Mathematical imagination and embodied cognition

Nemirovsky, Ricardo; Ferrara, Francesca

doi:10.1007/s10649-008-9150-4

Cited by 121 publications

(75 citation statements)

References 8 publications

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“…There's a double sense of controlling and being controlled in this simulation. Nemirovsky and Ferrara (2009) illustrate gestural/diagrammatic interplay in their description of one girl's gestures tracing the motion of two laser lights in order to discover a defined triangle shape that gives the trajectory of the composed motion.…”

Section: Machines Mathematics and Impulsementioning

confidence: 99%

Virtual encounters: the murky and furtive world of mathematical inventiveness

Sinclair

Freitas

Ferrara

2012

ZDM Mathematics Education

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Based on Châtelet's insights into the nature of mathematical inventiveness, drawn from historical analyses, we propose a new way of framing creativity in the mathematics classroom. The approach we develop emphasizes the social and material nature of creative acts. Our analysis of creative acts in two case studies involving primary school classrooms also reveals the characteristic ways in which digital technologies can occasion such acts.

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Section: Machines Mathematics and Impulsementioning

confidence: 99%

Virtual encounters: the murky and furtive world of mathematical inventiveness

Sinclair

Freitas

Ferrara

2012

ZDM Mathematics Education

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“…On a theoretical level, we have not engaged with the implication that mathematical actions are thoughts, an issue which would require a longer exploration of work in the learning sciences (see, for example, the work of Nemirovsky and collaborators [49][50][51][52]). Taking this perspective would provide us with a foundation for modeling group interactions and group reasoning, a useful tool when our data come from authentic classroom group activities, like in this paper.…”

Section: Implications For Teachingmentioning

confidence: 99%

Mathematical actions as procedural resources: An example from the separation of variables

Wittmann

Black

2015

Phys. Rev. ST Phys. Educ. Res.

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[This paper is part of the Focused Collection on Upper Division Physics Courses.] Students learning to separate variables in order to solve a differential equation have multiple ways of correctly doing so. The procedures involved in separation include division or multiplication after properly grouping terms in an equation, moving terms (again, at times grouped) from one location on the page to another, or simply carrying out separation as a single act without showing any steps. We describe student use of these procedures in terms of Hammer's resources, showing that each of the previously listed procedures is its own "piece" of a larger problem solving activity. Our data come from group examinations of students separating variables while solving an air resistance problem in an intermediate mechanics class. Through detailed analysis of four groups of students, we motivate that the mathematical procedures are resources and show the issues that students must resolve in order to successfully separate variables. We use this analysis to suggest ways in which new resources (such as separation) come to be.

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“…The embodied character of gestures may facilitate the process of reaching abstract concepts through the visual and concrete form of gestures. Moreover, as a consequence of this process, students can communicate mathematical concepts more easily (Gallese and Lakoff 2005;Nemirovsky and Ferrara 2009).…”

Section: Space and Shape Conceptsmentioning

confidence: 99%

The role of gestures in making connections between space and shape aspects and their verbal representations in the early years: findings from a case study

2014

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In recent educational research, it is well acknowledged that gestures are an important source of developing abstract thinking in early childhood and can serve as an additional window to the mind of the developing child. The present paper reports on a case study which explores the function of gestures in a geometrical activity at kindergarten level. In the study, the spontaneous gestures of the child are investigated, as well as the influence of the teacher's gestures on the child's gestures. In the first part of the activity, the child under study transforms a spatial array of blocks she has constructed by herself into a verbal description, so that another person, i.e., the teacher, who cannot see what the child has built, makes the same construction. Next, the teacher builds a new construction and describes it so that the child can build it. Hereafter, it is again the turn of the child to build another construction and describe it to the teacher. The child was found to spontaneously use iconic and deictic gestures throughout the whole activity. These gestures, and primarily the iconic ones, helped her make apparent different space and shape aspects of the constructions. Along with her speech, gestures acted as semiotic means of objectification to successfully accomplish the task. The teacher's gestures were found to influence the child's gestures when describing aspects of shapes and spatial relationships between shapes. This influence results in either mimicking or extending the teacher's gestures. These findings are discussed and implications for further research are drawn.

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Mathematical imagination and embodied cognition

Cited by 121 publications

References 8 publications

Virtual encounters: the murky and furtive world of mathematical inventiveness

Virtual encounters: the murky and furtive world of mathematical inventiveness

Mathematical actions as procedural resources: An example from the separation of variables

The role of gestures in making connections between space and shape aspects and their verbal representations in the early years: findings from a case study

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