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1.
Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately. Electronic supplementary material  The online version of the original article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

2.
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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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.
Michela MaschiettoEmail:
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5.
An experiment with 72 three-year-olds investigated whether encoding events while seeing iconic gestures boosts children's memory representation of these events. The events, shown in videos of actors moving in an unusual manner, were presented with either iconic gestures depicting how the actors performed these actions, interactive gestures, or no gesture. In a recognition memory task, children in the iconic gesture condition remembered actors and actions better than children in the control conditions. Iconic gestures were categorized based on how much of the actors was represented by the hands (feet, legs, or body). Only iconic hand-as-body gestures boosted actor memory. Thus, seeing iconic gestures while encoding events facilitates children's memory of those aspects of events that are schematically highlighted by gesture.  相似文献   

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Building on the papers in this special issue as well as on our own experience and research, we try to shed light on the construct of example spaces and on how it can inform research and practice in the teaching and learning of mathematical concepts. Consistent with our way of working, we delay definition until after appropriate reader experience has been brought to the surface and several ‘examples’ have been discussed. Of special interest is the notion of accessibility of examples: an individual’s access to example spaces depends on conditions and is a valuable window on a deep, personal, situated structure. Through the notions of dimensions of possible variation and range of permissible change, we consider ways in which examples exemplify and how attention needs to be directed so as to emphasise examplehood (generality) rather than particularity of mathematical objects. The paper ends with some remarks about example spaces in mathematics education itself.  相似文献   

8.
Modelling mathematical argumentation: the importance of qualification   总被引:2,自引:0,他引:2  
In recent years several mathematics education researchers have attempted to analyse students’ arguments using a restricted form of Toulmin’s [The Uses of Argument, Cambridge University Press, UK, 1958] argumentation scheme. In this paper we report data from task-based interviews conducted with highly talented postgraduate mathematics students, and argue that a superior categorisation of genuine mathematical argumentation is provided by the use of Toulmin’s full scheme. In particular, we suggest that modal qualifiers play an important and previously unrecognised role in mathematical argumentation, and that one of the goals of instruction should be to develop students’ abilities to appropriately match up warrant-types with modal qualifiers.  相似文献   

9.
In the current shifts in mathematics classrooms, teachers are challenged to use effective pedagogy to develop inquiry communities in which all participants are offered opportunities to engage in the reasoning discourse of proficient mathematical practices. The challenge for teachers is to know how to implement these pedagogical changes. This article outlines how a teacher and researcher worked together in a collaborative partnership using a purposely designed communication and participation framework as a tool to scaffold development of collective reasoning in the inquiry community. The findings illustrate the interconnections between the teacher’s beliefs, past experiences, and current, and future expectations for her diverse students. Explanations are provided of how different, often conflicting, voices emerged including one that drew on the teacher’s cultural knowledge. This provided many learning opportunities for the researcher as the teacher developed her students’ voices in culturally appropriate ways.  相似文献   

10.
In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud’s approach enriches the study of freshmen’s processes at university. The mathematical analysis and the results specifically underscore the in-action definitions and the zero-definitions and highlight the need of similar mathematical experiences in education, particularly focused on defining processes and the exploration of a research problem.  相似文献   

11.
Mathematics homework is an activity done by large numbers of students across the world. However, it is not without controversy, with concerns being raised about its academic value and whether parents have the appropriate resources to actively support or teach their children. In this article, we use the narratives of two 10-year-old girls to consider how emotional and mathematical trauma can arise from doing mathematics homework with family help. This is often the undiscussed outcome of homework interactions, but one that can have profound implications for relationships between children, their parents, the school and mathematics as a discipline. The way that the children described their and other participants’ actions in the narratives provided information about the children’s agency whilst doing school mathematics in the home. We discuss the opportunities and constraints on children doing homework as a consequence of the social and institutional relations that they operate within. The constraining influence of schooling over the opportunities provided within the home situations was the main determiner of the emotional and mathematical trauma experienced by the children.  相似文献   

12.
This study took a novel approach to understanding the role of language in spatial development by combining approaches from spatial language and gesture research. It analyzed forty-three 4.5- to 6-year-old’s speech and gesture production during explanations of reasoning behind performance on Spatial Analogies and Children’s Mental Transformation Tasks. Results showed that speech and gesture relevant for solving the trials (disambiguating correct choices) predicted spatial performance when controlling for age, gender, and spatial words and gestures produced. Children performed the spatial tasks well if they produced relevant information either verbally through speech or nonverbally through gesture. These results highlight the importance of not only focusing on concepts children can reference but also on how such concepts are used in spatial tasks.  相似文献   

13.
Learners studying mechanical or technical processes via dynamic visualizations often fail to build an accurate mental representation of the system’s movements. Based on embodied theories of cognition assuming that action, perception, and cognition are closely intertwined, this paper proposes that the learning effectiveness of dynamic visualizations could be enhanced by grounding the movements of the presentation in people’s own bodily experiences during learning. We discuss recent research on embodied cognition and provide specific strategies for how the body can be used to ground movements during the learning process: (1) making or observing gestures, (2) manipulating and interacting with objects, (3) using body metaphors, and (4) using eye movements as retrieval cues. Implications for the design of dynamic visualizations as well as directions for future research are presented.  相似文献   

14.
In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students’ collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution methods. The second theory emerges from microlinguistic analysis of students’ mathematical choices and use of warrants in substantial argumentation to communicate, clarify, and convince others of the validity of their conjectures and mathematical work. Our goal was to illuminate mathematical argumentation by collaborative groups of calculus students at a qualitative level of detail sufficient to reveal one view of how these students satisfied the creative drive for mathematical meaning, communication, and accuracy in problem solving as evidenced in one classroom over several days.  相似文献   

15.
This study examines the effects of teachers' speech and hand gestures on the task performances of students with Attention‐Deficit/Hyperactivity Disorder (ADHD). Forty‐five 7½‐year‐old students clinically diagnosed with ADHD participated in the study. The students were asked to solve three sets of puzzles. The teachers supported the students in the tasks by using three different scaffolding modalities: speech‐only, gesture‐only and speech in conjunction with gestures. The results indicate that when the teachers used the scaffolding that contained gesture components (either speech scaffolding in conjunction with gesture scaffolding or gesture‐only scaffolding), the ADHD students were more responsive, focused longer on the tasks and were more successful in completing the tasks. Moreover, teachers' representational and deictic gestures were found to be the most effective gestures in scaffolding. This study suggests that when teachers' hand gestures are used together with speech, they are a powerful pedagogical means to engage ADHD children in tasks.  相似文献   

16.
It is well established that observing and producing gesture by a learner can enhance comprehension of verbal messages, including narratives. What is less well understood, however, is under which conditions gestures benefit comprehension most. This study examined the role of gesture observation and production in adult narrative comprehension, through investigating whether gesture production moderates the effect of gesture observation. Crucially, observing typical gestures, but not atypical gestures, significantly benefited narrative comprehension. Furthermore, no significant benefit of producing gestures was found, and there was no evidence that gesture production moderated the differential effects of observing typical and atypical gestures on narrative comprehension. Overall, the current study not only provides evidence that iconic gestures can benefit adult narrative comprehension, but also highlights under which conditions gestures are likely to be of benefit.  相似文献   

17.
Explanations are typically accompanied by hand gestures. While research has shown that gestures can help learners understand a particular concept, different learning effects in different types of gesture have been less understood. To address the issues above, the current study focused on whether different types of gestures lead to different levels of improvement in understanding. Two types of gestures were investigated, and thus, three instructional videos (two gesture videos plus a no gesture control) of the subject of mitosis—all identical except for the types of gesture used—were created. After watching one of the three videos, participants were tested on their level of understanding of mitosis. The results showed that (1) differences in comprehension were obtained across the three groups, and (2) representational (semantic) gestures led to a deeper level of comprehension than both beat gestures and the no gesture control. Finally, a language proficiency effect is discussed as a moderator that may affect understanding of a concept. Our findings suggest that a teacher is encouraged to use representational gestures even to adult learners, but more work is needed to prove the benefit of using gestures for adult learners in many subject areas.  相似文献   

18.
Pedagogical agents in multimedia learning environments have frequently been designed to produce pointing gestures (deictic) to direct spatial awareness. Although this might be beneficial for native English-speaking students who possess high levels of comprehension, only using pointing gestures with foreign language students learning English is problematic because these students need more assistance with language comprehension than just directing spatial awareness. The purpose of this study was to explore how gesture type and gesture frequency help foreign language students perceive the agent’s persona and the ability to recall procedural information. The results found one significant interaction between average gestures and no gesture in terms of facilitation, but all other conditions and persona subscales were not significant. For learning outcomes, the enhanced gesture condition significantly recalled more information than the no gesture condition (p = 0.017), and was approaching significance with the conversational gesture condition (p = 0.059). The findings suggest that when the learning population consists of foreign language students, pedagogical agents should use representational and beat gestures to help students comprehend more of the language, and the gesture frequency needs to be increased to account for the lack of verbal listening skills with this population.  相似文献   

19.
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   

20.
This paper reveals how the provision of teacher professional development is conceptualised within the Australian Government Quality Teacher Programme (AGQTP) policy text and its predecessors, and uses these texts to infer the nature of the production practices associated with the development of these policies. The paper argues that multiple tensions within these texts gesture towards support for complex and contested approaches to professional development during the policy production process. To make sense of this contestation, the paper draws suggestively upon Bourdieu’s field theory, which conceptualises the social world as consisting of social spaces or “fields”, and extensions of his theory, which reveal fields as exerting considerable influence upon one another. The paper argues that “Quality Teacher Programme” texts infer support for more progressive, social democratic approaches to the provision of teacher professional development within the educational policy field, as well as more economistic and neoliberal approaches.  相似文献   

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