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1.
Most research on gestures (especially in the field of Mathematics Education) has focused on gestures in communication with others. In contrast, here, we focus on gestures which are not directed at others, but which we assume accompany inner speech or embodied thought, such as the gesticulation one makes by touching one??s fingers whilst silently counting; that is, whilst thinking, or communicating with oneself. Typically, these gestures are accompanied by eye gaze, which is detached from others who are present and turned either inwards or towards relevant artefacts present. Additionally, these gestures??whilst structurally similar??are much smaller than ??normal?? gestures used in interpersonal communication, suggesting an attenuation parallel to that found in inner speech. These physical gestures are in effect objectifications for oneself, which we can interpret as a not-quite-yet ??underground?? part of embodied thought. We suggest that they might be particularly vital for understanding the imagistic, visuospatial dimension of mathematics in general and fractions in particular. 相似文献
2.
It is our presupposition that there is still a need for more research about how classroom practices can exploit the use and power of visualization in mathematics education. The aim of this article is to contribute in this direction, investigating how visual representations can structure geometry activity in the classroom and discussing teaching practices that can facilitate students’ visualization of mathematical objects. We present one illustrative episode that shows how drawings of geometrical figures have a powerful role in structuring and modifying the mathematical activity in the classroom. It was selected from a database that we have been building to investigate the learning of mathematics in public elementary schools in Brazil. The framework of Activity Theory helped in the characterization of the episode as a system of interconnected activities. We discuss the changes and transformations perceived in those activities; and we explore the idea of miniature cycles of learning actions to focus on the mathematical learning that is taking place. We describe the dynamics and the complexity of the ongoing activity in the calculation of areas; and, how drawings form a part, and show their influence, in it. We argue that part of this influence was associated with the contradiction between abstract mathematical ideas and their empirical representations, revealed by the tensions perceived in the activities analysed; and, simultaneously, that we could see as an impelling force for the learning of the rules and norms which regulate the use of visual representations in school mathematics. 相似文献
3.
Much of the evidence provided in support of the argument that mathematical knowing is embodied/enacted is based on the analysis
of gestures and bodily configurations, and, to a lesser extent, on certain vocal features (e.g., prosody). However, there
are dimensions involved in the emergence of mathematical knowing and the production of mathematical communication that have
not yet been investigated. The purpose of this article is to theorize one of these dimensions, which we call incarnate sonorous
consciousness. Drawing on microanalyses of two exemplary episodes in which a group of third graders are sorting geometric
solids, we show how sound has the potential to mark mathematical similarities and distinctions. These “audible” similarities
and distinctions, which may be produced by incarnate dimensions such as beat gestures and prosody, allow children to objectify
certain geometrical properties of the objects with which they transact. Moreover, the analysis shows that sonorous production
is intertwined with other dimensions of students’ bodily activity. These findings are interpreted according to the “theory
of mathematics in the flesh,” an alternative to current embodiment/enactivist theories in mathematics education. 相似文献
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5.
Psychologists, philosophers, and educators have traditionally interpreted the phenomenon of insight learning as the result of the sudden comprehension of abstract/conceptual ideas. The present article shows that such phenomenon may also follow and emerge from the kinetic movements of the human body; that is, we conceptualize insight learning as a post-kinetic phenomenon. Further, it is suggested that kinetic movement constitutes the ground of all human knowing. To illustrate this innovative conceptualization of insight learning, we present the analysis of an exemplary classroom episode taken from a two-year longitudinal video-based ethnographic project. Our project is concerned with elementary students?? mathematical knowing and learning. In the episode, which was selected among other structurally similar examples, three children are sorting geometrical objects. The evidence shown is interpreted as support for the theory of mathematics in the flesh, a radical approach to embodied cognition. In contrast to other embodiment/ enactivist theories in the field of mathematics education, we suggest that the kinetic movement of the human body constitutes a necessary condition for the emergence of abstract mathematical knowledge, and more specifically for the emergence of geometrical insight. 相似文献
6.
Luciana Bazzini 《Educational Studies in Mathematics》2001,47(3):259-271
The mutual relationship between real objects and mathematical constructions is at the very base of studies concerned with
making sense in mathematics. In this wider perspective recent research studies have been concerned with the cognitive roots
of mathematical concepts. Human perception and movement and, more generally, interaction with space and time are recognized
as being of crucial importance for knowledge construction. A new approach to the cognitive science of mathematics, based on
the notion of ‘embodied cognition’ assumes that mathematics cannot be considered as mind free. Accordingly, mathematical concepts
derive from the cognitive activities of subjects and are highly influenced by the body structure. This article reports some
examples of teaching experiments based on body-related metaphors. Some of them are carried out by means of technological devices.
A call for legitimacy in school mathematics is made, both for an embodied cognition perspective and for a related use of technology.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
Judit N. Moschkovich 《Educational Studies in Mathematics》2004,55(1-3):49-80
This case study uses a sociocultural perspective and the concept of appropriation (Newman, Griffin and Cole, 1989; Rogoff, 1990) to describe how a student learned to work with linear functions. The analysis describes in detail the impact that interaction with a tutor had on a learner, how the learner appropriated goals, actions, perspectives, and meanings that are part of mathematical practices, and how the learner was active in transforming several of the goals that she appropriated. The paper describes how a learner appropriated two aspects of mathematical practices that are crucial for working with functions (Breidenbach, Dubinsky, Nichols and Hawks, 1992; Even, 1990; Moschkovich, Schoenfeld and Arcavi, 1993; Schwarz and Yerushalmy, 1992; Sfard, 1992): a perspective treating lines as objects and the action of connecting a line to its corresponding equation in the form y = mx + b. I use examples from the analysis of two tutoring sessions to illustrate how the tutor introduced three tasks (estimating y-intercepts, evaluating slopes, and exploring parameters) that reflect these two aspects of mathematical practices in this domain and describe how the student appropriated goals, actions, meanings, and perspectives for carrying out these tasks. I describe how appropriation functioned in terms of the focus of attention, the meaning for utterances, and the goals for these three tasks. I also examine how the learner did not merely repeat the goals the tutor introduced but actively transformed some of these goals. 相似文献
8.
Julian Williams 《Educational Studies in Mathematics》2009,70(2):201-210
I begin by appreciating the contributions in the volume that indirectly and directly address the questions: Why do gestures and embodiment matter to mathematics education, what has understanding of these achieved and what might they achieve? I argue, however, that understanding gestures can in general only play an important role in ‘grasping’ the meaning of mathematics if the whole object-orientated ‘activity’ is taken into account in our perspective, and give examples from my own work and from this Special Issue. Finally, I put forward the notion of a ‘threshold’ moment, where seeing and grasping at the nexus of two or more activities often seem to be critical to breakthroughs in learning. 相似文献
9.
This paper reports a part of a study on the construction of mathematical meanings in terms of development of semiotic systems
(gestures, speech in oral and written form, drawings) in a Vygotskian framework, where artefacts are used as tools of semiotic
mediation. It describes a teaching experiment on perspective drawing at primary school (fourth to fifth grade classes), starting
from a concrete experience with a Dürer’s glass to the interpretation of a new artefact. We analyse the long term process
of appropriation of the mathematical model of perspective drawing (visual pyramid) through the development of gestures, speech
and drawings under the teacher’s guidance.
相似文献
| Michela MaschiettoEmail: |
10.
In this paper we make an argument for paying close attention to the materiality of practice in understanding the work of teacher educators; specifically, the meanings of artefacts used by teacher educators in the course of their daily work. We locate this analysis within a dialectical materialist understanding of the development of human activity, providing examples of artefacts-in-use in initial teacher education and the meanings accorded to these artefacts by the teacher educators we observed and interviewed. Our aim is to make a case for what is afforded epistemologically when researchers pay attention to artefacts from a dialectical materialist viewpoint. In the final part of the paper, we argue that paying attention to how teacher educators engage with artefacts can help us understand the unity of psychological and social processes within dominant approaches to teacher education, as well as providing clues about how adaptation of artefacts can drive cultural change. 相似文献
11.
Based on principles of constructivism, an analysis is made of how practice in mathematical education might be reformed towards a professional practice. In addition to the widespread recommendations that mathematical teaching be based on interactive communication and that mathematical learning be active, we argue that conventional school mathematics be replaced by a constructivist school mathematics. A constructivist school mathematics is based on children's use of their schemes of action and operation in learning situations, and whatever accommodation the children make in these schemes as they use them. Through examples of our learning of the numerical schemes of five year old children we illustrate what we mean by a constructivist school mathematics. In our examples, we characterize the schemes of action and operation that we attribute to children as our interpretations of the children's activities. For this reason, we define a constructivist school mathematics to be the results of the observer's experiential abstractions in the context of interacting with children mathematically. A professional teacher is cast as one with the intellectual autonomy and power to produce a constructivist school mathematics, including the involved situations of learning and interactive mathematical communication. 相似文献
12.
This study examines the consequences of whole-body, multi-party activity for mathematics learning, both in and out of the classroom. We develop a theoretical framework that brings together contemporary theories related to social space, embodied cognition, and mathematical activity. Then, drawing on micro-ethnographic and case-comparative techniques, we examine and juxtapose two cases of implementing whole-body, collaborative movement to engage learners in the mathematics of number sense and ratio and proportion. Analytically foregrounding the interdependence among setting, embodied activity, and mathematical tools and practices, we illustrate how whole-body collaboration can transform how learners experience learning environments and make sense of important mathematical ideas. The analysis enriches our understanding of the changing spatial landscapes for learning and doing mathematics as well as how re-instating bodies in mathematics education can open up new forms of collective mathematical sense-making and activity. 相似文献
13.
We ground Cultural-Historical Activity Theory (CHAT) in studies of workplace practices from a mathematical point of view.
We draw on multiple case study visits by college students and teacher-researchers to workplaces. By asking questions that
‘open boxes’, we ‘outsiders and boundary-crossers’ sought to expose contradictions between College and work, induce breakdowns
and identify salient mathematics. Typically, we find that mathematical processes have been historically crystallised in ‘black
boxes’ shaped by workplace cultures: its instruments, rules and divisions of labour tending to disguise or hide mathematics.
These black boxes are of two kinds, signalling two key processes by which mathematics is put to work. The first involves automation,
when the work of mathematics is crystallised in instruments, tools and routines: this process tends to distribute and hide
mathematical work, but also evolves a distinct workplace ‘genre’ of mathematical practice. The second process involves sub-units
of the community being protected from mathematics by a division of labour supported by communal rules, norms and expectations.
These are often regulated by boundary objects that are the object of activity on one side of the boundary but serve as instruments
of activity on the other side. We explain contradictions between workplace and College practices in analyses of the contrasting
functions of the activity systems that structure them and that consequently provide for different genres and distributions
of mathematics, and finally draw inferences for better alignment of College programmes with the needs of students. 相似文献
14.
The idea that mathematical knowledge is embodied is increasingly taking hold in the mathematics education literature. Yet there are challenges to the existing conceptualizations: There tend to be breaks between (a) the living and experienced body (flesh) and linguistic forms of thought, (b) individual and collective forms of knowing, and (c) the material body and the source of intentionality. Grounded in material phenomenology, we theorize the living body as semiotic expression that not only grounds thought but also leads to its development. We provide a detailed case study that elucidates the three ways in which the living body serves as sign for the growth of a second-grade student??s geometric understanding and the other bodies he interacts with. 相似文献
15.
数学术语的隐喻歧义及其人文内涵 总被引：2，自引：0，他引：2
数学术语指的是指称或限定某类数学对象的字、词或词组。通常是用词语的一般意义隐喻其数学意义。这种隐喻存在着歧义现象,主要包括指称对象的模糊或变异,限定对象的语义转换以及种属关系的误解。这些现象会给相关数学概念的学习造成障碍或误解。同时,这些隐喻现象中蕴涵着人文因素,挖掘这些人文因素并将之用于数学课程与教学,有益于数学与人文的沟通。 相似文献
16.
Michael C. Wittmann Virginia J. Flood Katrina E. Black 《Educational Studies in Mathematics》2013,82(2):169-181
We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of embodied cognition and use conceptual metaphors such as the path-source-goal schema and the idea of fictive motion. We find that students solving the problem correctly and efficiently do not use overt mathematical language like multiplication or division. Instead, their gestures and ambiguous speech of moving are the only algebra used at that moment. 相似文献
17.
18.
Mijung Kim Wolff-Michael Roth Jennifer Thom 《International Journal of Science and Mathematics Education》2011,9(1):207-238
There is mounting research evidence that contests the metaphysical perspective of knowing as mental process detached from
the physical world. Yet education, especially in its teaching and learning practices, continues to treat knowledge as something
that is necessarily and solely expressed in ideal verbal form. This study is part of a funded project that investigates the
role of the body in knowing and learning mathematics. Based on a 3-week (15 1-h lessons) video study of 1-s grade mathematics
classroom (N = 24), we identify 4 claims: (a) gestures support children’s thinking and knowing, (b) gestures co-emerge with peers’ gestures
in interactive situations, (c) gestures cope with the abstractness of concepts, and (d) children’s bodies exhibit geometrical
knowledge. We conclude that children think and learn through their bodies. Our study suggests to educators that conventional
images of knowledge as being static and abstract in nature need to be rethought so that it not only takes into account verbal
and written languages and text but also recognizes the necessary ways in which children’s knowledge is embodied in and expressed
through their bodies. 相似文献
19.
In this paper, we argue that history might have a profound role to play for learning mathematics by providing a self-evident
(if not indispensable) strategy for revealing meta-discursive rules in mathematics and turning them into explicit objects
of reflection for students. Our argument is based on Sfard’s theory of Thinking as Communicating, combined with ideas from historiography of mathematics regarding a multiple perspective approach to the history of practices
of mathematics. We analyse two project reports from a cohort of history of mathematics projects performed by students at Roskilde
University. These project reports constitute the experiential and empirical basis for our claims. The project reports are
analysed with respect to students’ reflections about meta-discursive rules to illustrate how and in what sense history can
be used in mathematics education to facilitate the development of students’ meta-discursive rules of mathematical discourse. 相似文献