Academia.eduAcademia.edu

Mathematical imagination and embodied cognition

Profile image of Francesca FerraraFrancesca Ferrara

2009, Educational Studies in Mathematics

Abstract

The goal of this paper is to explore qualities of mathematical imagination in light of a classroom episode. It is based on the analysis of a classroom interaction in a high school Algebra class. We examine a sequence of nine utterances enacted by one of the students whom we call Carlene. Through these utterances Carlene illustrates, in our view, two phenomena: (1) juxtaposing displacements, and (2) articulating necessary cases. The discussion elaborates on the significance of these phenomena and draws relationships with the perspectives of embodied cognition and intersubjectivity.

Figures (13)
mathematical entities through symbolizing them, not by observing them as _ such. Analogously to the case of literature, many mathematical conversations are hybrids encompassing empirical and pure possibilities, but the difference between them often becomes conspicuous to the participants in the course of analysis or disagreements.
mathematical entities through symbolizing them, not by observing them as _ such. Analogously to the case of literature, many mathematical conversations are hybrids encompassing empirical and pure possibilities, but the difference between them often becomes conspicuous to the participants in the course of analysis or disagreements.
device consists of two laser pointers held up at 90° from each other (see Fig. 4). The lase: ights reflect on two side panels set up along perpendicular axes (see vertical panel on the eft side of the student in Fig. 4 along one of the axes). The idea is to move the device tracing a certain figure (for instance a triangle, shown with black lines in Fig. 4) whils keeping the orientation of the laser pointers always perpendicular to the side panels or which their light shines. In this way, the points of light shining on the two panels reflect < parametric decomposition, say along X and Y axes, for the path of the traced figure. Ir other words, each point traced on the flat figure (e.g. the triangle shown in Fig. 4) get: decomposed in X and Y coordinates made visible by the laser lights on the two sid panels. The students worked in teams of three, each with a laser pointer device and ar open folder standing vertical for the XY side panels. They studied the correspondenc« between the lines traced on the flat sheet of paper and the trajectory of the two laser light: on the side panels.
device consists of two laser pointers held up at 90° from each other (see Fig. 4). The lase: ights reflect on two side panels set up along perpendicular axes (see vertical panel on the eft side of the student in Fig. 4 along one of the axes). The idea is to move the device tracing a certain figure (for instance a triangle, shown with black lines in Fig. 4) whils keeping the orientation of the laser pointers always perpendicular to the side panels or which their light shines. In this way, the points of light shining on the two panels reflect < parametric decomposition, say along X and Y axes, for the path of the traced figure. Ir other words, each point traced on the flat figure (e.g. the triangle shown in Fig. 4) get: decomposed in X and Y coordinates made visible by the laser lights on the two sid panels. The students worked in teams of three, each with a laser pointer device and ar open folder standing vertical for the XY side panels. They studied the correspondenc« between the lines traced on the flat sheet of paper and the trajectory of the two laser light: on the side panels.
The class was able to see only the movement of the points of light shining through the translucent panels; in other words, the class did not see which figure Tracy was tracing but the moving points of light she generated with the laser pointer device on the two side panels. The ensuing class discussion was about the sort of triangle that corresponded to the motion of the lights they had seen. As can be seen from Fig. 6, the triangle had been an equilateral one oriented in such a way that the tracing of the first side (labeled ‘1’ in Fig. 6) corresponded to both lights moving toward the vertex of the side panels, the second side left one light still and moved the other one away from the vertex, and the tracing of the third side of the triangle moved one light toward the vertex and the other one away from it. The students discussed several ideas, such as that the triangle had only one side parallel to the XY panels: the one whose trace had left one of the lights still.
The class was able to see only the movement of the points of light shining through the translucent panels; in other words, the class did not see which figure Tracy was tracing but the moving points of light she generated with the laser pointer device on the two side panels. The ensuing class discussion was about the sort of triangle that corresponded to the motion of the lights they had seen. As can be seen from Fig. 6, the triangle had been an equilateral one oriented in such a way that the tracing of the first side (labeled ‘1’ in Fig. 6) corresponded to both lights moving toward the vertex of the side panels, the second side left one light still and moved the other one away from the vertex, and the tracing of the third side of the triangle moved one light toward the vertex and the other one away from it. The students discussed several ideas, such as that the triangle had only one side parallel to the XY panels: the one whose trace had left one of the lights still.
I I In Utterance 2 (Fig. 7) Carlene re-positioned the imaginary panels for them to coincide with the edges of her desk, so that her index fingers, “touching” the position of each light, moved along these edges. The physicality of the desk’s edges facilitated the marking of the lights’ movement for Carlene: it made their path more salient and better defined. In terms of Hutchins’ (2005) analysis, the edges of the desk functioned as opportunistic “material anchors” that helped Carlene stabilize the events she imagined. Noble (2007) analyzed how material anchors generate sensory-motor feedback for the user, offering a kind of feedback that participates in the thinking itself. In this case, the edges of the desk might have guided her fingers, in a perceptuo-motor sense, as Carlene traced the motion of the laser lights, letting her feel that the lights followed a clearly defined linear path. Fig. 7 Utterances 1-3
I I In Utterance 2 (Fig. 7) Carlene re-positioned the imaginary panels for them to coincide with the edges of her desk, so that her index fingers, “touching” the position of each light, moved along these edges. The physicality of the desk’s edges facilitated the marking of the lights’ movement for Carlene: it made their path more salient and better defined. In terms of Hutchins’ (2005) analysis, the edges of the desk functioned as opportunistic “material anchors” that helped Carlene stabilize the events she imagined. Noble (2007) analyzed how material anchors generate sensory-motor feedback for the user, offering a kind of feedback that participates in the thinking itself. In this case, the edges of the desk might have guided her fingers, in a perceptuo-motor sense, as Carlene traced the motion of the laser lights, letting her feel that the lights followed a clearly defined linear path. Fig. 7 Utterances 1-3
The motions of the laser light Carlene referred to in Utterances 2 and 3 (Fig. 7) were similar to the ones generated by side ‘3’ of the triangle traced by Tracy in front of the class, as seen from her position (see Fig. 6). In other words, Carlene moved both lights from her left side to her right side, which is how she, and the rest of the students, had seen the lights moving when side ‘3’ had been traced (Fig. 6). In Utterances | and 2 Carlene looks at her own desk as if watching the motion of the lights from left to right, as she had seen them moving on the large panels in front of the class. In Utterance 3 she lifts her gaze toward Apolinario Barros, to whom she is directing her talk.
The motions of the laser light Carlene referred to in Utterances 2 and 3 (Fig. 7) were similar to the ones generated by side ‘3’ of the triangle traced by Tracy in front of the class, as seen from her position (see Fig. 6). In other words, Carlene moved both lights from her left side to her right side, which is how she, and the rest of the students, had seen the lights moving when side ‘3’ had been traced (Fig. 6). In Utterances | and 2 Carlene looks at her own desk as if watching the motion of the lights from left to right, as she had seen them moving on the large panels in front of the class. In Utterance 3 she lifts her gaze toward Apolinario Barros, to whom she is directing her talk.
VeTIeX, WHICH IS We pommel aimed DY We Ment Nand MOVING along a OISECUNS UNE, INO Wat ner whole right hand stresses directionality and aim of the motion, which is something that changes in Utterance 5: now her hands contract, letting the index fingers indicate the position of the points of light moving on the side panels. Carlene looks at her moving hands, the right one in Utterance 4 and both hands approaching the vertex in Utterance 5. Listeners usually fix their gaze on the face of the speaker, except when the speaker looks at something away from the listeners themselves. Carlene’s look at her moving hands might have been a way of emphasizing for herself and for her listeners, the most critical aspects of her utterances. In Utterances 6-8 (Fig. 10) Carlene illustrates a second case. Now the line is oriented “backwards”. Her left arm is again marking one of the side panels, as in Utterance 4, but now the right hand aims at her elbow. Instead of approaching the vertex located in the “forward” extreme of the table, it approaches the opposite side which is “backward” with respect to her. Her right hand is extended to stress this backward directionality for the imaginary line. She then extends her index fingers to indicate the corresponding motion of the laser lights, breaking their temporal simultaneity in a sequence similar to Utterances 2 and 3. In Utterance 7 Carlene makes apparent the intricate and multilayered aspects of hand motion: she describes the movement as “up” (“‘pa riba”), which reflects the natural motion of the arm forward (i.e. as we move the hand away from us in the forward direction we tend to move it up also). The class had differentiated three cases for the motion of the laser lights corresponding to the three sides of the triangle traced by Tracy. Carlene articulated two of them corresponding to the sides ‘1’ and ‘3’ of the triangle used by Tracy (see Fig. 6). Side 2 was
VeTIeX, WHICH IS We pommel aimed DY We Ment Nand MOVING along a OISECUNS UNE, INO Wat ner whole right hand stresses directionality and aim of the motion, which is something that changes in Utterance 5: now her hands contract, letting the index fingers indicate the position of the points of light moving on the side panels. Carlene looks at her moving hands, the right one in Utterance 4 and both hands approaching the vertex in Utterance 5. Listeners usually fix their gaze on the face of the speaker, except when the speaker looks at something away from the listeners themselves. Carlene’s look at her moving hands might have been a way of emphasizing for herself and for her listeners, the most critical aspects of her utterances. In Utterances 6-8 (Fig. 10) Carlene illustrates a second case. Now the line is oriented “backwards”. Her left arm is again marking one of the side panels, as in Utterance 4, but now the right hand aims at her elbow. Instead of approaching the vertex located in the “forward” extreme of the table, it approaches the opposite side which is “backward” with respect to her. Her right hand is extended to stress this backward directionality for the imaginary line. She then extends her index fingers to indicate the corresponding motion of the laser lights, breaking their temporal simultaneity in a sequence similar to Utterances 2 and 3. In Utterance 7 Carlene makes apparent the intricate and multilayered aspects of hand motion: she describes the movement as “up” (“‘pa riba”), which reflects the natural motion of the arm forward (i.e. as we move the hand away from us in the forward direction we tend to move it up also). The class had differentiated three cases for the motion of the laser lights corresponding to the three sides of the triangle traced by Tracy. Carlene articulated two of them corresponding to the sides ‘1’ and ‘3’ of the triangle used by Tracy (see Fig. 6). Side 2 was
Fig. 11 Utterance 9 In Section 6, we analyzed three utterances in which Carlene enacted juxtaposed displacements (See Fig. 12). First she mirror-reflected the side panels, then she anchored the side panels on the edges of her table, a third displacement was the translation of each of the lights’ movements preserving the left/right orientation they had had from her point of view; the fourth displacement was temporal: enacting two simultaneous motions in sequence (U2)— (U3).
Fig. 11 Utterance 9 In Section 6, we analyzed three utterances in which Carlene enacted juxtaposed displacements (See Fig. 12). First she mirror-reflected the side panels, then she anchored the side panels on the edges of her table, a third displacement was the translation of each of the lights’ movements preserving the left/right orientation they had had from her point of view; the fourth displacement was temporal: enacting two simultaneous motions in sequence (U2)— (U3).
In Section 3 we suggested the notion of “thought” as an interpretation of one or more utterances. We can use the present example to clarify this idea. What were Carlene’s thoughts that she expressed through her utterances? The most succinct description of her thoughts was produced by Mr. Barros in Utterance 9: “Oh, OK. So one time they go in the same direction. And another time they go in the opposite direction”. However, we avoid reifying thoughts as entities with causal powers that manifest themselves in contingent and contextualized utterances. What is actually experienced and felt are the utterances themselves, with their overt and covert aspects, each of them embedded in a “just past” (its origin) and an “about to happen” (its future-oriented aim). In our example, Carlene’s thoughts are interpretations of her utterances oriented to grasping their unity or overall “point”. Like all interpretations, they are open-ended descriptions that reflect a certain “take” on the interpreted phenomena. Mr. Barros’ interpretation was his way of making sense of Carlene’s utterances—an interpretation that coincided with Carlene’s own, as she indicated through her animated approval. At another moment Mr. Barros, Carlene, Tracy, or any of the other students, might offer a complementary or alternative account for her thoughts. There is not an ultimate thought to be ascertained. By re-contextualizing Carlene’s utterances, the question of what she thought remains open. ee a ae ee ce en a ee ee a, a ee re. (a. a ae
In Section 3 we suggested the notion of “thought” as an interpretation of one or more utterances. We can use the present example to clarify this idea. What were Carlene’s thoughts that she expressed through her utterances? The most succinct description of her thoughts was produced by Mr. Barros in Utterance 9: “Oh, OK. So one time they go in the same direction. And another time they go in the opposite direction”. However, we avoid reifying thoughts as entities with causal powers that manifest themselves in contingent and contextualized utterances. What is actually experienced and felt are the utterances themselves, with their overt and covert aspects, each of them embedded in a “just past” (its origin) and an “about to happen” (its future-oriented aim). In our example, Carlene’s thoughts are interpretations of her utterances oriented to grasping their unity or overall “point”. Like all interpretations, they are open-ended descriptions that reflect a certain “take” on the interpreted phenomena. Mr. Barros’ interpretation was his way of making sense of Carlene’s utterances—an interpretation that coincided with Carlene’s own, as she indicated through her animated approval. At another moment Mr. Barros, Carlene, Tracy, or any of the other students, might offer a complementary or alternative account for her thoughts. There is not an ultimate thought to be ascertained. By re-contextualizing Carlene’s utterances, the question of what she thought remains open. ee a ae ee ce en a ee ee a, a ee re. (a. a ae

Related papers

EMBODIED MATHEMATICAL IMAGINATION AND COGNITION (EMIC) WORKING GROUP
Erin Ottmar, Caroline "Caro" Williams, Dor Abrahamson

Embodied cognition is growing in theoretical importance and as a driving set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to attract engaged and inspired colleagues into a growing community of discourse around theoretical, technological, and methodological developments for advancing the study of embodied cognition for mathematics education. A thriving, informed, and interconnected community of scholars organized around embodied mathematical cognition will broaden the range of activities, practices, and emerging technologies that count as mathematical. EMIC builds upon our 2015 working group, and investigations in formal and informal education and workplace settings to bolster and refine the theoretical underpinnings of an embodied view of mathematical thinking and teaching, while reaching educational practitioners at all levels of administration and across the lifespan. Motivations for This Working Group Recent empirical, theoretical and methodological developments in embodied cognition and gesture studies provide a solid and generative foundation for the establishment of an Embodied Mathematical Imagination and Cognition (EMIC) Working Group for PME-NA. The central aim of EMIC is to attract engaged and inspired colleagues into a growing community of discourse around theoretical, technological, and methodological developments for advancing the study of embodied cognition for mathematics education, including, but not limited to, studies of mathematical reasoning, instruction, the design and use of technological innovations, learning in and outside of formal educational settings, and across the lifespan. The interplay of multiple perspectives and intellectual trajectories is vital for the study of embodied mathematical cognition to flourish. Partial confluences and differences have to be maintained throughout the conversations; this is because instead of being oriented towards a single and unified theory of mathematical cognition, EMIC strives to establish a philosophical/educational " salon " in which entrenched dualisms, such as mind/body, language/materiality, or signifier/signified are subject to an ongoing and stirring criticism. A thriving, informed, and interconnected community of scholars organized around embodied mathematical cognition will broaden the range of activities and emerging technologies that count as mathematical, and envision alternative forms of engagement with mathematical ideas and practices (e.g., De Freitas & Sinclair, 2014). This broadening is particularly important at a time when schools and communities in North America face persistent achievement gaps between groups of students from many ethnic backgrounds, geographic regions, and socioeconomic circumstances (Ladson-Billings, 1995; Moses & Cobb, 2001; Rosebery, Warren, Ballenger & Ogonowski, 2005). There also is a need to articulate evidence-based findings and principles of embodied cognition to the research and development communities that are looking to generate and disseminate innovative programs for promoting mathematics learning through

View PDFchevron_right
Embodied cognition as grounding for situatedness and context in mathematics education
Laurie D Edwards

Educational Studies in …, 1999

In this paper we analyze, from the perspective of 'Embodied Cognition', why learning and cognition are situated and context-dependent. We argue that the nature of situated learning and cognition cannot be fully understood by focusing only on social, cultural and contextual factors. These factors are themselves further situated and made comprehensible by the shared biology and fundamental bodily experiences of human beings. Thus cognition itself is embodied, and the bodily-grounded nature of cognition provides a foundation for social situatedness, entails a reconceptualization of cognition and mathematics itself, and has important consequences for mathematics education. After framing some theoretical notions of embodied cognition in the perspective of modern cognitive science, we analyze a case study -continuity of functions. We use conceptual metaphor theory to show how embodied cognition, while providing grounding for situatedness, also gives fruitful results in analyzing the cognitive difficulties underlying the understanding of continuity.

View PDFchevron_right
Towards an embodied, cultural, and material conception of mathematics cognition
Luis Radford

ZDM – The international journal on Mathematics Education, 2014

In this paper I sketch an embodied, cultural, and material conception of cognition and discuss some of the implications for mathematics education. This approach, which I term sensuous cognition, rests on a cultural and historical dialectical materialist understanding of the senses, sensation, and the material and conceptual worlds. Sensation and matter are considered to be the substrate of mind, and of all psychic activity (cognitive, affective, volitional, etc.). I argue that human cognition can only be understood as a culturally and historically constituted multimodal sentient form of creatively responding, acting, feeling, transforming, and making sense of the world. To illustrate these ideas I briefly refer to a classroom episode involving 7-to 8-year-old students dealing with pattern generalization.

View PDFchevron_right
Embodied cognitive science and mathematics
Laurie D Edwards

2011

The purpose this paper is to describe two theories drawn from second-generation cognitive science: the theory of embodiment and the theory of conceptual integration. The utility of these theories in understanding mathematical thinking will be illustrated by applying them to the analysis of selected mathematical ideas and processes, including proof. The argument is made that mathematical ideas are grounded in embodied physical experiences, either directly or indirectly, through mechanisms involving conceptual mappings among mental spaces.

View PDFchevron_right
DEVELOPING A MATHEMATICAL VISION Mathematics as a Discursive and Embodied Practice
Jack Dieckmann

This chapter examines major lines of inquiry in mathematics education through the prism of cultural historical activity theory, focusing on the language and discursive practices in the teaching and learning of school mathematics. We make an analytic distinction between the language in and of mathematics learning in classrooms, noting the pitfalls of dichotomizing the language of the classroom and the language in mathematical learning or ignoring their interrelations. Specifically, we reviewed work that framed the role of everyday discourse practices as supporting the development of scientific discourse practices. In line with several mathematics education scholars, we challenge this framing by revisiting the theoretical principles from the work of Vygotsky, Engeström, and Cole, among others, to show how scientific or school-based mathematical learning "grows down into" the everyday, and © 2 0 1 0 I A P A l l r i g h t s r e s e r v e d e s e r v e d 30 K. D. GUTIÉRREZ, T. SENGUPTA-IRVING, and J. DIECKMANN

View PDFchevron_right

Related topics

  • Algebra
  • Embodied Cognition
  • Classroom Interaction
  • Curriculum and Pedagogy

    • Related papers

    Where mathematics comes from: How the embodied mind brings mathematics into being
    George Lakoff

    2000

    A metaphor is an alteration of a woorde from the proper and naturall meanynge, to that which is not proper, and yet agreeth thereunto, by some lykenes that appeareth to be in it. ... —Thomas Wilson, The Arte of Rhetorique ...

    View PDFchevron_right
    DISCURSIVE ROUTINES AND ENDORSED NARRATIVES AS INSTANCES OF MATHEMATICAL COGNITION
    Donna Kotsopoulos

    pmena.org

    View PDFchevron_right
    There is More to Discourse than Meets the Ears: Looking at Thinking as Communicating to Learn More About Mathematical Learning
    Anna Sfard

    Traditional approaches to research into mathematical thinking, such as the study of misconceptions and tacit models, have brought significant insight into the teaching and learning of mathematics, but have also left many important problems unresolved. In this paper, after taking a close look at two episodes that give rise to a number of difficult questions, I propose to base research on a metaphor of thinking-as-communicating. This conceptualization entails viewing learning mathematics as an initiation to a certain well defined discourse. Mathematical discourse is made special by two main factors: first, by its exceptional reliance on symbolic artifacts as its communication-mediating tools, and second, by the particular meta-rules that regulate this type of communication. The meta-rules are the observer’s construct and they usually remain tacit for the participants of the discourse. In this paper I argue that by eliciting these special elements of mathematical communication, one has a better chance of accounting for at least some of the still puzzling phenomena. To show how it works, I revisit the episodes presented at the beginning of the paper, reformulate the ensuing questions in the language of thinking-ascommunication, and re-address the old quandaries with the help of special analytic tools that help in combining analysis of mathematical content of classroom interaction with attention to meta-level concerns of the participants.

    View PDFchevron_right
    Handling problems: embodied reasoning in situated mathematics
    Dor Abrahamson

    2007

    Objectives The objective of this study is to contribute to research on mathematical cognition by illuminating implicit processes of embodied reasoning in situated problem solving. I argue that situated mathematical reasoning transpires as an embodied negotiation between material/perceptual affordances of phenomena and evolved cultural–historical cognitive artifacts that include physical utensils, symbolical forms, and figures of speech.

    View PDFchevron_right
    Investigating imagination as a cognitive space for learning mathematics
    Michelle Cordy

    Educational Studies in Mathematics, 2009

    Our work is inspired by the book Imagining Numbers (particularly the square root of minus fifteen), by Harvard University mathematics professor Barry Mazur (Imagining numbers (particularly the square root of minus fifteen), Farrar, Straus and Giroux, New York, 2003). The work of Mazur led us to question whether the features and steps of Mazur's re-enactment of the imaginative work of mathematicians could be appropriated pedagogically in a middle-school setting. Our research objectives were to develop the framework of teaching mathematics as a way of imagining and to explore the pedagogical implications of the framework by engaging in an application of it in middle school setting. Findings from our application of the model suggest that the framework presents a novel and important approach to developing mathematical understanding. The model demonstrates in particular the importance of shared visualizations and problemposing in learning mathematics, as well as imagination as a cognitive space for learning.

    View PDFchevron_right
    Relationships between embodied objects and symbolic procepts: an explanatory theory of success and failure in mathematics
    David Tall

    2001

    In this paper we propose a theory of cognitive construction in mathematics that gives a unified explanation of the power and difficulty of cognitive development in a wide range of contexts. It is based on an analysis of how operations on embodied objects may be seen in two distinct ways: as embodied configurations given by the operations, and as refined symbolism that dually represents processes to do mathematics and concepts to think about it. An example is the embodied configuration of five fingers, the process of counting five and the concept of the number five. Another is the embodied notion of a locally straight curve, the process of differentiation and the concept of derivative. Our approach relates ideas in the embodied theory of Lakoff, van Hiele's theory of developing sophistication in geometry, and the processobject theories of Dubinsky and Sfard. It not only offers the benefit of comparing strengths and weaknesses of a variety of differing theoretical positions, it also reveals subtle similarities between widely occurring difficulties in mathematical growth.

    View PDFchevron_right
    Mathematical Cognitive Processes Between the Poles of Mathematical Technical Terminology and the Verbal Expressions of Pupils
    Melanie Huth

    2010

    Verbal expressions by students in mathematical conversational situations provide insight into the individual mathematical imagination and express what patterns and contexts children recognize in mathematical problems. Children just starting school utilize means of expression of their mathematical ideas that go from everyday speech descriptions to detailed action sequences. They already use technical facets, even though their repertoire of mathematical language of instruction has to be considered initially as tentative. In our article, by dint of methods of qualitative analysis, we want to present initial descriptions in terms of the identified capability of mathematical expression of pupils just starting school, based on a conversational situation about a combinatorial problem.

    View PDFchevron_right
    Grounding Mathematical Justifications in Concrete Embodied Experience: The Link between Action and Cognition
    Candace Walkington

    Purpose A central issue in mathematics education relates to grounding, or the question of how abstract, mathematical ideas can be connected to students&#x27; prior knowledge and experience, such that their meaning becomes connected with concrete, perceptual referents that can be readily understood (Goldstone & Son, 2005; Koedinger, Alibali, & Nathan, 2008). Recent research on grounding interventions in mathematics classrooms has shown that tying mathematical formalisms to students&#x27; concrete, everyday experiences can support ...

    View PDFchevron_right
    The existence of mathematical objects in the classroom discourse
    Vicenç Font

    CERME 6–WORKING …, 2009

    In this paper we are interested in the understanding of how the classroom discourse helps to develop the students' comprehension of the non ostensive mathematical objects as objects that have "existence". First, we examine the role of the objectual metaphor in the understanding of the mathematical entities as "objects with existence", as well as in some of the conflicts that the use of this type of metaphor can provoke in the students' interpretations. Second, we examine the mathematics discourse from the perspective of the ostensives representing non ostensives that do not exist.

    View PDFchevron_right
    Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language
    Candace Walkington

    Cognitive research: principles and implications, 2017

    We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants&#39; actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students&#39; mathematical insights and informal proofs by eliciting dynamic gestures through in-gam...

    View PDFchevron_right