HPM与数学教师专业发展
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摘要
数学教育课程改革凸显了教师专业发展的重要性与应然性,HPM教学设计能力是数学教师专业素养的重要组成部分。如何提升教师的HPM教学设计能力,成为数学教育界面临的一项重要任务。研究者从教师专业发展的主要途径与策略入手,分析教育工作室对教师专业发展的独特优势和HPM教学面临的问题,针对一个数学教育工作室开展了HPM设计研究。通过分析HPM教学设计、实施过程对数学教育工作室、教师以及HPM教学对学生学习的影响,研究者总结归纳了HPM设计研究的作用、意义和产出的具体成果。
研究对象是一个数学教育工作室及其8位成员教师。工作室8位教师,除主持人(一位教学名师)和一位具有“市教坛新秀”称号的教师,没有直接进行HPM教学设计外,其余6位教师都参与了HPM教学的三轮设计、实施、改进、完善的过程。研究的主要问题是：
1.HPM设计研究过程对数学教育工作室产生了怎样的影响?
2.HPM教学设计与实施的循环过程在哪些方面促进教师的专业发展?
3.HPM视角下的数学教学对学生的学习产生哪些积极的影响?
4.通过开展HPM设计研究,能获得哪些具体成果?
本文以设计研究方法为主,辅之以叙事研究方法和参与式行动研究方法。从每一课题第一轮的HPM教学设计,到“设计→执教→干预→修正”过程中的集中评课、研讨,为教师提供修改建议等一系列活动,研究者始终参与其中。通过课堂听课、深度访谈、自评问卷等多种方式收集相关研究数据,经过对数据进行量的统计与质的分析,获得研究结论,并以纵向比较和横向比较两种方式呈现研究结果。纵向比较针对参与设计、执教的每一位教师在三轮设计、改进的循环过程中的前后变化。横向比较则针对工作室教师及工作室外围教师基于HPM设计的专业成长的比较。
本研究以“促进高中数学教师的HPM教学设计能力”为主旨,以高中必修和选修教材中六个专题的起始课为主线,设计开发“文化取向”、“探究取向”和“发生取向”三种HPM教学设计模式,从不同侧面展示,高中数学教学不同分支内容的HPM教学设计的基本思路和模式,为高中数学起始课教学的HPM教学设计提供了范例。
经过对参与教师进行跟踪研究,通过纵向比较我们发现,HPM介入数学教学后,6位教师的HPM教学设计能力逐步提高,从以附加式使用为主逐步过渡到根据教学需求选择不同的使用方式,从单纯追求使用量的多少,到根据教学需要,关注量和质的协调一致。
与工作室外围教师的横向比较发现,他们的数学史知识、数学学科教学知识、融合数学史的数学学科内容知识、融合数学史的教学法知识、融合数学史的数学教学知识和教学科研能力显著优于外围教师,但数学知识、教学知识无显著差异。
本研究的基本结论是：
1.设计研究过程对于工作室的主要作用是：(1)促成了工作室活动开展的内容与目标定位；(2)促成了工作室教师培训策略的制定及实施；(3)HPM教学设计活动使工作室的学习活动富有实效。
2.HPM教学设计与实施的循环过程对教师的作用是：(1)对HPM教学的态度发生转变,由排斥到当作外加任务,再到接纳,直至最后由成功体验产生自主开展HPM教学的愿望；(2)教师的数学教学观念发生改变；(3)教师的数学观、数学教学观和学生观得到改善；(4)教师的HPM教学设计能力、沟通交流及合作能力、教学科研能力得到提升。
3.HPM教学对学生的积极影响是：(1)促进了学生对数学知识的深入理解；(2)通过建立跨学科联系,使得学生对数学知识的认识更为全面；(3)培育积极的数学学习情感,改变了学生的数学观和数学学习观。
4.开展HPM设计研究的意义和具体成果是：(1)对其它工作室的计划拟定、活动开展等具有借鉴意义；(2)为中学数学教学提供了三种HPM教学模式的六个教学案例,并给出了进行HPM教学设计的基本原则和步骤。
对HPM和教师专业发展的启示是：(1)课题带动的设计研究对教师培训具有重要意义；(2)应重视职前教师的HPM教学知识与能力培养；(3)应持续、深入开展HPM课堂教学实践研究及案例开发。
对HPM领域的后续研究展望是：(1)为教学的数学史原始资源的开发研究；(2)HPM与教师专业发展关系的持续研究；(3)HPM领域的实证研究及理论框架。
The Mathematics Education Curriculum Reform highlights the significance and certainty of teachers' professional development. The capability of HPM teaching design is an essential part of the mathematics teachers'professionalism. How to improve the teachers' HPM teaching design capability is an important task facing mathematics teacher trainers. Based on the analysis of current approaches and strategies of teachers' professional development, unique advantages of the mathematics education studio and problems in HPM teaching, a design research of HPM teaching was carried out on a mathematics education studio in order to understand about the influence of the HPM designs and teaching on mathematics teachers in the studio as well as on their students.
A mathematics education studio and its members, eight senior high school teachers, were chosen as subjects, six of whom participated the complete process of the three rounds of HPM design research. The research questions include:
1. What are the effects of HPM design research on the mathematics education studio?
2. In which aspects do the HPM designs and teaching process promote the studio teachers'professional development?
3. What are the positive impacts of the HPM teaching on students'mathematics learning?
4. What productions can we get from the HPM design research?
The main methodology is design research, supplemented by the narrative research and the participatory action research. From the first round of HPM design and teaching, the author participated all activities of the studio. The data are collected from video-taped lessons, interviews with teachers before and after lessons, teachers' reflective diaries, audio-taped activities of teaching research and the questionnaire developed by the researcher,"Teachers' Self-rating Scale on Professional Growth Basing on HPM". The research findings were presented in both dimensions of transverse and longitudinal comparison. The longitudinal comparative study aimed at the changes of both the teacher who participated the HPM design and teaching and all other members of the studio during the period of a complete round of three times of designs and teaching. The transverse comparative study aimed at the differences between the teachers inside and outside the studio.
With the main task of HPM design of the beginning lessons of six topics in senior high school compulsory and elective textbooks, three patterns of HPM designs are developed:cultural orientation, explorative orientation and genetic orientation, and lesson models and design principles in different topics of the senior high school mathematics are provided.
Through the longitudinal comparison, it is found that, in all the three rounds of teaching, teachers' capabilities of HPM design and teaching are improved. In the first design, they used historical materials with the single complementation approach simply paying attention to the quantity of the historical materials; but in the third design, they tend to ad8pt suitable approaches to meet the need of the teaching objectives, paying attention to the quality as well as the quantity of historical materials.
Through the transverse comparison, it is revealed that the teachers inside the studio are significantly better than the outside teachers in the following aspects:(1) the knowledge of history of mathematics;(2) the ability and knowledge of HPM design and teaching;(3) the knowledge of the relation between history and mathematics;(4) the research ability and knowledge;(5) the ability of reflection;(6) the ability of cooperation and communication, and so on. But their mathematics knowledge and pedagogical knowledge are not significantly better than the teachers outside the studio.
The basic conclusions of this study are as following:
1. The effects of HPM design research on the mathematics education studio are mainly shown in the following three aspects:(1) the design research on HPM contributed to the operation and orientation of activities and objectives of the whole studio;(2) it also contributed to the development and implementation of the studio's strategies of training teachers;(3) HPM design research makes the studio's learning activities productive.
2. The main roles of the HPM design and implementation cycles for teachers in the studio are:(1) changing teachers'attitudes towards HPM instruction, from rejecting to accepting and at last to desiring;(2) changing teachers'conceptions of mathematics;(3) improving the teachers'conceptions of mathematics teaching learning;(4) enhancing the teachers'abilities of HPM instructional design, self-reflection, teaching research and communication and collaboration with peers and experts, and so on.
3. The teaching from the perspective of HPM has positive impacts on students' learning, including:(1) having promoted the students'in-depth understanding of mathematical knowledge;(2) having established the linkage between mathematics and other disciplines, which makes the students'mathematics conceptions more comprehensive;(3) having cultivated students'positive emotion of mathematics and changed students'conceptions both of mathematics and mathematics learning.
4. The significances and productions of the HPM design research mainly include the following two aspects:providing references to the other studio activities; presenting three HPM models and six teaching cases and giving the basic principles and steps of the HPM design.
Based on the above conclusions, the following educational implications are obtained:(1) The topic-driven design research is of great significance for teachers training;(2) More attention should be paid to the pre-service teachers' HPM teaching knowledge and capacity;(3) Importance should be attached to the HPM classroom teaching practice and cases development.
As far as the HPM research is concerned, further researches should be carried out on the following areas:(1) the relation between HPM and teachers' professional development and training approaches;(2) the history of mathematics for mathematics teaching;(3) the theoretical framework and other empirical researches.
研究对象是一个数学教育工作室及其8位成员教师。工作室8位教师,除主持人(一位教学名师)和一位具有“市教坛新秀”称号的教师,没有直接进行HPM教学设计外,其余6位教师都参与了HPM教学的三轮设计、实施、改进、完善的过程。研究的主要问题是：
1.HPM设计研究过程对数学教育工作室产生了怎样的影响?
2.HPM教学设计与实施的循环过程在哪些方面促进教师的专业发展?
3.HPM视角下的数学教学对学生的学习产生哪些积极的影响?
4.通过开展HPM设计研究,能获得哪些具体成果?
本文以设计研究方法为主,辅之以叙事研究方法和参与式行动研究方法。从每一课题第一轮的HPM教学设计,到“设计→执教→干预→修正”过程中的集中评课、研讨,为教师提供修改建议等一系列活动,研究者始终参与其中。通过课堂听课、深度访谈、自评问卷等多种方式收集相关研究数据,经过对数据进行量的统计与质的分析,获得研究结论,并以纵向比较和横向比较两种方式呈现研究结果。纵向比较针对参与设计、执教的每一位教师在三轮设计、改进的循环过程中的前后变化。横向比较则针对工作室教师及工作室外围教师基于HPM设计的专业成长的比较。
本研究以“促进高中数学教师的HPM教学设计能力”为主旨,以高中必修和选修教材中六个专题的起始课为主线,设计开发“文化取向”、“探究取向”和“发生取向”三种HPM教学设计模式,从不同侧面展示,高中数学教学不同分支内容的HPM教学设计的基本思路和模式,为高中数学起始课教学的HPM教学设计提供了范例。
经过对参与教师进行跟踪研究,通过纵向比较我们发现,HPM介入数学教学后,6位教师的HPM教学设计能力逐步提高,从以附加式使用为主逐步过渡到根据教学需求选择不同的使用方式,从单纯追求使用量的多少,到根据教学需要,关注量和质的协调一致。
与工作室外围教师的横向比较发现,他们的数学史知识、数学学科教学知识、融合数学史的数学学科内容知识、融合数学史的教学法知识、融合数学史的数学教学知识和教学科研能力显著优于外围教师,但数学知识、教学知识无显著差异。
本研究的基本结论是：
1.设计研究过程对于工作室的主要作用是：(1)促成了工作室活动开展的内容与目标定位；(2)促成了工作室教师培训策略的制定及实施；(3)HPM教学设计活动使工作室的学习活动富有实效。
2.HPM教学设计与实施的循环过程对教师的作用是：(1)对HPM教学的态度发生转变,由排斥到当作外加任务,再到接纳,直至最后由成功体验产生自主开展HPM教学的愿望；(2)教师的数学教学观念发生改变；(3)教师的数学观、数学教学观和学生观得到改善；(4)教师的HPM教学设计能力、沟通交流及合作能力、教学科研能力得到提升。
3.HPM教学对学生的积极影响是：(1)促进了学生对数学知识的深入理解；(2)通过建立跨学科联系,使得学生对数学知识的认识更为全面；(3)培育积极的数学学习情感,改变了学生的数学观和数学学习观。
4.开展HPM设计研究的意义和具体成果是：(1)对其它工作室的计划拟定、活动开展等具有借鉴意义；(2)为中学数学教学提供了三种HPM教学模式的六个教学案例,并给出了进行HPM教学设计的基本原则和步骤。
对HPM和教师专业发展的启示是：(1)课题带动的设计研究对教师培训具有重要意义；(2)应重视职前教师的HPM教学知识与能力培养；(3)应持续、深入开展HPM课堂教学实践研究及案例开发。
对HPM领域的后续研究展望是：(1)为教学的数学史原始资源的开发研究；(2)HPM与教师专业发展关系的持续研究；(3)HPM领域的实证研究及理论框架。
The Mathematics Education Curriculum Reform highlights the significance and certainty of teachers' professional development. The capability of HPM teaching design is an essential part of the mathematics teachers'professionalism. How to improve the teachers' HPM teaching design capability is an important task facing mathematics teacher trainers. Based on the analysis of current approaches and strategies of teachers' professional development, unique advantages of the mathematics education studio and problems in HPM teaching, a design research of HPM teaching was carried out on a mathematics education studio in order to understand about the influence of the HPM designs and teaching on mathematics teachers in the studio as well as on their students.
A mathematics education studio and its members, eight senior high school teachers, were chosen as subjects, six of whom participated the complete process of the three rounds of HPM design research. The research questions include:
1. What are the effects of HPM design research on the mathematics education studio?
2. In which aspects do the HPM designs and teaching process promote the studio teachers'professional development?
3. What are the positive impacts of the HPM teaching on students'mathematics learning?
4. What productions can we get from the HPM design research?
The main methodology is design research, supplemented by the narrative research and the participatory action research. From the first round of HPM design and teaching, the author participated all activities of the studio. The data are collected from video-taped lessons, interviews with teachers before and after lessons, teachers' reflective diaries, audio-taped activities of teaching research and the questionnaire developed by the researcher,"Teachers' Self-rating Scale on Professional Growth Basing on HPM". The research findings were presented in both dimensions of transverse and longitudinal comparison. The longitudinal comparative study aimed at the changes of both the teacher who participated the HPM design and teaching and all other members of the studio during the period of a complete round of three times of designs and teaching. The transverse comparative study aimed at the differences between the teachers inside and outside the studio.
With the main task of HPM design of the beginning lessons of six topics in senior high school compulsory and elective textbooks, three patterns of HPM designs are developed:cultural orientation, explorative orientation and genetic orientation, and lesson models and design principles in different topics of the senior high school mathematics are provided.
Through the longitudinal comparison, it is found that, in all the three rounds of teaching, teachers' capabilities of HPM design and teaching are improved. In the first design, they used historical materials with the single complementation approach simply paying attention to the quantity of the historical materials; but in the third design, they tend to ad8pt suitable approaches to meet the need of the teaching objectives, paying attention to the quality as well as the quantity of historical materials.
Through the transverse comparison, it is revealed that the teachers inside the studio are significantly better than the outside teachers in the following aspects:(1) the knowledge of history of mathematics;(2) the ability and knowledge of HPM design and teaching;(3) the knowledge of the relation between history and mathematics;(4) the research ability and knowledge;(5) the ability of reflection;(6) the ability of cooperation and communication, and so on. But their mathematics knowledge and pedagogical knowledge are not significantly better than the teachers outside the studio.
The basic conclusions of this study are as following:
1. The effects of HPM design research on the mathematics education studio are mainly shown in the following three aspects:(1) the design research on HPM contributed to the operation and orientation of activities and objectives of the whole studio;(2) it also contributed to the development and implementation of the studio's strategies of training teachers;(3) HPM design research makes the studio's learning activities productive.
2. The main roles of the HPM design and implementation cycles for teachers in the studio are:(1) changing teachers'attitudes towards HPM instruction, from rejecting to accepting and at last to desiring;(2) changing teachers'conceptions of mathematics;(3) improving the teachers'conceptions of mathematics teaching learning;(4) enhancing the teachers'abilities of HPM instructional design, self-reflection, teaching research and communication and collaboration with peers and experts, and so on.
3. The teaching from the perspective of HPM has positive impacts on students' learning, including:(1) having promoted the students'in-depth understanding of mathematical knowledge;(2) having established the linkage between mathematics and other disciplines, which makes the students'mathematics conceptions more comprehensive;(3) having cultivated students'positive emotion of mathematics and changed students'conceptions both of mathematics and mathematics learning.
4. The significances and productions of the HPM design research mainly include the following two aspects:providing references to the other studio activities; presenting three HPM models and six teaching cases and giving the basic principles and steps of the HPM design.
Based on the above conclusions, the following educational implications are obtained:(1) The topic-driven design research is of great significance for teachers training;(2) More attention should be paid to the pre-service teachers' HPM teaching knowledge and capacity;(3) Importance should be attached to the HPM classroom teaching practice and cases development.
As far as the HPM research is concerned, further researches should be carried out on the following areas:(1) the relation between HPM and teachers' professional development and training approaches;(2) the history of mathematics for mathematics teaching;(3) the theoretical framework and other empirical researches.
引文
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