Mathematical working space and paradigms as an analysis tool for the teaching and learning of analysis

Delgadillo, Elizabeth Montoya; Vivier, Laurent

doi:10.1007/s11858-016-0777-9

Cited by 18 publications

(5 citation statements)

References 13 publications

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“…Regarding the first research question, the results indicate that the majority of authors of the studies reviewed are from Chile, Spain, France, or Mexico. In this sense, it should be mentioned that participation in joint international projects (e.g., French-Chilean ECOS-Sud C13H03 project) have contributed to developing and deepening understanding of important theoretical aspects of MWS (e.g., Montoya-Delgadillo & Vivier, 2016). Also, proceedings of MWS Symposium and issues dedicated to theory in prestigious mathematics education journals have had a strong impact on number of documents found and analyzed in this review.…”

Section: Links/connections With Other Theories or Perspectivesmentioning

confidence: 96%

“…MWS theory considers the epistemological principles of the objects that are studied within a mathematical domain (e.g., geometry and probability) (Kuzniak, 2011;Montoya-Delgadillo & Vivier, 2016). Likewise, the theory integrates the human (or social) component, which entails considering a cognitive dimension related to the epistemological dimension (Kuzniak, 2022).…”

Section: Theoretical Framework Mathematical Working Spacesmentioning

confidence: 99%

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Advances and trends in research on mathematical working spaces: A systematic review

Panqueban,

Henríquez-Rivas,

Kuzniak

2024

EURASIA J Math Sci Tech Ed

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This study addresses the research developed around the theory of mathematical working spaces (MWS). To this end, factors such as researchers’ country of origin are considered, as well as methodological characteristics, proposed objectives in each study, specific theoretical factors, and the links between MWS and other theoretical perspectives. This systematic review follows the guidelines stated by reporting items for systematic reviews and meta-analyses for documenting each stage of the review. In total, 102 studies were considered from databases including Dialnet, SciElo, Scopus, and Web of Science. The results help to illustrate research trends in MWS theory, as well as the possibility of fertile ideas for new studies and future lines of research for those interested in this theoretical approach.

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Section: Links/connections With Other Theories or Perspectivesmentioning

confidence: 96%

Section: Theoretical Framework Mathematical Working Spacesmentioning

confidence: 99%

Advances and trends in research on mathematical working spaces: A systematic review

Panqueban,

Henríquez-Rivas,

Kuzniak

2024

EURASIA J Math Sci Tech Ed

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“…Finally, we consider the paradigms of real analysis (Montoya-Delgadillo & Vivier, 2016), which guide the mathematical work in this field. In particular, the arithmetic/geometric analysis (GA) paradigm involves work of a perceptual type based on interpretations arising from graphs or numbers, taking into account the role of the figures or different visualisations that activate that work.…”

Section: Figurementioning

confidence: 99%

Articulación entre Modelización y Espacios de Trabajo Matemático. Análisis de una Tarea bajo el ciclo de Blomhøj en Educación Superior

et al. 2023

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Background: The Mathematical Working Spaces (MWS) theoretical framework has developed a growing interest in how mathematical modelling is recognised, analysed, and articulated from its theoretical and empirical scopes. Given the articulations identified in the literature, it is interesting to determine whether new networks with the MWS provide powerful strategies for analysing mathematical modelling task resolution. Objective: to characterise the modelling activity from the network composed by the Blomhøj modelling cycle and the MWS in engineering students. Design: This work is a case study with a qualitative approach, which analyses the resolution of a modelling task through the proposed network. Setting and participants: The experimentation was carried out in an integral calculus course for a computer civil engineering career at a Chilean university. Modelling practices are not usual in this second-year subject, although enhancing their use in professional education is necessary. Data collection and analysis: We collected the written records of the students, selecting one to perform the in-depth analysis due to its high representativeness and clarity, as evidenced in the documents. Three steps were followed to characterise the modelling activity in the written record: description, analysis, and interpretation. Results: The Blomhøj modelling cycle might present connections with the MWS at the formulation of the problem and not only at the systematisation, which is a novelty in this field of research. Conclusions: A novel approach with which to develop the network between the MWS and modelling emerges, emphasising the investigation of mathematical problems using the student’s reality in higher education.

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“…En esta investigación, para analizar el trabajo matemático del profesor se utiliza el marco del Espacio De Trabajo Matemático (ETM) (Kuzniak, 2011), concebido como un modelo que contribuye a la comprensión del trabajo de personas (profesor, estudiante o un matemático) que resuelven tareas matemáticas y permite caracterizar los caminos que emergen en su resolución (Kuzniak et al, 2016;Henríquez-Rivas y Montoya-Delgadillo, 2015). 39-2 (2021), 123-142 La investigación en ETM considera los principios epistemológicos de los objetos que se estudian dentro de un dominio matemático (como la geometría, el análisis o la probabilidad) (Kuzniak, 2011;Montoya-Delgadillo y Vivier, 2016). En este marco se diferencian dos tipos de elementos (representados por los planos epistemológico y cognitivo, en la figura 1), que pretenden captar los contenidos matemáticos del dominio estudiado y la actividad cognitiva del individuo cuando adquiere, desarrolla o utiliza esos contenidos matemáticos (Kuzniak, 2011).…”

Section: Espacios De Trabajo Matemáticounclassified

Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza

et al. 2021

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RESUMEN • El uso de tareas y ejemplos constituye una práctica fundamental en el trabajo del profesor en el aula para la enseñanza de un contenido. El objetivo de este artículo es caracterizar el trabajo matemático que propone un profesor a partir de las tareas y ejemplos que considera para la enseñanza de un teorema geométrico. Para ello, se analiza el espacio de trabajo matemático idóneo de un profesor de secundaria que participa en un taller formativo. Se presenta un estudio de caso basado en un diseño de caso único, a través de videograbaciones y observaciones. Los resultados revelan el privilegio de tratamientos algebraicos a partir de representaciones figurales y un cambio propuesto que involucra el uso de herramientas tecnológicas. Finalmente, se discute sobre aportes al estudio del trabajo matemático del profesor en el aula centrado en el uso de tareas y ejemplos. PALABRAS CLAVE: Espacio de trabajo matemático idóneo; Profesor; Teorema de Tales; Tareas; Ejemplos. ABSTRACT • The use of tasks and examples is a fundamental practice in the teacher's work in the classroom when it comes to teaching a content. The objective of this article is to characterize the mathematical work that a teacher proposes from the tasks and examples that he or she considers for the teaching of a geometric theorem. For this purpose, the suitable mathematical workspace of a secondary school teacher participating in a training workshop is analyzed. A case study is presented based on a unique case design, through video recordings and observations. The results reveal the privilege of algebraic treatments based on figurative representations, and a proposed change that involves the use of technological tools. Finally, contributions to the study of the teacher's mathematical work in the classroom focused on the use of tasks and examples are discussed.

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Mathematical working space and paradigms as an analysis tool for the teaching and learning of analysis

Cited by 18 publications

References 13 publications

Advances and trends in research on mathematical working spaces: A systematic review

Advances and trends in research on mathematical working spaces: A systematic review

Articulación entre Modelización y Espacios de Trabajo Matemático. Análisis de una Tarea bajo el ciclo de Blomhøj en Educación Superior

Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza

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