数学教师教学决策研究
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摘要
课堂教学的有效性决定课程实施的水平和人才培养的质量,教师的教学行为直接影响课堂教学的有效性,而教学决策是影响教学行为的决定因素。因此,教师教学决策的质量关乎课程实施的水平和人才培养的质量。自上世纪70年代以来,对教师教学决策的研究已经成为国外教师和教学研究的核心内容,并被视作未来教学研究的根本方向。然而,国内对教师教学决策,特别是数学教师教学决策的研究尚属起步阶段,该领域相关研究的不足势必直接或间接影响数学课堂教学的有效性以及数学课程的有效实施。因此,研究数学教师教学决策显得更加必要而迫切。
教学决策是教师内隐的认知思维过程,研究者需要通过“内心的理解”“进入”到教师头脑中,才能充分探索教师教学决策的具体过程。“内心的理解”比表层行为研究、纸笔测验和标准访谈能使对教师教学行为的理解更加深入,这是质的研究的基本假设。可以说,质的研究的假设与研究教师教学决策的主要前提是相当一致的。因此,质的研究成为本研究的必然选择。同时,个案研究是质的研究方法之一,通过对个案系统的整体探索,挖掘有代表性个案的内在特性(内在性个案研究)或者以某个案为工具归纳一般性结论(工具性个案研究)。本研究具体遵循扎根理论研究思路,实施工具性个案研究,即扎根各类资料,分析、探索、总结、归纳出一般性的研究结论,并期望推广到其他个案或者对其他个案有所启发。
本研究采用的具体研究方法有:文献分析法、口语报告法、课堂观察法、访谈法、归纳分析法、比较分析法等。
本研究首先通过分析个案的口语报告,结合课后访谈和研究者观察资料的三角互证,对个案教学计划决策的具体过程进行追踪研究,分析归纳出如下初步结论:(1)教学信念、教学思维方式和数学知识是影响数学教师教学计划决策的主要因素;(2)数学教师教学计划决策的思维方式具有“拼凑”与“线性”的特点,应该从拼凑思维走向理解性思维,从线性思维走向创造性思维。
同时,本研究通过分析个案的课堂实录,结合课后访谈、学生访谈、口语报告和研究者观察资料、作品资料等的多角互证,对个案教学交互决策的具体过程进行追踪研究,分析归纳出如下初步结论:(1)教学信念、教学思维方式、教师知识、课堂情境是影响数学教师教学交互决策的主要因素;(2)数学教师教学交互决策的思维方式具有“迫降”与“随意”的特点,应该从“迫降”思维走向“登攀”思维,从“随意”思维走向“随机”思维。
进一步,基于上述研究和已有文献,本研究对教学决策重要影响因素之教学信念进行检视,对个案的口语报告、课后访谈、综合访谈等资料进行类属分析。通过对个案的“本土概念”和“关注的焦点教学因素”进行追问,检讨了个案的数学教学信念系统,初步描述了数学教师教学决策各主要影响因素与教学决策的关系;归纳出教学信念系统折射出的个案教学思维方式具有“支配性”、“对立性”和“忽视学生实际思维过程”的特点。
更进一步,基于上述研究,本研究从一般意义上对相关问题进行学理探讨,提升、归纳出如下研究结论:
(1)教学思维方式是数学教师教学决策的重要影响因素。数学教师教学思维方式是教学信念输出、输入的通道,是教师知识结构化的框架,是沟通教师隐存的教学信念、教师知识,并与现实情境相互作用,进而影响教师教学决策并形成教师具体教学行为的桥梁;
(2)数学教师的教学信念应该由“知识传授为本”的取向走向“知识传授与数学思维发展相融合”的取向。“知识传授与数学思维发展相融合”信念取向的数学教师应具备两条基本信念:帮助学生学习数学,为思维而教数学。可以通过设置丰富的、多维的课程计划,并以恰当的问题情境呈现,激发教师们的怀疑和批判精神等路径实现数学教师教学信念的转变。
(3)数学教师的教学思维方式应由“知识给予型思维”走向“教育学思维”。教育学思维方式的数学教师应从数学思维的特质入手寻找数学思维与数学教学思维之间的平衡点,使数学教学思维实现“过程——对象性”思维方式以及生成性思维方式的转变。可以通过“依托个体思维方式的生成机制设置培训课程”以及“实现数学思维与数学教学思维的平衡与转化”等路径加以实现。
本研究力图在以下几方面有所创新:其一,在选题方面:目前,国内研究数学教师教学决策及教师教学决策的文献尚不多见。尤其是,本论文属国内首篇专门研究数学教师教学决策的博士学位论文;二,在研究方法方面:本研究采用质的研究以及工具性个案研究策略,这在学科教育,尤其是数学学科教育中尚不多见;其三,在研究内容和结论方面,本研究提出了教学思维方式是数学教师教学决策的重要影响因素,并对数学教师教学决策的四个主要影响因素即教学信念、教学思维方式、教师知识和现实情境的关系进行了深入探讨;归纳提出了评价数学教师教学计划决策和交互决策的理论框架;归纳提出了实现数学教师教学信念和教学思维方式转变的具体内容和路径。这些研究结论能够充实和完善国内数学教学理论的框架和内容。
在今后的研究中,将继续关注以下课题:数学教师教学决策的影响因素;数学教师教学决策的评价;数学教师教学决策的理论脉络;在数学教师职前、职中和职后的培养中,教学信念和思维方式养成或转变的可操作性策略;不同背景下数学教师教学决策的比较研究等。
The effectiveness of classroom teaching determines the degree to which the curriculum is implemented as well as the quality of talents cultivating. The key of the mathematics curriculum reform lies in the implementation of the curriculum; teacher's teaching behavior affects directly the effectiveness of the implementation of the curriculum, while the decision-making is a determinant factor affecting the teaching behavior. Therefore, the quality of the mathematics teachers' decision-making determines the level of curriculum implementation and the quality of talents cultivating. Since 1970s, studies on teachers' teaching decision has become a central content in the field of teacher and teaching study abroad, and is thought of as the direction of future study. However, the study on teachers' decision-making, especially that of the mathematics teachers just starts at home, the insufficiency of relevant study will inevitably affect the effective teaching in mathematics classroom and the implementation of the curriculum in either a direct or indirect way. Thereby, it is necessary and urgent to study the mathematics teachers' decision-making.
Decision-making is the teacher's implicit cognitive thinking process, researchers can not fully probe this specific decision-making process without "entering" the teacher's mind through "internal understanding". The basic hypothesis of the qualitative study is that this internal understanding enables a deeper understanding on teachers' teaching behavior than the surface behavior study, the regular quiz with paper and pen and the standard interview. So to speak, the hypothesis of the qualitative study is in correspondence with the major presupposition of teachers' decision-making, therefore the former becomes the necessary choice. On the other hand, the case study is one of mathods of qualitative study. By probing case system whole, digging representative case's intrinsic characteristic(intrinsic case study) or inducing common conclusion from instrumental case(instrumental case study). Based on the study pathway of theory grounded, instrumental case study is adopted in this study. Namely, through the analysis of case data, a general conclusion is reached, hoping to be generalized or have implications to other cases.
This research adopts specific methods as: literature analytical method, oral report method, classroom observed mathod, interview method, induced analytical method, comparatively analytical method, and so on.
This research firstly makes a trace study on the specific process of the decision-making of case teaching plan from three aspects, namely, the analysis of the oral report of the case study, the after-class interview and the researchers' observed material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, and teacher's knowledge are the main influential factors of teachers' planning decision-making. Secondly, the subject's thinking mode on planning decision-making has the feature of "scrambles" and "linearity". it is proposed that mathematics teachers' thinking in the decision-making of teaching plan should switch from scrambling thinking to apprehensive thinking, and from linear thinking to creative thinking.
Meanwhile, the present research also makes a follow-up study on the specific process of the interactive decision-making of the case study from different perspectives, such as the classroom record, after-class interview, students' interview, oral report, researcher's observed material and the production material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, teacher's knowledge and classroom context are the main influential factors of teachers' interactive decision-making. Secondly, the subject's thinking mode on interactive decision-making has the feature of the "forced landing" and "random". it is proposed that their thinking of interactive decision-making should switch from forced landing thinking to ascending thinking, from free thinking to random thinking.
Based on the two questions and in combination with literature review, the subject's "domestic conception" and "the focus of the teaching factors" are further discussed. The subject's belief system is reflected from the perspective of decision-making while such material as the oral report of the case, after-class interview, and comprehensive interview is analyzed into categories. meanwhile, the main factor of instructional decision-making are described, namely the relationship among teaching beliefs, instructional thinking mode, teacher's knowledge, and real context. It is put forward that the subject's instructional thinking mode has the characteristics of dominance, independence, and ignorance of students' thinking process, which are reflected by the system of teaching beliefs.
From the studies mentioned above, this dissertation made further theoretical investigation on relevant issues, and came to the following conclusions:
First, Mathematic teachers' instructional thinking mode is an important factor in decision-making. It is the channel for input and output of teaching beliefs, the framework of teachers' knowledge. It interacts with the real context, bridging teachers' implicit teaching belief and their knowledge, and thereby, it influences teachers' decision-making and the formation of teachers' specific teaching behaviors.
Second, Mathematic teachers' beliefs is supposed to transform from being knowledge transmission-based to the integration of knowledge transmission and the development of mathematics thinking-orientation, the knowledge transmission orientation firmly holds the basic teacher-standard, conservative, static and restrictive point of view, while the latter with a free, open, dynamic, child-based, and development-directed point of view. While teachers who believe the integration of the knowledge transmission and the development of mathematical thinking should bear in mind the two basic beliefs that they should help children learn mathematics and teach mathematics for improving their matjematics thinking mode. They can set up rich teaching plans and present them by means of appropriate situation to arouse teachers' suspicion and way of critical thinking.
Thirdly, Mathematic teachers' instructional thinking mode should transform from "the thinking mode of knowledge-giving" to "the thinking mode of pedagogy". The former has the characteristics of subject-centeredness, emphasizing mastery of knowledge, considering knowledge as absolute truth, implementing academic elitism, considering teachers as professionals, adopting one-way transmission of teaching, having answers before raising questions, and teachers having the power of decision-making. The latter has the characteristics of learning-centeredness, students' self-construction, emphasis on students' development of intelligence, pursuit of broad and balanced development, considering teachers as helper and facilitator, encouraging critical thinking and experiential learning as well as the share of decision-making between students and teachers. Mathematic teachers with educational thinking mode should, based on the characteristics of mathematic instructional thinking mode, try to find the balancing point between mathematic thinking and thinking of mathematic teaching realizing the transformation of mathematic thinking from process mode to generation mode. This transformation can be realized by setting up training course on the basis of mechanism of generation thinking mode as well as by achieving balance and transformation between mathematical thinking and mathematical teaching thinking.
To sum up, the significance and innovation of the present dissertation are as follows: firstly, as far as the choice of the topic is concerned, there are few relevant literatures about mathematics teachers' decision-making as well as teachers' decision-making in China. So to speak, this is the first doctoral dissertation on the study of mathematics teachers' decision-making. Secondly, with respect to the research methodology, the present dissertation adopts a qualitative case study, this is very rare in the field of subject teaching, particularly that of mathematics teaching. Thirdly, as for the content and conclusion of the dissertation, the present study proposes that instructional thinking mode is an important factor of mathematic teachers' decision-making, makes a further discussion about the relationship among the four major factors of mathematic teachers' decision-making, namely, teaching beliefs, instructional thinking mode, teachers' knowledge, and real context. A theoretical framework is proposed to evaluate planning and interactive decision-making. Besides, detailed content and means of the transformation of mathematic teachers' teaching beliefs and instructional thinking mode are put forward. Those researches enrich the mathematic theories in China.
The following subjects will be our foci in the further study: influential factors of mathematic teachers' decision-making, the evaluation of mathematic teachers' decision-making and the theoretical framework of mathematic teachers' decision-making; as to the pre-service, in-service, and post-service training of mathematic teachers, emphasis shall be placed on the operable strategies of the transformation of teaching beliefs and instructional thinking mode as well as the comparison of decision-making between teachers under different background.
教学决策是教师内隐的认知思维过程,研究者需要通过“内心的理解”“进入”到教师头脑中,才能充分探索教师教学决策的具体过程。“内心的理解”比表层行为研究、纸笔测验和标准访谈能使对教师教学行为的理解更加深入,这是质的研究的基本假设。可以说,质的研究的假设与研究教师教学决策的主要前提是相当一致的。因此,质的研究成为本研究的必然选择。同时,个案研究是质的研究方法之一,通过对个案系统的整体探索,挖掘有代表性个案的内在特性(内在性个案研究)或者以某个案为工具归纳一般性结论(工具性个案研究)。本研究具体遵循扎根理论研究思路,实施工具性个案研究,即扎根各类资料,分析、探索、总结、归纳出一般性的研究结论,并期望推广到其他个案或者对其他个案有所启发。
本研究采用的具体研究方法有:文献分析法、口语报告法、课堂观察法、访谈法、归纳分析法、比较分析法等。
本研究首先通过分析个案的口语报告,结合课后访谈和研究者观察资料的三角互证,对个案教学计划决策的具体过程进行追踪研究,分析归纳出如下初步结论:(1)教学信念、教学思维方式和数学知识是影响数学教师教学计划决策的主要因素;(2)数学教师教学计划决策的思维方式具有“拼凑”与“线性”的特点,应该从拼凑思维走向理解性思维,从线性思维走向创造性思维。
同时,本研究通过分析个案的课堂实录,结合课后访谈、学生访谈、口语报告和研究者观察资料、作品资料等的多角互证,对个案教学交互决策的具体过程进行追踪研究,分析归纳出如下初步结论:(1)教学信念、教学思维方式、教师知识、课堂情境是影响数学教师教学交互决策的主要因素;(2)数学教师教学交互决策的思维方式具有“迫降”与“随意”的特点,应该从“迫降”思维走向“登攀”思维,从“随意”思维走向“随机”思维。
进一步,基于上述研究和已有文献,本研究对教学决策重要影响因素之教学信念进行检视,对个案的口语报告、课后访谈、综合访谈等资料进行类属分析。通过对个案的“本土概念”和“关注的焦点教学因素”进行追问,检讨了个案的数学教学信念系统,初步描述了数学教师教学决策各主要影响因素与教学决策的关系;归纳出教学信念系统折射出的个案教学思维方式具有“支配性”、“对立性”和“忽视学生实际思维过程”的特点。
更进一步,基于上述研究,本研究从一般意义上对相关问题进行学理探讨,提升、归纳出如下研究结论:
(1)教学思维方式是数学教师教学决策的重要影响因素。数学教师教学思维方式是教学信念输出、输入的通道,是教师知识结构化的框架,是沟通教师隐存的教学信念、教师知识,并与现实情境相互作用,进而影响教师教学决策并形成教师具体教学行为的桥梁;
(2)数学教师的教学信念应该由“知识传授为本”的取向走向“知识传授与数学思维发展相融合”的取向。“知识传授与数学思维发展相融合”信念取向的数学教师应具备两条基本信念:帮助学生学习数学,为思维而教数学。可以通过设置丰富的、多维的课程计划,并以恰当的问题情境呈现,激发教师们的怀疑和批判精神等路径实现数学教师教学信念的转变。
(3)数学教师的教学思维方式应由“知识给予型思维”走向“教育学思维”。教育学思维方式的数学教师应从数学思维的特质入手寻找数学思维与数学教学思维之间的平衡点,使数学教学思维实现“过程——对象性”思维方式以及生成性思维方式的转变。可以通过“依托个体思维方式的生成机制设置培训课程”以及“实现数学思维与数学教学思维的平衡与转化”等路径加以实现。
本研究力图在以下几方面有所创新:其一,在选题方面:目前,国内研究数学教师教学决策及教师教学决策的文献尚不多见。尤其是,本论文属国内首篇专门研究数学教师教学决策的博士学位论文;二,在研究方法方面:本研究采用质的研究以及工具性个案研究策略,这在学科教育,尤其是数学学科教育中尚不多见;其三,在研究内容和结论方面,本研究提出了教学思维方式是数学教师教学决策的重要影响因素,并对数学教师教学决策的四个主要影响因素即教学信念、教学思维方式、教师知识和现实情境的关系进行了深入探讨;归纳提出了评价数学教师教学计划决策和交互决策的理论框架;归纳提出了实现数学教师教学信念和教学思维方式转变的具体内容和路径。这些研究结论能够充实和完善国内数学教学理论的框架和内容。
在今后的研究中,将继续关注以下课题:数学教师教学决策的影响因素;数学教师教学决策的评价;数学教师教学决策的理论脉络;在数学教师职前、职中和职后的培养中,教学信念和思维方式养成或转变的可操作性策略;不同背景下数学教师教学决策的比较研究等。
The effectiveness of classroom teaching determines the degree to which the curriculum is implemented as well as the quality of talents cultivating. The key of the mathematics curriculum reform lies in the implementation of the curriculum; teacher's teaching behavior affects directly the effectiveness of the implementation of the curriculum, while the decision-making is a determinant factor affecting the teaching behavior. Therefore, the quality of the mathematics teachers' decision-making determines the level of curriculum implementation and the quality of talents cultivating. Since 1970s, studies on teachers' teaching decision has become a central content in the field of teacher and teaching study abroad, and is thought of as the direction of future study. However, the study on teachers' decision-making, especially that of the mathematics teachers just starts at home, the insufficiency of relevant study will inevitably affect the effective teaching in mathematics classroom and the implementation of the curriculum in either a direct or indirect way. Thereby, it is necessary and urgent to study the mathematics teachers' decision-making.
Decision-making is the teacher's implicit cognitive thinking process, researchers can not fully probe this specific decision-making process without "entering" the teacher's mind through "internal understanding". The basic hypothesis of the qualitative study is that this internal understanding enables a deeper understanding on teachers' teaching behavior than the surface behavior study, the regular quiz with paper and pen and the standard interview. So to speak, the hypothesis of the qualitative study is in correspondence with the major presupposition of teachers' decision-making, therefore the former becomes the necessary choice. On the other hand, the case study is one of mathods of qualitative study. By probing case system whole, digging representative case's intrinsic characteristic(intrinsic case study) or inducing common conclusion from instrumental case(instrumental case study). Based on the study pathway of theory grounded, instrumental case study is adopted in this study. Namely, through the analysis of case data, a general conclusion is reached, hoping to be generalized or have implications to other cases.
This research adopts specific methods as: literature analytical method, oral report method, classroom observed mathod, interview method, induced analytical method, comparatively analytical method, and so on.
This research firstly makes a trace study on the specific process of the decision-making of case teaching plan from three aspects, namely, the analysis of the oral report of the case study, the after-class interview and the researchers' observed material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, and teacher's knowledge are the main influential factors of teachers' planning decision-making. Secondly, the subject's thinking mode on planning decision-making has the feature of "scrambles" and "linearity". it is proposed that mathematics teachers' thinking in the decision-making of teaching plan should switch from scrambling thinking to apprehensive thinking, and from linear thinking to creative thinking.
Meanwhile, the present research also makes a follow-up study on the specific process of the interactive decision-making of the case study from different perspectives, such as the classroom record, after-class interview, students' interview, oral report, researcher's observed material and the production material. The following preliminary conclusion is reached: firstly, teaching beliefs, ways of thinking, teacher's knowledge and classroom context are the main influential factors of teachers' interactive decision-making. Secondly, the subject's thinking mode on interactive decision-making has the feature of the "forced landing" and "random". it is proposed that their thinking of interactive decision-making should switch from forced landing thinking to ascending thinking, from free thinking to random thinking.
Based on the two questions and in combination with literature review, the subject's "domestic conception" and "the focus of the teaching factors" are further discussed. The subject's belief system is reflected from the perspective of decision-making while such material as the oral report of the case, after-class interview, and comprehensive interview is analyzed into categories. meanwhile, the main factor of instructional decision-making are described, namely the relationship among teaching beliefs, instructional thinking mode, teacher's knowledge, and real context. It is put forward that the subject's instructional thinking mode has the characteristics of dominance, independence, and ignorance of students' thinking process, which are reflected by the system of teaching beliefs.
From the studies mentioned above, this dissertation made further theoretical investigation on relevant issues, and came to the following conclusions:
First, Mathematic teachers' instructional thinking mode is an important factor in decision-making. It is the channel for input and output of teaching beliefs, the framework of teachers' knowledge. It interacts with the real context, bridging teachers' implicit teaching belief and their knowledge, and thereby, it influences teachers' decision-making and the formation of teachers' specific teaching behaviors.
Second, Mathematic teachers' beliefs is supposed to transform from being knowledge transmission-based to the integration of knowledge transmission and the development of mathematics thinking-orientation, the knowledge transmission orientation firmly holds the basic teacher-standard, conservative, static and restrictive point of view, while the latter with a free, open, dynamic, child-based, and development-directed point of view. While teachers who believe the integration of the knowledge transmission and the development of mathematical thinking should bear in mind the two basic beliefs that they should help children learn mathematics and teach mathematics for improving their matjematics thinking mode. They can set up rich teaching plans and present them by means of appropriate situation to arouse teachers' suspicion and way of critical thinking.
Thirdly, Mathematic teachers' instructional thinking mode should transform from "the thinking mode of knowledge-giving" to "the thinking mode of pedagogy". The former has the characteristics of subject-centeredness, emphasizing mastery of knowledge, considering knowledge as absolute truth, implementing academic elitism, considering teachers as professionals, adopting one-way transmission of teaching, having answers before raising questions, and teachers having the power of decision-making. The latter has the characteristics of learning-centeredness, students' self-construction, emphasis on students' development of intelligence, pursuit of broad and balanced development, considering teachers as helper and facilitator, encouraging critical thinking and experiential learning as well as the share of decision-making between students and teachers. Mathematic teachers with educational thinking mode should, based on the characteristics of mathematic instructional thinking mode, try to find the balancing point between mathematic thinking and thinking of mathematic teaching realizing the transformation of mathematic thinking from process mode to generation mode. This transformation can be realized by setting up training course on the basis of mechanism of generation thinking mode as well as by achieving balance and transformation between mathematical thinking and mathematical teaching thinking.
To sum up, the significance and innovation of the present dissertation are as follows: firstly, as far as the choice of the topic is concerned, there are few relevant literatures about mathematics teachers' decision-making as well as teachers' decision-making in China. So to speak, this is the first doctoral dissertation on the study of mathematics teachers' decision-making. Secondly, with respect to the research methodology, the present dissertation adopts a qualitative case study, this is very rare in the field of subject teaching, particularly that of mathematics teaching. Thirdly, as for the content and conclusion of the dissertation, the present study proposes that instructional thinking mode is an important factor of mathematic teachers' decision-making, makes a further discussion about the relationship among the four major factors of mathematic teachers' decision-making, namely, teaching beliefs, instructional thinking mode, teachers' knowledge, and real context. A theoretical framework is proposed to evaluate planning and interactive decision-making. Besides, detailed content and means of the transformation of mathematic teachers' teaching beliefs and instructional thinking mode are put forward. Those researches enrich the mathematic theories in China.
The following subjects will be our foci in the further study: influential factors of mathematic teachers' decision-making, the evaluation of mathematic teachers' decision-making and the theoretical framework of mathematic teachers' decision-making; as to the pre-service, in-service, and post-service training of mathematic teachers, emphasis shall be placed on the operable strategies of the transformation of teaching beliefs and instructional thinking mode as well as the comparison of decision-making between teachers under different background.
引文
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