初中数学教师数学教学知识的发展研究
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摘要
教师知识的发展一直以来是教师专业发展的一个重要部分。对于数学教师来说,并非只要具备充足的数学知识就能成为一位好的数学教师,还需要具有针对特定数学内容的教学知识,即数学教学知识。它是数学教师专业性的重要体现,是区别数学教师与数学家、数学教师与其它学科教师的重要特征。数学教学知识的发展作为数学教师专业发展的核心,影响着教师的数学教学行为、影响着数学课堂教学的质量,对教师专业成长的意义重大。
新一轮数学课程改革提高了对教师数学教学知识的要求,但在课程实施的过程中,教师的数学教学知识发展状况不容乐观;在职前和职后教师的培养中,教师数学教学知识的发展处于一种被忽视的状态。由于数学教学知识概念本身的抽象性及内涵的广泛性,以及其发展机制的不明确性,使得已有的关于教师数学教学知识的研究中很少有切实可行的发展办法。基于我国数学教师长期注重数学知识的专门学习,本研究以“如何有效地实现初中数学教师数学知识向数学教学知识的转化,以促进其数学教学知识的发展?”为核心问题,在对数学教师数学知识向数学教学知识转化(以下简称“教师知识转化”)的内涵进行探究的基础上,采用新手与专家型教师比较的研究范式,运用个案研究与调查研究相结合的方式重点探讨了初中数学教师知识转化的影响因素,尝试架构了促进其数学教学知识发展的策略,并运用微型实验法对策略的有效性进行了初步检验。通过研究,获得以下的初步结论:
其一,关于教师知识转化内涵的研究得出:教师知识转化的起点是教师所拥有的数学知识,由数学本体性知识、关于本体性知识的组织结构的知识、数学思想方法的知识等三大部分构成。教师所拥有的数学教学知识作为转化的目标,不能简单地等同于“数学知识+教学知识”,它是一种综合性知识,主要由两大类五方面的知识构成:特定数学内容与教学联合的知识(包括对数学知识的组织、表述的知识)、特定数学内容与学生联合的知识(包括关于学生的认知特点和误解、学生学习困难、处理学生学习误解和困难的策略的知识)。从外在来看,教师知识转化过程由理解、表征、适应三个环节构成,由此实现教师对某一数学知识归类与解释、表达与呈现、调整与适应,以满足学生的个性特点和需要。从内部来讲,教师知识转化的过程是在已有的数学知识和经验的基础上,同化和顺应一般教学法知识、关于学生的知识、关于数学课程和教科书的知识、以及关于教学情境的知识,主动建构出数学知识教学认知图式的过程。
其二,关于初中数学教师知识转化的影响因素研究分为两个阶段,第一阶段,运用个案研究法对6位数学教师关于《图形的平移与旋转》、《四边形性质探索》和《一次函数》这三个单元的教学进行了课堂观察、录像编码和深度访谈,得出新手教师与专家型教师在知识转化上的主要差异表现在六个方面,即对数学知识的理解程度不同、对教学任务运用的水平不同、所使用的呈现方式不同、使用呈现方式要达到的目的不同、对教科书上的任务的调整情况不同、对表征的适应性的关注程度不同。并在差异研究的基础上,通过深度访谈了解到造成两类教师以上差异的原因大致可以归纳为三个方面:教师所拥有的知识、教师所持的观念、教师所拥有的经验。这为下一阶段进一步探寻教师知识转化的影响因素奠定了基础。
第二阶段,以个案研究的结论为依据,设计问卷对8所中学的150名初中数学教师进行了调查分析,得出初中数学教师知识转化的主要影响因素及其影响程度。总的来说,对初中数学教师知识转化影响最大的是教师的经验系统,其次是教师的观念系统,再次是教师的知识系统。具体来说,影响的直接因素有三个,按影响程度由大到小,它们依次是教师的数学教学经验、教师的问题解决取向的数学观、教师对数学知识理解的贯通度。有间接影响的因素有教师的个人教学效能感、教师的一般教学效能感、教师对数学知识理解的深度、教师对数学知识理解的广度、教师的工具主义取向的数学观等五个因素。
其三,教师知识转化的内涵及影响因素的研究,为促进教师数学教学知识发展策略的建立提供了重要的依据。结合已有的关于教师专业发展的策略,运用认知负荷理论,本研究尝试架构了促进初中数学教师数学教学知识发展的策略——“基于概念构图的行动学习”,该策略以概念图为载体,注重教师知识系统、观念系统、经验系统的整体调动,注重“操作——图式”的活动方式,实现了数学教学知识的外化与内化的结合,实现了自我反思与同伴互助、专业引领的一体化。并运用微型实验研究的方法,初步验证了该策略的有效性。
本研究的创新之处在于:首次提出了通过数学知识向数学教学知识的转化这一新视角来研究教师数学教学知识的发展:运用扎根理论的研究方法定性和定量地尝试探究了教师知识转化的影响因素,运用概念构图的方法初步分析和促进了教师的知识转化:尝试提出了促进初中数学教师数学教学知识发展的策略——“基于概念构图的行动学习”。本研究的不足之处:受研究条件的限制,研究样本的选取范围、层次与数量只局限于小范围,微型实验只采用个别试点的方式,其实验结果有待进一步验证和推广。
The development of teacher's knowledge has always been being one important part of teacher's professional development. A mathematics teacher can not be a good one only with enough knowledge on mathematics. He/she is also supposed to possess the knowledge on how to teach the mathematics, i.e. mathematics pedagogical content knowledge. It shows the specialization of mathematics teachers and it is the key characteristics of mathematics teachers, which make them different from mathematicians and the teachers of other projects. As the core of mathematics teachers' professional development, the development of mathematics pedagogical content knowledge affects teachers' mathematics teaching activities and the quality of mathematics classroom teaching. So it is significant to the teacher's professional development.
The new mathematics curriculum reform demands a higher requirement to the teachers' mathematics pedagogical content knowledge. But in the process of implementing the new curriculum, the development status of teachers' mathematics pedagogical content knowledge is not so good as it was supposed to be, for it has been ignored in teachers' pre- and pro- service education. Nevertheless, because the concept of mathematics pedagogical content knowledge itself is quite abstract, its connotation is universe and its development mechanism is uncertain, so seldom researches which study teachers' mathematics pedagogical content knowledge provide feasible development methods. Considering that mathematics teachers in China pay attention to long-term learning the mathematics knowledge, Therefore the key research problem of this thesis is how to transform mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge effectively so as to promote the development of mathematics pedagogical content knowledge.Basing on exploring the connotation of transforming the mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge (shortened "The knowledge transformation" ), this dissertation adopts comparative research method of expert teacher and novice teacher, Combining case study and researches to explore the factors which influence the transformation. And it also try to proposes some strategies to promote the development of middle school mathematics teachers' mathematics pedagogical content knowledge, moreover it adopts the method of micro-experiment to test the effectiveness of these strategies. It gets the following conclusions:
Firstly, About the connotation of the knowledge transformation. The transformation from the Teachers's mathematics knowledge, it contains three aspects: about noumenal mathematics knowledge, about the structure and orgnize of the mathematics, about the methodology in mathematics. As the aim of the transformation, Teachers' mathematics pedagogical content knowledge does not simply equal mathematical knowledge and teaching knowledge, and it is a kind of comprehensive knowledge. It mainly contains two categories and five aspects: the knowledge on combining certain mathematics content with teaching (including knowledge about organizing and expressing the mathematical knowledge); the knowledge about combining certain mathematical contents and students (including knowledge about students' cognition characteristics and their misinterpretation, their learning-difficulties, and also the knowledge about strategies of dealing with students' misinterpretation and difficulties). Apparently, there are three parts, i.e. understanding, representation, and adaptation in the process of transforming teachers' mathematical knowledge to their mathematics pedagogical content knowledge. Deeply, the knowledge transformation can be defined as following: on the basis of their mathematical knowledge and teaching experience, teachers assimilate and adapt to their knowledge about general teaching method, students, mathematics curriculum and teaching situation to construct cognition schema of mathematical knowledge teaching.
Secondly, About the factors that influence middle school math teachers' knowledge transformation. This research consists of two stages: Stage one, observing 6 teachers' teaching of Translation and Rotation of Graphic, the Property of quadrilateral and Linear Function, videotaping their teaching process and interviewing bother teachers and students deeply, it obtains the main differences on knowledge transformation between new teachers and expert ones. It exhibits the following six facets: the degree of understand and interpret mathematical knowledge , the level of applying teaching tasks , the methods of demonstrating teaching contents , purposes of representation, adjusting the tasks of text book , adaptation of representation. And on the basis of the study on difference, it explores the reasons why there are differences on knowledge transformation between these two kinds of teachers, we can conclude that there are 3 factors leading three different representations between new teachers and expert teachers: the knowledge teachers possess, the ideas teachers hold, the experience teachers have. It is which lay a foundation for the research on influencing factors of the transformation.
Stage two, it designs convey questions according to the conclusion of the case study. It finds out the factors that influence the knowledge transformation by interviewing and studying 150 mathematics teachers in 8 middles schools, and it also finds out the extent those factors influence the transformation: As a whole, The best influencing factor is teacher's experience system, teacher's conception system is in the next place, teacher's knowledge system as following. Concretely, there are 3 factors that directly influence the transformation by extent: teachers' mathematics teaching experience, their mathematics view with which they tend to handle mathematical problems, and the transfixion degree of their understanding about mathematical knowledge. Furthermore, there are more 5 direct factors: teachers' own teaching efficacy, teachers' general efficacy, and the width of teachers' understanding about mathematical knowledge, and teachers' mathematical view of instrumentalism orientation tendency
Thirdly, About the strategies of developing middle-school mathematics teachers' mathematics pedagogical content knowledge. Researches on the connotation and the influencing factors of the knowledge transformation provides important evidence for construction of transformation strategy. Combining with existed strategies on developing teachers' specialization and applying the cognitiveload theory, this dissertation try to propose the strategy------"Action Learning based on Cmap" ,ituses the concept map, pays attention to adjusting of teachers' knowledge system, concept system and experience system generally, pays attention to "operation-schema" activity mode, realizes combination of externalization and internalization of mathematics teaching knowledge, realizes integration of self-reflection, partners' mutual aid, and specialization guidance. It also carries on micro-experimental study to verify that this strategy can improve the transformation and promote the development of mathematics pedagogical content knowledge.
The creative points of this dissertation are in the following: It is the first one that suggests to study the development of teacher's mathematics pedagogical content knowledge through translation from their mathematical knowledge to it. This is a new research perspective; this study adopts Grounded Theory method to try to explore the factors that influence the knowledge transformation , applying the Cmap method to analysis and promate the transformation; and try to propose the strategy of developing middle-school teachers' mathematics pedagogical content knowledge—"Action Learning basing on Cmap".
新一轮数学课程改革提高了对教师数学教学知识的要求,但在课程实施的过程中,教师的数学教学知识发展状况不容乐观;在职前和职后教师的培养中,教师数学教学知识的发展处于一种被忽视的状态。由于数学教学知识概念本身的抽象性及内涵的广泛性,以及其发展机制的不明确性,使得已有的关于教师数学教学知识的研究中很少有切实可行的发展办法。基于我国数学教师长期注重数学知识的专门学习,本研究以“如何有效地实现初中数学教师数学知识向数学教学知识的转化,以促进其数学教学知识的发展?”为核心问题,在对数学教师数学知识向数学教学知识转化(以下简称“教师知识转化”)的内涵进行探究的基础上,采用新手与专家型教师比较的研究范式,运用个案研究与调查研究相结合的方式重点探讨了初中数学教师知识转化的影响因素,尝试架构了促进其数学教学知识发展的策略,并运用微型实验法对策略的有效性进行了初步检验。通过研究,获得以下的初步结论:
其一,关于教师知识转化内涵的研究得出:教师知识转化的起点是教师所拥有的数学知识,由数学本体性知识、关于本体性知识的组织结构的知识、数学思想方法的知识等三大部分构成。教师所拥有的数学教学知识作为转化的目标,不能简单地等同于“数学知识+教学知识”,它是一种综合性知识,主要由两大类五方面的知识构成:特定数学内容与教学联合的知识(包括对数学知识的组织、表述的知识)、特定数学内容与学生联合的知识(包括关于学生的认知特点和误解、学生学习困难、处理学生学习误解和困难的策略的知识)。从外在来看,教师知识转化过程由理解、表征、适应三个环节构成,由此实现教师对某一数学知识归类与解释、表达与呈现、调整与适应,以满足学生的个性特点和需要。从内部来讲,教师知识转化的过程是在已有的数学知识和经验的基础上,同化和顺应一般教学法知识、关于学生的知识、关于数学课程和教科书的知识、以及关于教学情境的知识,主动建构出数学知识教学认知图式的过程。
其二,关于初中数学教师知识转化的影响因素研究分为两个阶段,第一阶段,运用个案研究法对6位数学教师关于《图形的平移与旋转》、《四边形性质探索》和《一次函数》这三个单元的教学进行了课堂观察、录像编码和深度访谈,得出新手教师与专家型教师在知识转化上的主要差异表现在六个方面,即对数学知识的理解程度不同、对教学任务运用的水平不同、所使用的呈现方式不同、使用呈现方式要达到的目的不同、对教科书上的任务的调整情况不同、对表征的适应性的关注程度不同。并在差异研究的基础上,通过深度访谈了解到造成两类教师以上差异的原因大致可以归纳为三个方面:教师所拥有的知识、教师所持的观念、教师所拥有的经验。这为下一阶段进一步探寻教师知识转化的影响因素奠定了基础。
第二阶段,以个案研究的结论为依据,设计问卷对8所中学的150名初中数学教师进行了调查分析,得出初中数学教师知识转化的主要影响因素及其影响程度。总的来说,对初中数学教师知识转化影响最大的是教师的经验系统,其次是教师的观念系统,再次是教师的知识系统。具体来说,影响的直接因素有三个,按影响程度由大到小,它们依次是教师的数学教学经验、教师的问题解决取向的数学观、教师对数学知识理解的贯通度。有间接影响的因素有教师的个人教学效能感、教师的一般教学效能感、教师对数学知识理解的深度、教师对数学知识理解的广度、教师的工具主义取向的数学观等五个因素。
其三,教师知识转化的内涵及影响因素的研究,为促进教师数学教学知识发展策略的建立提供了重要的依据。结合已有的关于教师专业发展的策略,运用认知负荷理论,本研究尝试架构了促进初中数学教师数学教学知识发展的策略——“基于概念构图的行动学习”,该策略以概念图为载体,注重教师知识系统、观念系统、经验系统的整体调动,注重“操作——图式”的活动方式,实现了数学教学知识的外化与内化的结合,实现了自我反思与同伴互助、专业引领的一体化。并运用微型实验研究的方法,初步验证了该策略的有效性。
本研究的创新之处在于:首次提出了通过数学知识向数学教学知识的转化这一新视角来研究教师数学教学知识的发展:运用扎根理论的研究方法定性和定量地尝试探究了教师知识转化的影响因素,运用概念构图的方法初步分析和促进了教师的知识转化:尝试提出了促进初中数学教师数学教学知识发展的策略——“基于概念构图的行动学习”。本研究的不足之处:受研究条件的限制,研究样本的选取范围、层次与数量只局限于小范围,微型实验只采用个别试点的方式,其实验结果有待进一步验证和推广。
The development of teacher's knowledge has always been being one important part of teacher's professional development. A mathematics teacher can not be a good one only with enough knowledge on mathematics. He/she is also supposed to possess the knowledge on how to teach the mathematics, i.e. mathematics pedagogical content knowledge. It shows the specialization of mathematics teachers and it is the key characteristics of mathematics teachers, which make them different from mathematicians and the teachers of other projects. As the core of mathematics teachers' professional development, the development of mathematics pedagogical content knowledge affects teachers' mathematics teaching activities and the quality of mathematics classroom teaching. So it is significant to the teacher's professional development.
The new mathematics curriculum reform demands a higher requirement to the teachers' mathematics pedagogical content knowledge. But in the process of implementing the new curriculum, the development status of teachers' mathematics pedagogical content knowledge is not so good as it was supposed to be, for it has been ignored in teachers' pre- and pro- service education. Nevertheless, because the concept of mathematics pedagogical content knowledge itself is quite abstract, its connotation is universe and its development mechanism is uncertain, so seldom researches which study teachers' mathematics pedagogical content knowledge provide feasible development methods. Considering that mathematics teachers in China pay attention to long-term learning the mathematics knowledge, Therefore the key research problem of this thesis is how to transform mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge effectively so as to promote the development of mathematics pedagogical content knowledge.Basing on exploring the connotation of transforming the mathematics teachers' mathematical knowledge to their mathematics pedagogical content knowledge (shortened "The knowledge transformation" ), this dissertation adopts comparative research method of expert teacher and novice teacher, Combining case study and researches to explore the factors which influence the transformation. And it also try to proposes some strategies to promote the development of middle school mathematics teachers' mathematics pedagogical content knowledge, moreover it adopts the method of micro-experiment to test the effectiveness of these strategies. It gets the following conclusions:
Firstly, About the connotation of the knowledge transformation. The transformation from the Teachers's mathematics knowledge, it contains three aspects: about noumenal mathematics knowledge, about the structure and orgnize of the mathematics, about the methodology in mathematics. As the aim of the transformation, Teachers' mathematics pedagogical content knowledge does not simply equal mathematical knowledge and teaching knowledge, and it is a kind of comprehensive knowledge. It mainly contains two categories and five aspects: the knowledge on combining certain mathematics content with teaching (including knowledge about organizing and expressing the mathematical knowledge); the knowledge about combining certain mathematical contents and students (including knowledge about students' cognition characteristics and their misinterpretation, their learning-difficulties, and also the knowledge about strategies of dealing with students' misinterpretation and difficulties). Apparently, there are three parts, i.e. understanding, representation, and adaptation in the process of transforming teachers' mathematical knowledge to their mathematics pedagogical content knowledge. Deeply, the knowledge transformation can be defined as following: on the basis of their mathematical knowledge and teaching experience, teachers assimilate and adapt to their knowledge about general teaching method, students, mathematics curriculum and teaching situation to construct cognition schema of mathematical knowledge teaching.
Secondly, About the factors that influence middle school math teachers' knowledge transformation. This research consists of two stages: Stage one, observing 6 teachers' teaching of Translation and Rotation of Graphic, the Property of quadrilateral and Linear Function, videotaping their teaching process and interviewing bother teachers and students deeply, it obtains the main differences on knowledge transformation between new teachers and expert ones. It exhibits the following six facets: the degree of understand and interpret mathematical knowledge , the level of applying teaching tasks , the methods of demonstrating teaching contents , purposes of representation, adjusting the tasks of text book , adaptation of representation. And on the basis of the study on difference, it explores the reasons why there are differences on knowledge transformation between these two kinds of teachers, we can conclude that there are 3 factors leading three different representations between new teachers and expert teachers: the knowledge teachers possess, the ideas teachers hold, the experience teachers have. It is which lay a foundation for the research on influencing factors of the transformation.
Stage two, it designs convey questions according to the conclusion of the case study. It finds out the factors that influence the knowledge transformation by interviewing and studying 150 mathematics teachers in 8 middles schools, and it also finds out the extent those factors influence the transformation: As a whole, The best influencing factor is teacher's experience system, teacher's conception system is in the next place, teacher's knowledge system as following. Concretely, there are 3 factors that directly influence the transformation by extent: teachers' mathematics teaching experience, their mathematics view with which they tend to handle mathematical problems, and the transfixion degree of their understanding about mathematical knowledge. Furthermore, there are more 5 direct factors: teachers' own teaching efficacy, teachers' general efficacy, and the width of teachers' understanding about mathematical knowledge, and teachers' mathematical view of instrumentalism orientation tendency
Thirdly, About the strategies of developing middle-school mathematics teachers' mathematics pedagogical content knowledge. Researches on the connotation and the influencing factors of the knowledge transformation provides important evidence for construction of transformation strategy. Combining with existed strategies on developing teachers' specialization and applying the cognitiveload theory, this dissertation try to propose the strategy------"Action Learning based on Cmap" ,ituses the concept map, pays attention to adjusting of teachers' knowledge system, concept system and experience system generally, pays attention to "operation-schema" activity mode, realizes combination of externalization and internalization of mathematics teaching knowledge, realizes integration of self-reflection, partners' mutual aid, and specialization guidance. It also carries on micro-experimental study to verify that this strategy can improve the transformation and promote the development of mathematics pedagogical content knowledge.
The creative points of this dissertation are in the following: It is the first one that suggests to study the development of teacher's mathematics pedagogical content knowledge through translation from their mathematical knowledge to it. This is a new research perspective; this study adopts Grounded Theory method to try to explore the factors that influence the knowledge transformation , applying the Cmap method to analysis and promate the transformation; and try to propose the strategy of developing middle-school teachers' mathematics pedagogical content knowledge—"Action Learning basing on Cmap".
引文
[1]袁维新.学科教学知识:一个教师专业发展的新视角[J].外国教育研究.2005,(3):10-14.
[2]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)[M].北京:北京师范大学出版社,2001:1-2。
[1]宋乃庆,程广文.用科学发展观审视基础教育课程改革[J].中国教育学刊,2008,(7):1-7.
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