed using the procedural-conceptual dichotomy. Grade 11 learners, who had engaged with graphical representations in Grade 10, were interviewed in two schools. This research indicated a strong tendency of these learners to use procedural knowledge to explain simple concepts and, further showed that the learners' visual understanding was weak and dependent on the diagrams that educators use in the classroom.

show abstract

Diagrammatic Thinking

Cited by 20 publications

References 5 publications

Raciocínio Diagramático Em Atividades De Modelagem Matemática No Ensino Fundamental

Raciocínio Diagramático Em Atividades De Modelagem Matemática No Ensino Fundamental

Onto-semiotic Analysis of Diagrammatic Reasoning

The role of visualisation in learners' conceptual understanding of graphical functional relationships

Contact Info

Product

Resources

About