小学数学课堂师生对话的特征分析
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摘要
课堂教学是教师与学生交流互动和共同发展的过程。对小学数学课堂师生对话的特征进行实证分析,不仅符合当前国际教育研究的潮流,更是深化我国小学数学课堂有效教学改革的迫切需求。这一研究对诊断与改进小学数学课堂师生对话问题,完善小学数学课堂师生对话评价理论与技术,以及提升小学数学教师课堂师生对话水平,都具有重要的理论价值和实践意义。
本研究综合理论和实践方法构建了小学数学课堂师生对话分析框架,并运用这个分析框架对上海市Y小学数学教师课堂师生对话特征进行个案剖析。研究内容包括：①小学数学课堂师生对话特征的分析框架是什么?这是本研究的基础,具体回答小学数学课堂师生对话“分析什么”和“怎么分析”的问题；②以上海市Y小学作为研究个案,小学数学课堂师生对话具有怎样的特征?这是整项研究的核心,具体探讨当前小学数学课堂师生对话特征是什么,不同教学水平的教师在课堂师生对话中存在哪些差异性特征,这些特征是如何影响学生数学学习的。
整个研究过程分为两个阶段。第一阶段研究重点在于构建小学数学课堂师生对话分析框架。具体做法为：以社会文化理论为基础,综合文献研究和访谈调查研究等方法,探索小学数学课堂师生对话分析的理论框架,经本土化的实践修正后,形成小学数学课堂师生对话分析框架。第二阶段研究目的在于全面收集数据和分析小学数学课堂师生对话特征。具体做法为：以上海市Y小学10位数学教师作为研究对象,以分别代表职初教师、有经验教师和骨干教师的3位教师四年级的常态课为重点,通过课堂观察、教学录像、教师访谈、学生问卷、教学反思等方式采集数据,借助NVivo8质性分析软件,综合运用个案比较、录像研究、系统观察、会话分析和互动分析等量与质的研究方法,解读Y小学数学课堂师生对话的具体特征。
研究结论包括五个方面：
第一,构建了小学数学课堂师生对话分析框架。这个分析框架包含内容体系、编码体系和操作流程三个部分。内容体系是核心,具体由三个维度十个要素构成。三个维度分别是数学课堂语言、数学意义建构和数学课堂文化。十个要素分别是师生话语信息流、语言表达准确性、教师语言使用量及转换方式、师生对话功能属性、数学问题或任务的特性、教师倾听与回应学生的方式、学生参与数学结论形成的心智水平、师生对话机会、师生对话互动结构和师生对话关系。
第二,师生话语是维系课堂有效对话的重要介质。从个案研究中发现,目前小学数学课堂师生对话中的师生话语特征表现有：“教师提问—学生陈述”是主要的师生对话形式,教师话语超过学生话语,教师“数学教学语言”使用量远远超过“数学语言”,学生话语以“被动”应答教师的提问为主,生生对话明显不足。
第三,数学问题或任务的特性以及教师倾听回应学生的方式,对学生理解与建构数学意义起关键作用。从个案研究中发现,目前小学数学课堂中预设性、封闭性和概念性问题偏多,生成性、开放性和“做数学联结”的问题偏少,数学问题的思维水平总体不高。教师倾听与回应学生时,较多地关注自身而对学生特定想法的关注则较少。
第四,师生对话反映出师生话语机会、师生互动结构和师生关系等文化特征。从个案研究发现,教师拥有教学话语权,学生参与高层次数学思维的话语机会较少。旨在传递信息和教师控制的单义性对话偏多,旨在促进数学意义理解与建构的对话性对话偏少。师生之间表现有三类对话结构,即教师对学生单向作用的单向度对话结构、教师和学生双向互动作用的双向度对话结构、以及师生生生多向交互作用成话语共同体的多向度对话结构。
第五,不同教学水平的教师在小学数学课堂师生对话中存在特征差异。随着教师教学水平提高,教师对学生经验的关注越趋明显,教师话语逐渐减少而学生话语逐渐增多,数学问题的开放程度和学生选择机会逐步增大,教师倾听回应学生的关注点逐步由“教师”转向“学生”,学生参与数学意义理解与建构的思维水平逐步提高。职初教师多表现出单向度对话结构,有经验教师多表现出双向度对话结构,骨干教师则在多向度对话结构上表现明显。
上述研究结论,对于有效诊断小学数学课堂师生对话问题和开展针对性强的教师培训,尤其是提高职初教师的课堂对话水平,让小学数学课堂从“封闭性对话”走向“开放性对话”、从“教师控制性对话”走向“师生话语共同体”,从“知识传递教学”走向“知识建构教学”,都具有重要实践意义。
Primary mathematics classroom instruction is a process of teacher-student interaction and mutual development. An empirical analysis of the teacher-student conversation in the primary mathematics classroom is in accordance with the educational study trend of the world, and also meets the urgent need for an effective classroom instruction in the primary mathematics in China. It is of theoretical value and practical significance in terms of diagnosing the problems in teacher-student conversation in the primary mathematics classroom, perfecting the assessment theory and technique of the primary mathematics classroom conversation, and improving the quality of the teacher-student classroom conversation.
The study first constructs a framework for the analysis of the primary mathematics classroom teacher-student conversation by combining theory and practice, and then the framework is used to conduct an analytical and comparative study of the conversational cases taken from Y Primary School in Shanghai. The study includes two parts.①What is the framework for the analysis of the primary mathematics classroom teacher-student conversation? It answers questions of "what to be analyzed" and "how to analyze".②What are the features of the primary mathematics classroom teacher-student conversation at Y Primary School in Shanghai? As the core of the whole study, this part discusses the features of the primary mathematics classroom teacher-student conversation, the differential features of the conversation conducted by teachers of different teaching abilities, and how these features influence the students'mathematics learning.
The whole study is divided into two stages. The first stage aims at the construction of an analytical framework for the primary mathematics classroom teacher-student conversation. Based on the sociocultural theory and combining the methods of literature research and interview survey, the analytical framework is formed by exploring the theoretical framework for the analysis of the primary mathematics classroom teacher-student conversation and localizing the theory in practice. The second stage aims at a full collection of data and analyzing the features of the primary mathematics classroom teacher-student conversation. The subjects investigated are10mathematics teachers in Y Primary School, and the research focus is the normal classes of grade4about "the Verticality and Mutually Perpendicular" presented by3teachers who represent the novice teacher, the experienced teacher and the expert teacher respectively. The data are collected through classroom observations, videos of classroom teaching, interviews with teachers, student questionnaires, and teachers'reflections on teaching. Using NVivo8software for qualitative data analysis and combining case study, video study, systematic observation, conversation analysis and interaction analysis, the features of the mathematics classroom teacher-student conversation in Y Primary School are fully interpreted.
The conclusions of the dissertation are as follows:
First, a "three dimensions and ten factors" analytical framework for primary mathematics classroom teacher-student conversation is constructed. This framework includes3parts of the content system, encoding system, and operation procedure. The content system is made up of three dimensions (mathematics classroom language, mathematics meaning making and mathematics classroom culture) and ten elements (teacher-student discourse information flow, accuracy of expression, the amount of the teacher's language and way of switching, the function attribute of the teacher-student conversation, the nature of the mathematical questions or tasks, the ways of teacher's listening to and responding to students, students'intellectual powers to participate in drawing conclusions, the chances of teacher-student conversation, the interactive structure of the teacher-student conversation and the relationship of the teacher-student conversation). The encoding system is the requirements and standards for classifying and encoding the above mentioned factors. The operation procedure shows the operation steps of the conversation analysis in practice.
Second, the verbal communication between the teacher and the students is an important medium maintaining effective conversations. At present, the verbal features of the primary mathematics classroom teacher-student conversation are "the teacher asks-the students state" which means in such conversational form the teacher talks more than the students do;"mathematical instruction language" occupies more high proportion than "mathematical language"; students discourse is "passive" answers to the teacher's questions; the conversations among students are inadequate.
Third, the quality and quantity of the mathematical questions or tasks and the ways of the teacher's listening to and responding to the students play important roles in students'understanding and construction of mathematical meanings. At present, there are more predesigned, closed and conceptual questions than generating, open and "making mathematical connections" questions, and the thinking level of mathematical questions is not high. When listening to and responding to the students, the teachers pay more attention to themselves than to the special thinking of the students.
Forth, the verbal communications between the teacher and students are full of cultural features. The teacher holds the teaching discourse power, and the students have fewer opportunities to participate in a high level of mathematical thinking. There are more one way interaction from the teacher to the students aiming to convey message and teacher control and fewer conversations aiming to promote understanding and construction of mathematical meaning. There are three interaction structures, the one way interaction from the teacher to the student, the two way interaction between the teacher and the student, the multi-way interaction between the teacher and the students and among the students.
Fifth, there are differential features of the conversation conducted by teachers of different teaching abilities. It is evident that with improved teaching abilities, the teacher pays more attention to the students'experiences, the teacher talks less and the students talk more, the degree of the openness of the mathematical questions and students' opportunities of choices are increased, the focusing points gradually turn from "teacher" to "students", and the thinking level of the students participating in the understanding and construction of mathematical meaning is gradually rising.
The above conclusions are of practical significance in the problem diagnosis of primary mathematics classroom teacher-student conversation and carrying out targeted teacher training programs, especially in improving new teachers'classroom conversation skills, turning the classroom conversation from "closed" to "open", from "teacher control" to "teacher-student discourse community", and changing mathematics teaching from "knowledge imparting" to "knowledge construction".
本研究综合理论和实践方法构建了小学数学课堂师生对话分析框架,并运用这个分析框架对上海市Y小学数学教师课堂师生对话特征进行个案剖析。研究内容包括：①小学数学课堂师生对话特征的分析框架是什么?这是本研究的基础,具体回答小学数学课堂师生对话“分析什么”和“怎么分析”的问题；②以上海市Y小学作为研究个案,小学数学课堂师生对话具有怎样的特征?这是整项研究的核心,具体探讨当前小学数学课堂师生对话特征是什么,不同教学水平的教师在课堂师生对话中存在哪些差异性特征,这些特征是如何影响学生数学学习的。
整个研究过程分为两个阶段。第一阶段研究重点在于构建小学数学课堂师生对话分析框架。具体做法为：以社会文化理论为基础,综合文献研究和访谈调查研究等方法,探索小学数学课堂师生对话分析的理论框架,经本土化的实践修正后,形成小学数学课堂师生对话分析框架。第二阶段研究目的在于全面收集数据和分析小学数学课堂师生对话特征。具体做法为：以上海市Y小学10位数学教师作为研究对象,以分别代表职初教师、有经验教师和骨干教师的3位教师四年级的常态课为重点,通过课堂观察、教学录像、教师访谈、学生问卷、教学反思等方式采集数据,借助NVivo8质性分析软件,综合运用个案比较、录像研究、系统观察、会话分析和互动分析等量与质的研究方法,解读Y小学数学课堂师生对话的具体特征。
研究结论包括五个方面：
第一,构建了小学数学课堂师生对话分析框架。这个分析框架包含内容体系、编码体系和操作流程三个部分。内容体系是核心,具体由三个维度十个要素构成。三个维度分别是数学课堂语言、数学意义建构和数学课堂文化。十个要素分别是师生话语信息流、语言表达准确性、教师语言使用量及转换方式、师生对话功能属性、数学问题或任务的特性、教师倾听与回应学生的方式、学生参与数学结论形成的心智水平、师生对话机会、师生对话互动结构和师生对话关系。
第二,师生话语是维系课堂有效对话的重要介质。从个案研究中发现,目前小学数学课堂师生对话中的师生话语特征表现有：“教师提问—学生陈述”是主要的师生对话形式,教师话语超过学生话语,教师“数学教学语言”使用量远远超过“数学语言”,学生话语以“被动”应答教师的提问为主,生生对话明显不足。
第三,数学问题或任务的特性以及教师倾听回应学生的方式,对学生理解与建构数学意义起关键作用。从个案研究中发现,目前小学数学课堂中预设性、封闭性和概念性问题偏多,生成性、开放性和“做数学联结”的问题偏少,数学问题的思维水平总体不高。教师倾听与回应学生时,较多地关注自身而对学生特定想法的关注则较少。
第四,师生对话反映出师生话语机会、师生互动结构和师生关系等文化特征。从个案研究发现,教师拥有教学话语权,学生参与高层次数学思维的话语机会较少。旨在传递信息和教师控制的单义性对话偏多,旨在促进数学意义理解与建构的对话性对话偏少。师生之间表现有三类对话结构,即教师对学生单向作用的单向度对话结构、教师和学生双向互动作用的双向度对话结构、以及师生生生多向交互作用成话语共同体的多向度对话结构。
第五,不同教学水平的教师在小学数学课堂师生对话中存在特征差异。随着教师教学水平提高,教师对学生经验的关注越趋明显,教师话语逐渐减少而学生话语逐渐增多,数学问题的开放程度和学生选择机会逐步增大,教师倾听回应学生的关注点逐步由“教师”转向“学生”,学生参与数学意义理解与建构的思维水平逐步提高。职初教师多表现出单向度对话结构,有经验教师多表现出双向度对话结构,骨干教师则在多向度对话结构上表现明显。
上述研究结论,对于有效诊断小学数学课堂师生对话问题和开展针对性强的教师培训,尤其是提高职初教师的课堂对话水平,让小学数学课堂从“封闭性对话”走向“开放性对话”、从“教师控制性对话”走向“师生话语共同体”,从“知识传递教学”走向“知识建构教学”,都具有重要实践意义。
Primary mathematics classroom instruction is a process of teacher-student interaction and mutual development. An empirical analysis of the teacher-student conversation in the primary mathematics classroom is in accordance with the educational study trend of the world, and also meets the urgent need for an effective classroom instruction in the primary mathematics in China. It is of theoretical value and practical significance in terms of diagnosing the problems in teacher-student conversation in the primary mathematics classroom, perfecting the assessment theory and technique of the primary mathematics classroom conversation, and improving the quality of the teacher-student classroom conversation.
The study first constructs a framework for the analysis of the primary mathematics classroom teacher-student conversation by combining theory and practice, and then the framework is used to conduct an analytical and comparative study of the conversational cases taken from Y Primary School in Shanghai. The study includes two parts.①What is the framework for the analysis of the primary mathematics classroom teacher-student conversation? It answers questions of "what to be analyzed" and "how to analyze".②What are the features of the primary mathematics classroom teacher-student conversation at Y Primary School in Shanghai? As the core of the whole study, this part discusses the features of the primary mathematics classroom teacher-student conversation, the differential features of the conversation conducted by teachers of different teaching abilities, and how these features influence the students'mathematics learning.
The whole study is divided into two stages. The first stage aims at the construction of an analytical framework for the primary mathematics classroom teacher-student conversation. Based on the sociocultural theory and combining the methods of literature research and interview survey, the analytical framework is formed by exploring the theoretical framework for the analysis of the primary mathematics classroom teacher-student conversation and localizing the theory in practice. The second stage aims at a full collection of data and analyzing the features of the primary mathematics classroom teacher-student conversation. The subjects investigated are10mathematics teachers in Y Primary School, and the research focus is the normal classes of grade4about "the Verticality and Mutually Perpendicular" presented by3teachers who represent the novice teacher, the experienced teacher and the expert teacher respectively. The data are collected through classroom observations, videos of classroom teaching, interviews with teachers, student questionnaires, and teachers'reflections on teaching. Using NVivo8software for qualitative data analysis and combining case study, video study, systematic observation, conversation analysis and interaction analysis, the features of the mathematics classroom teacher-student conversation in Y Primary School are fully interpreted.
The conclusions of the dissertation are as follows:
First, a "three dimensions and ten factors" analytical framework for primary mathematics classroom teacher-student conversation is constructed. This framework includes3parts of the content system, encoding system, and operation procedure. The content system is made up of three dimensions (mathematics classroom language, mathematics meaning making and mathematics classroom culture) and ten elements (teacher-student discourse information flow, accuracy of expression, the amount of the teacher's language and way of switching, the function attribute of the teacher-student conversation, the nature of the mathematical questions or tasks, the ways of teacher's listening to and responding to students, students'intellectual powers to participate in drawing conclusions, the chances of teacher-student conversation, the interactive structure of the teacher-student conversation and the relationship of the teacher-student conversation). The encoding system is the requirements and standards for classifying and encoding the above mentioned factors. The operation procedure shows the operation steps of the conversation analysis in practice.
Second, the verbal communication between the teacher and the students is an important medium maintaining effective conversations. At present, the verbal features of the primary mathematics classroom teacher-student conversation are "the teacher asks-the students state" which means in such conversational form the teacher talks more than the students do;"mathematical instruction language" occupies more high proportion than "mathematical language"; students discourse is "passive" answers to the teacher's questions; the conversations among students are inadequate.
Third, the quality and quantity of the mathematical questions or tasks and the ways of the teacher's listening to and responding to the students play important roles in students'understanding and construction of mathematical meanings. At present, there are more predesigned, closed and conceptual questions than generating, open and "making mathematical connections" questions, and the thinking level of mathematical questions is not high. When listening to and responding to the students, the teachers pay more attention to themselves than to the special thinking of the students.
Forth, the verbal communications between the teacher and students are full of cultural features. The teacher holds the teaching discourse power, and the students have fewer opportunities to participate in a high level of mathematical thinking. There are more one way interaction from the teacher to the students aiming to convey message and teacher control and fewer conversations aiming to promote understanding and construction of mathematical meaning. There are three interaction structures, the one way interaction from the teacher to the student, the two way interaction between the teacher and the student, the multi-way interaction between the teacher and the students and among the students.
Fifth, there are differential features of the conversation conducted by teachers of different teaching abilities. It is evident that with improved teaching abilities, the teacher pays more attention to the students'experiences, the teacher talks less and the students talk more, the degree of the openness of the mathematical questions and students' opportunities of choices are increased, the focusing points gradually turn from "teacher" to "students", and the thinking level of the students participating in the understanding and construction of mathematical meaning is gradually rising.
The above conclusions are of practical significance in the problem diagnosis of primary mathematics classroom teacher-student conversation and carrying out targeted teacher training programs, especially in improving new teachers'classroom conversation skills, turning the classroom conversation from "closed" to "open", from "teacher control" to "teacher-student discourse community", and changing mathematics teaching from "knowledge imparting" to "knowledge construction".
引文
①中华人民共和国教育部.全日制义务教育数学课程标准(实验稿)[S]北京：北京师范大学出版社,200l：2,6-7.
②中华人民共和国教育部.全日制义务教育数学课程标准[S]北京：北京师范大学出版社,2011：2,56.
① Ball D. L.,& Bass, H. (2000). Making believe:The collective construction of public mathematical knowledge in the elementary classroom. In Phillips, D. (Ed.), Yearbook of the national society for the study of education, Constructivism in education. (pp.193-224). Chicago:University of Chicago Press.
①如TIMSS-R研究和我国的黄金荣、李士锜、杨新荣等学者都有深入的研究.
②相关研究如上海市青浦实验研究所对小学数学新手和专家教师的PCK个案研究,吴卫东有关小学数学教师个人知识的研究,等.
③相关研究如C. Livingston和H. Borko对专家教师和新手教师中学数学复习课教学能力的比较,等.
④如T. Wood,1998; P. Cobb,1997; D. L. Ball,2000; P. Cobb,2006; A. Sfard,2008; M. P. Truxaw,2007;等.
⑤如中国大陆的顾泠沅、曹一鸣、李琼；香港的倪玉菁、黄毅英；美籍华人黄荣金、李业平;等.
① James, M. (2008). Assessment and learning. In Edited by Swaffield, S.. Unlocking Assessment:understanding for reflection and application. (pp.20-35). Routledge.
② Dalton, S. S. (2008). Five standards for effective teaching:How to succeed with all learners, Grades K-8. John Wiley & Sons, Inc. p.189-219.
③ Nolan, J. F.,& Hoover, L. A. (2008). Teacher supervision evaluation:theory into practice. John Wiley & Sons, Inc.
① Heddens, J. W.,& Speer, W. R. (2006). Today's mathematics concepts, methods, and instructional activities (11 th edition). John Wiley & Sons, Inc. p.21-40.
① National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA:Author.
② National Research Council. (2002). Adding it up:Helping children learn mathematics. In Kilpatrick, J., Swafford, J.,& Findell, B. (Eds.). Mathematics Learning Study Community, Center for Education. Division of Behavioral Academy Press.
③ Biggs, J. B.,& Collis, K.(1982). Evaluating Quality of Learning:The SOLO Txonomy,Academic Press,New York.
④LPS是澳大利亚墨尔本大学国际课堂研究中心领导的“学习者视角的研究(Learners'Perspective Study)"项目的简称。它利用所开发的Studiocode视频分析软件对16国优秀数学教师常态教学录像进行国际比较研究。
⑤ Clarke, D. J., Emanuelsson, J., Jablonka, E.,& Mok, I. A. C. (Eds.) (2006). Making connections:Comparing mathematics classrooms around the world. Sense Publishers. p.215-236.
① Crapanzano, V. (1990). On Dialogue. In Maranhao, T.. The interpretation of dialogue.(pp.276). Chicago: University of Chicago Press.
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④代表人物有:Jordan, A.(1997); Lambert, L.(1997);Sawyer, K. K.(2006); Mercer, N.,& Dawes, L.(2010);等.
⑤代表人物有:Buzzelli, C.A.,& Johnston, B.(2002); Hansen, D. T. (2001); Gallego, M.A.,& Cole, M.(2001);等.
⑥代表人物有：Garrison, D. R.(2007); Cobb, P.,& McClain, K.(2006);等.
① http://community of inquiry.com/
②代表人物有:Yackel, Cobb, & Merckel (1990); Cobb,Wood, &Yackel (1993); Hiebert, & Wearnc (1992); Stein, Grove, & Henningsen (1996);等.
①唐瑞芬,李士锜等编译.国际展望：数学教育评价研究(ICMI研究丛书之二).上海教育出版社,1996：213-224.
② Hiebert, J.,& Wearne, D. (1993). Instructional tasks, Classroom discourse, and students'learning in second-grade arithmetic. American Educational Research Journal,30(2,Summer):393-425.
③ O'Connor, M. C.,& Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. Anthropology and Education Quarterly,24(3):18-335.
④ Ellerton, N. F..& Clarkson, P. C.(1996). Language factors in mathematics teaching and learning. In Bishop, A. J. International handbook of mathematics education.(Vol.2). (pp.987-1034). Kluwer Academic Publishers.
⑤代表性的研究成果有：Silver (1996); Silver & Smith (1996); Stein & Lane(1996)；等.
① Hiebert, J., et al. (2003). Teaching mathematics in seven countries:Results from the TIMSS 1999 video study. National Center for Education Statistics(NCES), p.107-120.
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②代表人物有:Sfard, A. (2008); Truxaw, M. P.,& DeFranco T. C. (2008); Kumpulainen, K.(2005)等.
③ Truxaw, M. P.,& DeFranco, T. C. (2007). Mathematics in the making:Mapping verbal discourse in Polya's"Let Us Teach Guessing"lesson. Journal of Mathematical Behavior,26:96-114.
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② Cobb, P. (2006). Mathematics learning as a social process. In Maasz, J.,& Schloeglmann, W. (Eds.). New Mathematics Education Research and Practice.(pp.147-152).
③ Cobb, P.,& McClain, K. (2006). Guiding inquiry-based math learning.In Sawyer, R. K.. The Cambridge Handbook of Learning Sciences. (pp.181-186). London:Cambridge university Press.
④ Cobb, P.,& Hodge, L. L., (2011). Culture, identity, and equity in the mathematics classroom. A Journey in Mathematics Education Research,48, Part 5:179-195. Mathematics Education Library.
⑤ Nathan, M. J., Eilam, B.,& Kim, S. (2007) To disagree, we must also agree:How intersubjectivity structures and perpetuates discourse in a mathematics classroom. The Journal of the Learning Sciences,16(4),523-563.
⑥主要研究有：Mendez, E. P. (2007); Rosales, J. (2008); Imm, K.,& Stylianou, A.(2012)；等.
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②说明：此文通过网上查询,但原文中未注明出处。
③代表性研究成果有：徐赳赳(1995)；刘运同(2002)；朱永生(2003)；王明利(2006)；等等.
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② Hiebert, J., Gallimore, R., Gamier, H., et al. (2003).Teaching mathematics in seven countries:Results from the TIMSS 1999 video study. U.S. Department of Education, Institute of Education Sciences. National Center for Education Statistics.
① Davis, B. (1997). Listening for differences:an evolving conception of mathematics teaching. Journal for Research in Mathematics Education,28:355-376.
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① Mendez, E. P., Sherin, M. G.,& Louis, D. A. (2007). Multiple perspectives on the development of an eighth-grade mathematical discourse community. The Elementary School Journal,108(1):41-61.
① Nathan, M. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and instruction,21(2):175-207.
① Rosales, J., Orrantia, J., Vicente, S.,& Chamoso, J. M. (2008). Studying mathematics problem-solving classrooms. A comparison between the discourse of in-service teachers and student teachers. European Journal of Psychology of Education. vol.ⅩⅩⅢ 3:275-294.
① Imm, K.,& Stylianou, D. A. (2012). Talking mathematically:An analysis of discourse communities. Journal of Mathematical Behavior,31:130-148.
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① Truxaw, M. P.,& DeFranco, T. C. (2007). Mathematics in the making:Mapping verbal discourse in Poly's"Let Us Teach Guessing"lesson. Journal of Mathematical Behavior.26:96-114.
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② Clarke, J. A. (1987). A procedure for analyzing classroom dialogue. Paper presented at the Joint Conference of the Australian Association for Research in Education and the New Zealand Association for Research in Education(1st, Christchurch,New Zealand,December).
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③ Truxaw, M. P.,& DeFranco, T. C., (2008). Mapping mathematics classroom discourse and its implications for models of teaching. Journal for Research in Mathematics Education.39(5):489-525. NCTM.
④ Herbel-Eisenmann, B. A.,& Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education,42(5):451-485.
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④说明：限于篇幅,此处没有呈现具体内容。
⑤说明：指来自于从事数学教育研究和教学评价研究的七位专家学者。
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①表中的●表示该话轮的行为主体是教师,○表示该话轮的行为主体是学生,↘表示话轮转换方向.下同.
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①如TIMSS-R研究和我国的黄金荣、李士锜、杨新荣等学者都有深入的研究.
②相关研究如上海市青浦实验研究所对小学数学新手和专家教师的PCK个案研究,吴卫东有关小学数学教师个人知识的研究,等.
③相关研究如C. Livingston和H. Borko对专家教师和新手教师中学数学复习课教学能力的比较,等.
④如T. Wood,1998; P. Cobb,1997; D. L. Ball,2000; P. Cobb,2006; A. Sfard,2008; M. P. Truxaw,2007;等.
⑤如中国大陆的顾泠沅、曹一鸣、李琼；香港的倪玉菁、黄毅英；美籍华人黄荣金、李业平;等.
① James, M. (2008). Assessment and learning. In Edited by Swaffield, S.. Unlocking Assessment:understanding for reflection and application. (pp.20-35). Routledge.
② Dalton, S. S. (2008). Five standards for effective teaching:How to succeed with all learners, Grades K-8. John Wiley & Sons, Inc. p.189-219.
③ Nolan, J. F.,& Hoover, L. A. (2008). Teacher supervision evaluation:theory into practice. John Wiley & Sons, Inc.
① Heddens, J. W.,& Speer, W. R. (2006). Today's mathematics concepts, methods, and instructional activities (11 th edition). John Wiley & Sons, Inc. p.21-40.
① National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA:Author.
② National Research Council. (2002). Adding it up:Helping children learn mathematics. In Kilpatrick, J., Swafford, J.,& Findell, B. (Eds.). Mathematics Learning Study Community, Center for Education. Division of Behavioral Academy Press.
③ Biggs, J. B.,& Collis, K.(1982). Evaluating Quality of Learning:The SOLO Txonomy,Academic Press,New York.
④LPS是澳大利亚墨尔本大学国际课堂研究中心领导的“学习者视角的研究(Learners'Perspective Study)"项目的简称。它利用所开发的Studiocode视频分析软件对16国优秀数学教师常态教学录像进行国际比较研究。
⑤ Clarke, D. J., Emanuelsson, J., Jablonka, E.,& Mok, I. A. C. (Eds.) (2006). Making connections:Comparing mathematics classrooms around the world. Sense Publishers. p.215-236.
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② Jordan, A., Lindsay, L.,& Stanovich, P. J. (1997). Classroom teachers'instructional interactions with students: Who are exceptional, at risk, and typically achieving. Remedial and Special Education,18:82.
③ Mercer, N. (1996). The quality of talk in children's collaborative activity in the classroom. Learning and Instruction,6(4):369-370.
④代表人物有:Jordan, A.(1997); Lambert, L.(1997);Sawyer, K. K.(2006); Mercer, N.,& Dawes, L.(2010);等.
⑤代表人物有:Buzzelli, C.A.,& Johnston, B.(2002); Hansen, D. T. (2001); Gallego, M.A.,& Cole, M.(2001);等.
⑥代表人物有：Garrison, D. R.(2007); Cobb, P.,& McClain, K.(2006);等.
① http://community of inquiry.com/
②代表人物有:Yackel, Cobb, & Merckel (1990); Cobb,Wood, &Yackel (1993); Hiebert, & Wearnc (1992); Stein, Grove, & Henningsen (1996);等.
①唐瑞芬,李士锜等编译.国际展望：数学教育评价研究(ICMI研究丛书之二).上海教育出版社,1996：213-224.
② Hiebert, J.,& Wearne, D. (1993). Instructional tasks, Classroom discourse, and students'learning in second-grade arithmetic. American Educational Research Journal,30(2,Summer):393-425.
③ O'Connor, M. C.,& Michaels, S. (1993). Aligning academic task and participation status through revoicing: Analysis of a classroom discourse strategy. Anthropology and Education Quarterly,24(3):18-335.
④ Ellerton, N. F..& Clarkson, P. C.(1996). Language factors in mathematics teaching and learning. In Bishop, A. J. International handbook of mathematics education.(Vol.2). (pp.987-1034). Kluwer Academic Publishers.
⑤代表性的研究成果有：Silver (1996); Silver & Smith (1996); Stein & Lane(1996)；等.
① Hiebert, J., et al. (2003). Teaching mathematics in seven countries:Results from the TIMSS 1999 video study. National Center for Education Statistics(NCES), p.107-120.
① Lloyd, G. M., Wilson, M., Wilkins, J. L. M.,& Behm, S. L.(Eds.). (2005). Discussion group on mathematics classroom discourse. Proceedings of the 27th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Virginia Tech, October.
②代表人物有:Sfard, A. (2008); Truxaw, M. P.,& DeFranco T. C. (2008); Kumpulainen, K.(2005)等.
③ Truxaw, M. P.,& DeFranco, T. C. (2007). Mathematics in the making:Mapping verbal discourse in Polya's"Let Us Teach Guessing"lesson. Journal of Mathematical Behavior,26:96-114.
④ Herbel-Eisenmann, B.,& Wagner, D. (2010). Lexical bundle analysis in mathematics classroom discourse:the significance of stance.
⑤ Franke, M. L., Webb, N. M., Chan, A., et al. (2009). Teacher questioning to elicit students'mathematical thinking in elementary school classrooms. Journal of Teacher Education,60(4):380-392.
⑥ Young, R.W.,& Cates, C. M. (2010). Listening, play, and social attraction in the mentoring of new teachers. Mentoring & Tutoring:Partnership in Learning,18(3):215-231.
⑦ Wagner, D. (2007). Students'critical awareness of voice and agency in mathematics classroom discourse Mathematical Thinking and Learning,9(1):31-50.
⑧ Walshaw, M.,& Anthony, G, (2008). The teacher's role in classroom discourse:A review of recent research into mathematics classrooms. Educational Research Review,78 (3):516-551.
① Franke, M. L., Kazemi, E.,& Battey, D. (2007). Mathematics teaching and classroom practice. In Frank. K. Lestor, Jr.. Second Handbook of Research on Mathematics Teaching and Learning:a project of the national council of teachers of mathematics.(pp.225-256). Information Age Publishing Inc.
② Cobb, P. (2006). Mathematics learning as a social process. In Maasz, J.,& Schloeglmann, W. (Eds.). New Mathematics Education Research and Practice.(pp.147-152).
③ Cobb, P.,& McClain, K. (2006). Guiding inquiry-based math learning.In Sawyer, R. K.. The Cambridge Handbook of Learning Sciences. (pp.181-186). London:Cambridge university Press.
④ Cobb, P.,& Hodge, L. L., (2011). Culture, identity, and equity in the mathematics classroom. A Journey in Mathematics Education Research,48, Part 5:179-195. Mathematics Education Library.
⑤ Nathan, M. J., Eilam, B.,& Kim, S. (2007) To disagree, we must also agree:How intersubjectivity structures and perpetuates discourse in a mathematics classroom. The Journal of the Learning Sciences,16(4),523-563.
⑥主要研究有：Mendez, E. P. (2007); Rosales, J. (2008); Imm, K.,& Stylianou, A.(2012)；等.
①王坦.弗兰德斯相互作用分析理论及其教学应用[J].山东教育科研,1988(1)：64-68.
②说明：此文通过网上查询,但原文中未注明出处。
③代表性研究成果有：徐赳赳(1995)；刘运同(2002)；朱永生(2003)；王明利(2006)；等等.
④陈玉娟.心理学的话语分析研究[D].南京师范大学硕士学位论文,2007.
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③冯茁.论教育场域中的对话——基于教师视角的哲学解释学研究[D].东北师范大学博士学位论文,2008.
④慕君.阅读教学对话研究[Dl.华东师范大学：华东师范大学博士学位论文,2006.
⑤辜筠芳.哈贝马斯规范语用学视野下的课堂对话研究[D].上海：华东师范大学博士学位论文,2010.
⑥赵常友.中外教帅话语研究述评[J].曲靖师范学院学报,2010(1)：85-89.
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①曹一鸣,贺晨.初中数学课堂师生互动行为主体类型研究—基于LPS项目课堂录像资料[J].数学教育学报,2009(5)：38-41.
②曹一鸣,王玉蕾,王立东.中学数学课堂师生话语权的量化研究—基于LPS项目课堂录像资料[J].数学教育学报,2008(3)：1-3.
③曹一鸣.数学课堂教学实证系列研究[M].广西：广西教育出版社,2009.
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⑥叶立军,斯海霞.基于录像分析背景下的代数课堂教学语言研究[J].数学教育学报,2011(1)：42-44.
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③黄荣金,李业平.数学课堂教学研究[M].上海：上海教育出版社,2010.
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⑤杨承印,闫君.对课堂教学中师生互动语言行为的研究[J].基础教育,2010,,7(1)：45-49.
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②罗晓杰,王雪.专家—熟手—新手教师高中英语阅读课堂互动比较研究[J].课程·教材·教法,2011(12)：51-56.
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①Jacobs. J., Gamier. H.. Gallimore, R., et al.(2003). Third international mathematics and science study 1999 video study technical report. Volume 1:Mathematics technical report. U.S. Department of Education, Institute of Education Sciences, NCES.
② Hiebert, J., Gallimore, R., Gamier, H., et al. (2003).Teaching mathematics in seven countries:Results from the TIMSS 1999 video study. U.S. Department of Education, Institute of Education Sciences. National Center for Education Statistics.
① Davis, B. (1997). Listening for differences:an evolving conception of mathematics teaching. Journal for Research in Mathematics Education,28:355-376.
② Tannen, D. (1989). Talking voices:Repetition, dialogue, and imagery in conversational discourse. New York: Cambridge University Press.
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① Mendez, E. P., Sherin, M. G.,& Louis, D. A. (2007). Multiple perspectives on the development of an eighth-grade mathematical discourse community. The Elementary School Journal,108(1):41-61.
① Nathan, M. J. (2003). A study of whole classroom mathematical discourse and teacher change. Cognition and instruction,21(2):175-207.
① Rosales, J., Orrantia, J., Vicente, S.,& Chamoso, J. M. (2008). Studying mathematics problem-solving classrooms. A comparison between the discourse of in-service teachers and student teachers. European Journal of Psychology of Education. vol.ⅩⅩⅢ 3:275-294.
① Imm, K.,& Stylianou, D. A. (2012). Talking mathematically:An analysis of discourse communities. Journal of Mathematical Behavior,31:130-148.
① Sfard, A. (2008). Thinking as communicating:Human development, the growth of discourse, and mathematizing. Cambridge, UK:Cambridge University Press. p133-135,161,195-220.
② Truxaw, M. P.,& DeFranco, T. C. (2008). Mapping mathematics classroom discourse and its implications for models of teaching. Journal for Research in Mathematics Education,39 (5):489-525. NCTM.
① Truxaw, M. P.,& DeFranco, T. C. (2007). Mathematics in the making:Mapping verbal discourse in Poly's"Let Us Teach Guessing"lesson. Journal of Mathematical Behavior.26:96-114.
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① Jordan, A., Lindsay, L.,& Stanovich, P. J. (1997). Classroom teachers'instructional interactions with students: Who are exceptional, at risk, and typically achieving. Remedial and Special Education,18:82.
② Clarke, J. A. (1987). A procedure for analyzing classroom dialogue. Paper presented at the Joint Conference of the Australian Association for Research in Education and the New Zealand Association for Research in Education(1st, Christchurch,New Zealand,December).
③ Hutchby, I.,& Wooffitt, R. (1998). Conversation analysis. Cambridge, England:Polity Press. p.14.
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② Sfard, A. (2001a). There is more to discourse than meets the ears:Looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics,46:13-57.
③ Truxaw, M. P.,& DeFranco, T. C., (2008). Mapping mathematics classroom discourse and its implications for models of teaching. Journal for Research in Mathematics Education.39(5):489-525. NCTM.
④ Herbel-Eisenmann, B. A.,& Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education,42(5):451-485.
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④ Cobb, P.,& Whitenack, J. W. (1996). A method for conducting longitudingal analyses of classroom videorecordings and transcripts. Educational Studies in Mathematics.30(3):213-228.
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④说明：限于篇幅,此处没有呈现具体内容。
⑤说明：指来自于从事数学教育研究和教学评价研究的七位专家学者。
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①表中的●表示该话轮的行为主体是教师,○表示该话轮的行为主体是学生,↘表示话轮转换方向.下同.
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曹一鸣,等.国际视野下的中国中学数学课堂微观分析[M].北京：北京师范大学出版社,2011.
曹一鸣.数学课堂教学实证系列研究[M].广西：广西教育出版社,2009.
曹一鸣,贺晨.初中数学课堂师生互动行为主体类型研究——基于LPS项目课堂录像资料[J].数学教育学报,2009(5)：38-41.
曹一鸣,王玉蕾,王立东.中学数学课堂师生话语权的量化研究——基于LPS项目课堂录像资料[J].数学教育学报,2008(3)：1-3.
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[美]约翰·杜威著,赵祥麟,任钟印,吴志宏译.学校与社会·明日之学校[M].北京：人民教育出版社,2005.
冯茁.论教育场域中的对话——基于教师视角的哲学解释学研究[D].东北师范大学：东北师范大学博士学位论文,2008.
高文主编,徐斌艳等译.教育中的建构主义[M].上海：华东师范大学出版社,2002.
辜筠芳.哈贝马斯规范语用学视野下的课堂对话研究[D].华东师范大学：华东师范大学博士学位论文,2010.
顾泠沅,周卫.课堂教学的观察与研究[J].上海教育,1999.
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顾泠沅.教学任务的变革[J].教育发展研究,2001(10).
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