Mathematical connections from a networking of theories between extended theory of mathematical connections and onto-semiotic approach

Mathematical Connections Activated in High School Students’ Practice Solving Tasks on the Exponential and Logarithmic Functions

“…This analysis with the onto-semiotic methodology allows for the observation of a wide spectrum of possible causes why the students fail to establish a determined connection. This is related to a coherent result with the networking research between the EMCM and the OSA developed in Rodríguez-Nieto et al (2021).…”

“…The networking of theories was carried out in Rodríguez-Nieto et al (2021), between EMCM and the OSA. Especially, concordances and complementarities are identified in the respective conceptions of These authors conclude that the method used by the EMCM analyzes the mathematical activity carried out by a person to find mathematical connections among several elements related to this activity.…”

Exploring University Mexican Students’ Quality of Intra-Mathematical Connections When Solving Tasks About Derivative Concept

“…However, we consider, like Hiebert and Carpenter (1992), and Barmby et al (2009) that a student understands a mathematical concept depending on the strength and quality of mathematical connections and not the number of connections. In this sense, several studies suggest that, the quality of mathematical connections made by students and teachers should be investigated, and how the connections influence the understanding of mathematical concepts (Mhlolo, 2012;Mhlolo et al, 2012;García-García & Dolores-Flores, 2021a, 2021bRodríguez-Nieto, Font, Borji & Rodríguez-Vásquez, 2021;Rodríguez-Nieto, Rodríguez-Vásquez & Font, 2020;. Therefore, in this research we answer the question: What is the quality of the mathematical connections made by mexican university students when solving tasks that involve the derivative concept?…”

Enfoque Ontossemiótico da Cognição e Instrução Matemática: um estudo metanalítico das teses produzidas no Brasil

“…Nele, realiza-se uma descrição das várias abordagens dadas à noção de significado e se aterrissa à defendida pelo EOS− incorporar os pressupostos semióticos, ontológicos e epistemológicos de teorias semióticas gerais de Louis Hjelmslev, Charles Sanders Peirce e Ludwing Wittgenstein, além de analisar como os objetos matemáticos são abordados em três teorias: a lógico-realista de Friedrich Ludwig Gottlob Frege, a teoria dos campos conceituais de Gérard Vergnaud e o triângulo epistemológico de Horst Steinbring−identificando concordâncias e complementariedades entre estas e a abordagem EOS. Outro estudo realizado versa sobre às conexões matemáticas, por meio do estudo da Teoria Estendida das Conexões Matemáticas (ETC) e da abordagem Ontossemiótica (EOS) (RODRÍGUEZ-NIETO et al, 2021a;2021b). Em particular, identificam-se as concordâncias e complementaridades nas respetivas concepções de conexões matemáticas, em resultado da aplicação destes enquadramentos teóricos ao protocolo de resposta de um aluno na resolução de uma tarefa sobre a derivada.…”