先整理2014年以来的三篇SSCI期刊论文。

[1] Nardi, E., Ryve, A., Stadler, E., & Viirman, O. (2014). Commognitive analyses of the learning and teaching of mathematics at university level: the case of discursive shifts in the study of Calculus. Research in Mathematics Education, 16(2), 182-198.

慧，E.，ryve，A.，Stadler，E.，& viirman，O（2014年）。commognitive分析《大学数学学习与教学：以大学水平的情况discursive shifts结石的研究。在数学教育研究，16（2），182 198。

Abstract

摘要

In this paper we outline the main tenets of the commognitive approach and we exemplify its application in studies that investigate the learning and teaching of mathematics at university level. Following an overview of such applications, we focus on three studies that explore fundamental discursive shifts often occurring in the early stages of studying Calculus. These shifts concern the lecturers' and students' communicative practices, routines of constructing mathematical objects and ways of resolving commognitive conflicts. We then propose that commognitive constructs such as subjectification can be deployed towards ‘scaling-up’ the hitherto fine-grained focus of commognitive analyses. Finally, we conclude with observing how the commognitive approach relates to constructs from other sociocultural approaches to research in university mathematics education, such as “legitimate peripheral participation” from the theory of Communities of Practice and “didactic contract” from the Theory of Didactic Situations.

本文概括了交流教学法的主要原理，并举例说明了它在研究大学数学学习与教学中的应用。在综述这些应用之后，我们集中于三项研究，探讨在微积分学习的早期阶段经常发生的基本话语转移。这些转变涉及教师和学生的交际实践、构建数学对象的例行程序和解决共同冲突的方法。然后，我们建议，诸如主体化之类的共同性结构可以被部署到“放大”迄今为止共同性分析的细粒度焦点。最后，我们观察了社群主义方法如何与其他社会文化方法建构大学数学教育研究，如实践社群理论的“合法的外围参与”和说教情境理论。

Keywords: university mathematics education, discourse, commognitive conflict, Calculus, functions

关键词：大学数学教育、话语、交际冲突、微积分、函数

[2] Viirman, O. (2015). Explanation, motivation and question posing routines in university mathematics teachers' pedagogical discourse: a commognitive analysis. International journal of mathematical education in science and technology, 46(8), 1165-1181.

维尔曼，O（2015）。大学数学教师教学话语的解释、动机与提问例程：一个共同分析。国际科学和技术数学教育杂志，46（8），1165-1181。

Abstract

摘要

This paper investigates the teaching practices used by university mathematics teachers when lecturing, a topic within university mathematics education research which is gaining an increasing interest. In the study, a view of mathematics teaching as a discursive practice is taken, and Sfard's commognitive framework is used to investigate the teaching practices of seven Swedish university mathematics teachers on the topic of functions. The present paper looks at the discourse of mathematics teaching, presenting a categorization of the didactical routines into three categories – explanation, motivation and question posing routines. All of these are present in the discourses of all seven teachers, but within these general categories, a number of different sub-categories of routines are found, used in different ways and to different extent by the various teachers. The explanation routines include known mathematical facts, summary and repetition, different representations, everyday language, and concretization and metaphor; the motivation routines include reference to utility, the nature of mathematics, humour and result focus; and the question posing routines include control questions, asking for facts, enquiries and rhetorical questions. This categorization of question posing routines, for instance, complements those already found in the literature. In addition to providing a valuable insight into the teaching of functions at the university level, the categorizations presented in the study can also be useful for investigating the teaching of other mathematical topics.

本文研究了大学数学教师在教学中所使用的教学实践，这是大学数学教育研究中的一个越来越受关注的话题。在这项研究中，采取了数学教学作为话语实践的观点，并使用Sfard的认知框架研究了七位瑞典大学数学教师在功能方面的教学实践。本文从数学教学的角度出发，将教学过程归类为三类：解释、动机和提出问题的例程。所有这些都存在于所有七位教师的话语中，但在这些一般类别中，发现了许多不同的子类别的例程，以不同的方式和不同程度地被不同的教师使用。解释程序包括已知的数学事实、概括和重复、不同的表述、日常语言以及具体化和隐喻；动机程序包括效用参考、数学性质、幽默和结果焦点；以及提问程序。包括控制问题、询问事实、询问和修辞问题。例如，这种提问例行程序的分类是对文献中已经发现的那些例行程序的补充。除了对大学一级的函数教学提供有价值的见解之外，研究中提出的分类也可用于研究其他数学主题的教学。

Keywords: mathematics, university education, commognitive framework, function, discourse, teaching

关键词：数学、大学教育、交际框架、功能、话语、教学

[3] Heyd-Metzuyanim, E., & Graven, M. (2016). Between people-pleasing and mathematizing: South African learners’ struggle for numeracy. Educational Studies in Mathematics, 91(3), 349-373.

Heyd Metzuyanim，E，和GraveN，M.（2016）。在讨人喜欢的和数学化之间：南非学习者在算术上的斗争。数学教育研究，91（3），第34至第37页。

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

       然后，整理一篇2017年新加坡南洋理工大学的博士论文。

Chia, Su Ngin

大肠菌

Examining a teacher's use of multiple representations and noticing in theteaching of percentage : a commognitive perspectiveInstitute

审查一个多方面代表和诺言在评价百分比方面的使用情况：指导意见研究所

Thesis (M.Ed.) National Institute of Education, Nanyang Technological University

新加坡南洋理工大学国家教育研究所

Year2017 Supervisor(s) Choy, Ban Heng

Abstract

摘要

The use of multiple representations is prevalent in mathematics teaching. However, many studies suggest that using multiple representations would not automatically lead tomathematics teaching and learning. Teachers’ lack of awareness of the transitions amongthe different representations is one of the common factors which affect teachers’ use of multiple representations. Percentage, an important but challenging topic for primary school pupils, presents opportunities for teachers to use multiple representations and to deliberate on the use of mathematical language to support pupils’ learning.

多元表征在数学教学中的应用十分普遍。然而，许多研究表明使用多重表示不会自动引导数学教学和学习。教师缺乏对不同表征之间转换的意识是影响教师使用多种表征的共同因素之一。对于小学生来说，百分比是一个重要但具有挑战性的话题，它为教师提供了使用多种表示法并讨论使用数学语言支持学生学习的机会。

However, notmany studies have explored the use of multiple representations in the teaching of thepercentage topic. Using an exploratory qualitative case study, this study explores how ateacher, Mrs Hannah, used multiple representations in the teaching of percentage inSingapore through the lens of commognition and teacher noticing.

然而，没有多少研究探讨在百分比主题教学中使用多重表征。本研究采用探索性质的个案研究，探讨教师汉娜女士如何透过共同认知与教师注意的角度，在新加坡百分比教学中运用多元表征。

More specifically, this study introduces and demonstrates how the use of a mediationflowchart and a theoretical model created from a FOCUS framework can be used to studyteachers’ use of multiple representations in the teaching of percentage. Hence, using thelens of commognition and teacher noticing, Mrs Hannah’s use of multiple representationswere analysed to shed light on the interplay among representations in the teaching ofpercentage.The participants of the study include the researcher, the teacher participant, Mrs Hannah,and her class of seven Primary 5 pupils. A total of six lessons were recorded using aSwivl® robot. After a process of data condensation and data analysis, an episode whichreflected Mrs Hannah’s rich use of multiple representations was presented in this dissertation as a case study. The episode was divided into three segments, which will beanalysed and presented through the lens of commognitive framework and teacher noticing. A mediation flowchart was created to analyse Mrs Hannah’s use of representations froma commognitive perspective in each segment. Using the four characteristics ofmathematics discourse (keywords, visual mediators, narratives and routines), the studydiscovered that the fluent transition among multiple representations depends on a fewfactors.

更具体地说，本研究介绍并演示如何使用中介流程图和由FOCUS框架创建的理论模型来研究教师在百分比教学中使用多种表示。因此，本研究以师生互动及教师注意力为工具，分析汉娜女士对多重表征的使用，以揭示表征在百分比教学中的相互关系。小学七班5名学生。使用ASWIVL®机器人共记录了六节课。经过一个数据压缩和数据分析的过程，这篇论文以一个事件为例展示了汉娜夫人对多重表征的丰富运用。该剧分为三个部分，分别从交际框架和教师注意两个角度进行分析和呈现。创建了一个调解流程图，以分析汉娜夫人在每个片段中从共同视角使用表示。利用数学语篇的四个特征（关键词、视觉中介、叙事和例程），研究发现多重表征之间的流畅过渡取决于少数几个因素。

Firstly, use of keywords and gestures can mediate representations together, thusimproving representational fluency. Next, the use of an elaborated realising procedureduring the creation of signifiers-realisation pairs in a discourse and the types of routinesused also improves representational fluency. The study suggests that the interplay of thedifferent characteristics of a discourse also affects representational fluency.

首先，使用关键词和手势可以调解表征在一起，从而提高表征的流畅性。其次，使用精心设计的实现过程来创建语篇中的能指-实现对以及所使用的例程类型也提高了表征流畅性。研究表明，不同语篇特征的相互作用也会影响表征流畅性。

Next, a theoretical model created from FOCUS framework was also used to analyse MrsHannah’s use of multiple representations in each of the three segments. The FOCUS framework highlights two important characteristics of productive noticing which includesexplicit focus of noticing (What to notice) and focusing noticing of pedagogy reasoning(How to notice). With reference to Mrs Hannah’s explicit focus which includes theidentification of the concepts that pupils have to learn (Key point), how she made senseof pupils’ difficulties in learning of the concepts (Difficult point) and how she had decidedto respond to pupils’ difficulties (Critical point), and focusing noticing throughjustification of her teaching actions, this study demonstrates how a teacher’s noticing onthe use of multiple representations in the teaching of percentage may be productive andnon-productive.

接下来，还使用从FOCUS框架创建的理论模型来分析Hannah夫人在三个部分中的每个部分使用多个表示。FOCUS框架突出了生产性注意的两个重要特征，即显性注意焦点（注意什么）和教学推理注意焦点（如何注意）。关于汉娜女士的明确重点，包括确定学生必须学习的概念（重点），她如何感知学生在学习概念上的困难（难点），以及她如何决定对学生的困难作出反应（关键点）本研究以注意为切入点，通过对教学行为的论证，论证了教师在百分率教学中注意多重表征的使用可能具有生产性和非生产性。

【如上还只是翻译器翻译，有待进一步整理。】