Methodological Aspects in the Theory of Mathematical Working Spaces

Nechache, Assia; Chacón, Inés María Gómez

doi:10.1007/978-3-030-90850-8_2

Cited by 4 publications

(2 citation statements)

References 11 publications

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“…In this manner, MWS research is based on studying and understanding the dynamic of mathematical work through the role of each of these geneses and their interactions (Kuzniak, 2018), which is termed circulation in MWS . Thus, MWS, with its planes, components, and geneses, is a methodological and analytical tool used to identify the different phases of the process of problem-solving and to describe the evolution of mathematical work (Kuzniak & Nechache, 2021;Nechache & Gómez-Chacón, 2022). In the analysis of circulations, changes between two mathematical domains can be identified (Montoya-Delgadillo & Vivier, 2014), as well as barriers, difficulties, and restraints (Henríquez-Rivas & Montoya-Delgadillo, 2016;Kuzniak, 2022) and other cases in which varied interactions exist, which is known as complete mathematical work (Kuzniak et al, 2016a).…”

Section: Contribution To the Literaturementioning

confidence: 99%

“…The theory of MWS is currently in a period of advancement, which leads to the consideration of both theoretical and methodological aspects of research that is underpinned by this framework Kuzniak y Nechache, 2021;Nechache & Gómez-Chacón, 2022). Its main purpose within mathematics education is to describe, understand, and transform mathematical work in educational contexts (Kuzniak et al, 2022).…”

Section: Introductionmentioning

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: Contribution To the Literaturementioning

confidence: 99%

Section: Introductionmentioning

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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Mathematical attitudes transformation when introducing GeoGebra in the secondary classroom

Romero Albaladejo,

García López

2023

Educ Inf Technol

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The mathematical-related affect research agenda demands studies on the affect-cognition relationship, as well as interventions aimed at improving affective aspects of mathematical learning. The potential of technological environments for promoting cognitive changes in students has been widely informed and there is evidence of their influence in students´ attitudes towards mathematics, such as interest and enjoyment. Research on the so-called mathematical attitudes, more related to mental habits and closely tied to cognitive processes is much scarcer. In this study, we report the transformation of three such mathematical attitudes in the students: perseverance, precision-rigor, and autonomy, when introducing GeoGebra in two secondary classes. Quantitative and qualitative analyses performed on data from various sources, with the total number of students and with a representative sample, show how it is possible to capitalize on initial positive attitudes towards mathematics with technology to bring about a significant improvement in the three above-mentioned attitudes, deemed as genuine elements of mathematical work. GeoGebra affordances constructivity, navigability and interactivity made it possible for new forms of behaviour to emerge in the classroom. Namely, flexible and fluent perseverance on problem solving; increasing inclination for accuracy and realization of its importance for proper reasoning; and willingness to collaborate with peers, helping each other, as well as sharing insights and ideas, thus, gaining independence from the teacher to face non-routine tasks.

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Epistemic emotions and pre-service mathematics teachers’ knowledge for teaching

Gómez-Chacón,

Marbán

2024

ZDM Mathematics Education

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Affective and cognitive processes may be jointly researched to better understand mathematics learning, paying special interest to emotions related to knowledge acquisition. However, it remains necessary to explore these processes in studies linked to the education of pre-service mathematics teachers. This study aims to characterize epistemic emotions in different practices linked to the practice of mathematics teaching: problem-solving, anticipating what would happen with the students and reflecting on classroom implementation. It considers the theory of Mathematical Working Spaces to describe the mathematical and cognitive dimensions generated by epistemic emotions, paying special attention to the cognition-affect interaction and the workspace created. The results indicate that the epistemic emotions of the pre-service mathematics teachers associated with the distinct practices were different. Differences are observed in the interaction between emotions and cognitive epistemic actions, depending on whether the pre-service mathematics teachers analyze them within the framework of their own solving or anticipate them in their students. This reveals how personal work relates to what is considered to be suitable for students. Specifically, certain antecedents and consequences have been specified for the emotions of surprise and boredom in relation to the characteristics of the optimization problems and the cognitive activity of the subject when solving them. These results highlight the need to enhance the education of pre-service mathematics teachers through training that helps regulate their epistemic emotions and model effective strategies for regulating their own emotions and those of their students.

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Methodological Aspects in the Theory of Mathematical Working Spaces

Cited by 4 publications

References 11 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

Mathematical attitudes transformation when introducing GeoGebra in the secondary classroom

Epistemic emotions and pre-service mathematics teachers’ knowledge for teaching

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