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交流视角下的数学学习与教学研究

已有 1767 次阅读 2018-11-12 21:01 |系统分类:科研笔记

      整理文献过程中,意外发现,SSCI期刊《数学教育研究》(Educational Studies in Mathematics)在2016年的Volume 91, Issue 3, March,刊发了《交流视角下的数学学习与教学研究》(Communicational perspectives on learning and teaching mathematics)的系列专栏。该专栏的编辑为:Michal Tabach和Talli Nachlieli。

      这个专栏一共刊发了如下7篇文章,其中第1篇是Michal Tabach和Talli Nachlieli两位专栏主编写作的专栏序言论文,最后第7篇是对第2-6篇这5篇的评价性论文。中间第2-6篇这5篇则是该专栏的5篇论文论文,主要涉及语言手势关系、自主活动作用、愉悦化与数学化、功能话语规则、导数教科书讨论等。


[1] Communicational perspectives on learning and teaching mathematics: prologue

交流视角下的数学学习与教学研究:序言

Michal Tabach, Talli Nachlieli Pages 299-306


Abstract:This special issue comprises five studies which vary in their focus and mathematical content, yet they all share an underlying communicational theoretical framework commognition. Within this framework, learning mathematics is defined as a change in one’s mathematical discourse, that is, in the form of communication known as mathematical.Teaching can be defined as the communicational activity the motive of which is to bring the learners’ discourse closer to a canonic discourse. Reading the five research articles interconnected via their shared theoretical infrastructure has the potential to further develop insights about various aspects of teaching and learning mathematics.

摘要:专题包括五项研究,其重点和数学内容各不相同,但它们都有一个共同的交流理论框架。在这个框架内,学习数学被定义为一个人数学话语的变化,即以被称为数学的交际形式出现的。教学可以被定义为交际活动,其动机是使学习者的话语更接近于经典。当然。阅读这五篇通过它们共同的理论基础结构相互联系的研究文章,有可能进一步深入了解数学教学的各个方面。


Keywords Communicational perspective . Learning mathematics. Discourse analysis

关键词:传播学视角。学习数学。语篇分析


[2] The interplay between language, gestures, dragging and diagrams in bilingual learners’ mathematical communications

双语学习者数学交际中语言、手势、拖拽和图形的相互作用

Oi-Lam Ng Pages 307-326


Abstract:This paper discusses the importance of considering bilingual learners’ non-linguistic forms of communication for understanding their mathematical thinking. In particular, I provide a detailed analysis of communication involving a pair of high school bilingual learners during an exploratory activity where a touchscreen-based dynamic geometry environment (DGE) was used. The paper focuses on the word-use, gestures and dragging actions in student-pair communication about calculus concepts as they interacted with a touchscreen-based DGE. Findings suggest that the students relied on gestures and dragging as non-linguistic features of the mathematical discourse to communicate dynamic aspects of calculus. Moreover, by examining the interplay between language, gestures, dragging and diagrams, it was possible to identify bilingual learners’ competence in mathematical communications. This paper raises questions about new forms of communication mobilised in dynamic, touchscreen environments, particularly for bilingual learners.

摘要:论述了考虑双语学习者的非语言交际形式对于理解他们的数学思维的重要性。特别地,我提供了在使用基于触摸屏的动态几何环境(DGE)的探索活动期间涉及一对高中双语学习者的通信的详细分析。本文主要研究微积分概念与基于触摸屏的DGE交互过程中学生对交流中的词语使用、手势和拖曳行为。研究结果表明学生依靠手势和拖曳作为数学语篇的非语言特征来交流微积分的动态方面。此外,通过研究语言、手势、拖曳和图表之间的相互作用,有可能确定双语学习者的数学交际能力。本文就动态触摸屏环境下新形式的交流提出了问题,特别是对双语学习者而言。


Keywords:Thinking as communicating . Non-linguistic communication . Bilingual learners.Dynamic geometry environment . Touchscreen dragging

关键词:思维作为沟通。非语言交际。双语学习者,动态几何环境。触摸屏拖动


[3] Rituals and right answers: barriers and supports to autonomous activity

仪式与正确答案:自主活动的障碍与支持

Marcy B. Wood Pages 327-348


Abstract

摘要

Student autonomy has been an important object of study for mathematics educators for many years. Over time, framings of autonomy have moved from a focus on the individual to considerations of how an individual’s autonomy is entangled in classroom-level interactions. What has been less closely studied is how classroom interactions provide uneven access to autonomy for individuals. This study uses a communicational perspective to clarify Piaget’s intellectual autonomy and examine students’ mathematical interactions. The findings describe barriers and supports to autonomous activity for three students. Students were prevented from engaging in autonomous activity when they were seen as less capable than others, when they felt the need to manage the activities of their peers, or when they focused on being seen as knowledgeable. In contrast, students acted with autonomy when they took up the teacher’s request for explanations, noticed a contrast between their answer and the right answer, and worked on making connections across different representations.

多年来,学生自主性一直是数学教育工作者的一个重要研究对象。随着时间的推移,自治的框架已经从个人的焦点转移到个人的自治如何被纠缠在课堂层面的互动中。没有被仔细研究的是课堂互动如何为个人提供不平衡的自主性。本研究采用沟通的角度来澄清皮亚杰的智力自主性,并检查学生的数学互动。研究结果描述了三个学生自主活动的障碍和支持。当学生被认为比其他人能力差,当他们觉得需要管理同龄人的活动时,或者当他们专注于被看作知识渊博时,他们被阻止参与自主活动。相比之下,当学生接受老师的解释请求,注意到他们的答案和正确答案之间的对比,并且致力于在不同表示之间建立联系时,他们表现出了自主性。

Keywords

关键词

Communicational perspective;Autonomy Discourse ;Classroom interactions Learning

交际视角;自主性话语;课堂互动学习


[4] Between people-pleasing and mathematizing: South African learners’ struggle for numeracy

愉悦化与数学化之间:南非学习者的数字奋斗

Einat Heyd-Metzuyanim, Mellony Graven Pages 349-373


Abstract

摘要

The reported research attempts to trace possible reasons for third grade learners’ limited progress in numeracy in a low socioeconomic status (SES) South African context. This is done through two lenses, both stemming from Sfard’s commognitive (The term “commognition” has been offered by Sfard (2008) as an amalgam of “cognition” and “communication,” thus expressing the unity of these concepts. Since its original appearance, some authors (including Sfard herself) have preferred using the word “communicational” to describe Sfard’s framework. We chose to stick with “commognitive” because we believe it clearly points to the specific theoretical stance presented in Sfard (2008), whereas “communicational” might point to many other theories or frameworks that have something to do with human communication.) framework. One lens aims to analyze two learners’ (Mina and Ronaldo (all names are pseudonyms)) mathematical and identity discourse both in one-on-one interviews and in a small group “math club” lesson led by the second author. The other examines the mathematical milieu in which these learners have participated through the analysis of a school mathematics lesson which exemplifies prevalent instructional practices in this milieu. Relying on the distinction between ritual and explorative participation, we show that while Mina was acting in an extremely ritualized manner, Ronaldo was more explorative in his actions. However, the milieu, as seen in the school lesson, encouraged almost exclusively ritual participation. Thus, while Mina was identified as a good student, Ronaldo was identified as an outcast or “troublemaker.” We conclude by drawing implications to the tenacious nature of rituals in the mathematics classroom and the effects that these rituals may have on students’ identities.

报道的研究试图找出南非社会经济地位低下的三年级学生在算术能力上进展有限的可能原因。这是通过两个镜头完成的,这两个镜头都源自Sfard的共同性(术语“共同性”由Sfard(2008)提供,作为“认知”和“交流”的融合,从而表达了这些概念的统一。自从它最初出现以来,一些作者(包括Sfard本人)更喜欢使用“通信”这个词来描述Sfard的框架。我们选择坚持“共同性”是因为我们认为它清楚地指向了Sfard(2008)中提出的具体理论立场,而“交际性”可能指向许多与人类交际有关的其他理论或框架。一个镜头旨在分析两个学习者(米娜和罗纳尔多(所有的名字都是笔名))在一对一的访谈中和在第二作者领导的小组“数学俱乐部”中的数学和身份话语。另一项是通过分析学校数学课来考察这些学生所参与的数学环境,该课程举例说明了这种环境中普遍存在的教学实践。根据仪式参与和探索性参与的区别,我们发现米娜的行为极其仪式化,而罗纳尔多的行为更具探索性。然而,从学校课程中可以看出,这种氛围几乎只鼓励仪式的参与。因此,虽然米娜被认定为好学生,罗纳尔多被认定为弃儿或“捣乱者”。我们最后通过暗示数学课堂中仪式的顽固性以及这些仪式可能对学生身份的影响来得出结论。

Keywords

关键词

Commognition; Ritual learning; Explorative learning; Identity Discourse; Struggling students ;Mathematical milieu; Learning difficulties

交往;仪式学习;探究学习;身份话语;学生;数学情境;学习困难


[5] Making implicit metalevel rules of the discourse on function explicit topics of reflection in the classroom to foster student learning

在课堂中制定隐含的功能话语规则和显性反思话题来促进学生学习

Beste Güçler Pages 375-393


Abstract

摘要

Despite the existence of extensive literature on functions, fewer studies used sociocultural views to explore the development of student learning about the concept. This study uses a discursive lens to examine whether an instructional approach that specifically attends to particular metalevel rules in the mathematical discourse on functions supports students’ learning of the concept in a postsecondary mathematics classroom. The findings suggest that such instruction has the potential to foster learning as indicated by the changes in the ways students talked about functions, and their awareness and modifications of the assumptions shaping their thinking about functions.

尽管存在大量关于功能的文献,但很少有研究使用社会文化观点来探讨学生对概念的学习发展。本研究采用话语分析的方法,探讨在数学功能话语中特别关注特定金属层规则的教学方法是否支持学生在中学后数学课堂上学习该概念。研究结果显示,这种教学具有促进学习的潜力,如学生谈论功能的方式的变化,以及他们对形成他们对功能的思维的假设的认识和修改。

Keywords

关键词

Functions; Teaching experiment; Mathematical discourse; Metadiscursive rules; Student learning; Postsecondary education

功能;教学实验;数学语篇;元话语规则;学生学习;后二级教育


[6] Communicational approach to study textbook discourse on the derivative

交流视角下的导数教科书讨论研究

Jungeun Park Pages 395-421


Abstract

摘要

This paper investigates how three widely used calculus textbooks in the U.S. realize the derivative as a point-specific object and as a function using Sfard’s communicational approach. For this purpose, the study analyzed word-use and visual mediators for the limit process through which the derivative at a point was objectified, and word-use and visual mediators for the derivative process through which the derivative as a function was objectified. The analysis highlighted inconsistency in realizations of the limit process and object, and derivative process and object found in some instances, and implicit discussion on relations among different visual mediators. Specifically, the results of this study led to four observations about issues suggested by one or more of the textbooks: a) visual mediators of the initial and final objects, and the visual mediators of these processes were often inconsistent; b) transformations of visual mediators from initial object, through process, to final object were often implicit both in one visual mediator and across multiple visual mediators; c) visual mediators for the limit processes were sometimes disconnected from the initial and final objects, or the connections were not explicit; and d) realizations of both the derivative at a point and the derivative of a function were mediated with nearly identical symbols suggesting a possible difficulty with understanding the difference between them.

本文研究了美国三本广泛使用的微积分教材如何利用Sfard的交流方法实现导数作为点特定对象和函数。为此目的,本研究分析了词语使用和视觉中介对极限过程的影响,通过极限过程将某一点的导数客观化,以及词语使用和视觉中介对作为函数的导数客观化。分析强调了极限过程与对象、派生过程与对象在一些实例中的实现不一致,以及不同视觉中介体之间关系的隐式讨论。具体地说,这项研究的结果导致对一本或多本教科书提出的问题的四个观察:a)初始和最终对象的视觉中介,以及这些过程的视觉中介常常不一致;b)视觉中介从初始obj的转换ect,通过过程,到最终对象常常隐含在一个视觉中介中并且跨越多个视觉中介;c)用于限制过程的视觉中介有时从初始和最终对象断开,或者连接不明显;在某个点上的导数和函数的导数被用几乎相同的符号调和,表明理解它们之间的差异可能存在困难。

Keywords

关键词

Calculus; Function; Derivative Textbooks; Communicational approach

微积分;函数;衍生教材;交际法


[7] Commognition as a lens for research

作为研究透镜的交流认知

Norma Presmeg Pages 423-430


Abstract

摘要

This paper is a commentary on the theoretical formulations of the five empirical papers in this special issue. All five papers use aspects of the theory of commognition as presented by Anna Sfard; however, even when the same notions (e.g., rituals or explorations) are incorporated into theoretical frameworks undergirding the research, these notions are not always used in the same way. The analysis of how commognitive theory is used in the papers suggests that it is broad enough to be a useful theoretical lens in diverse settings. However, there are many aspects of Sfard’s careful theoretical formulation that are not touched upon, suggesting that there is much more potential for use of the theory than has been realized in these papers.

本文评述了本期五篇实证论文的理论表述。所有五篇论文都使用安娜·斯法德提出的共同交往理论的各个方面;然而,即使将相同的概念(例如,仪式或探索)纳入到支持研究的理论框架中,这些概念也不总是以相同的方式使用。对交际理论在文章中的运用的分析表明,它足够宽泛,可以在不同的环境下成为一个有用的理论透镜。然而,Sfard谨慎的理论公式中有许多方面没有被提及,这表明该理论的使用潜力远大于这些论文中实现的。

Keywords

关键词

Commognition; Communication theory; Theoretical framework

认知;传播理论;理论框架


【如上论文标题翻译,还是很简单的翻译,有待进一步优化。】



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