基于数学史课程的职前教师教学知识发展研究
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摘要
在教师教育中,课程的设置多以经验性为主,以实证研究作为决策基础的现象还不多。教师教学知识是教师专业化程度的重要标志,研究教师教育课程对教师教学知识有怎样的影响具有重要的意义。本研究对数学史课程与职前教师教学知识的联系进行了研究,主要探讨两个方面的问题：(1)在学习数学史课程前后,职前教师的教学知识有了哪些变化?(2)在学习数学史课程过程中,职前教师的教学知识是怎么变化的?其中每个问题再分成两个小问题进行研究。
本研究的教师教学知识以MKT理论框架为基础,从学科内容知识和教学内容知识两个方面,分析职前教师在学习数学史的过程中教学知识的变化情况。研究分为量化研究和质性研究两个部分,在量化研究中编制了教学知识问卷在学期前后对研究对象和控制班的职前教师进行了测量；质性研究则选取了11位职前教师,要求他们先对某知识点进行模拟教学,然后在数学史课程中听取了与该知识点相关的数学史内容后,对之前的模拟教学进行反思。研究者通过访谈,了解在数学史课堂后,职前教师在教学上出现了什么变化,哪些变化是由于数学史的因素引起的；并分析不同的类型的数学史内容和教学方式,对职前教师教学知识的影响有什么区别。
研究发现：(1a)数学史对职前教师的学科内容知识和教学内容知识都产生了影响,从总体上说在学科内容知识方面影响程度小于教学内容知识。(1b)数学史对A类职前教师(师范类)教学知识的影响大于B类职前教师(非师范生),尤其在教学内容知识方面。
(2a)在学习数学史的过程中,职前教师学科内容知识的变化是不连续的,与学习数学史的时间长短没有直接的联系,而与数学史内容的类型,以及史料的丰富程度有关；而教学内容知识的变化则存在连续性,不但与数学史内容有关,还与学习数学史时间的长短有关。(2b)演进史类型的数学史内容对职前教师教学知识变化最大,枚举史类型的内容对职前教师的教学知识变化最小；知识性和趣味性兼具的内容最受职前教师欢迎；数学史内容与HPM教学案例结合的方式最适合职前教师学习。课堂中组织讨论的教学方式有利于职前教师教学知识的提升；布置适当的作业有助于职前教师加深数学史与数学教育联系的理解；视频案例的教学方式可以帮助职前教师更好的将数学史内容转化成教学知识。
根据研究所获得的启示,研究者在基于教师教学知识的数学史课程建设和数学史融入数学教学的教学设计流程这两个方面提出了一些建议。在探讨了研究的不足之处后,对后续研究提出了若干展望。
In teacher education, the curriculum's setting are more on experience, but not on empirical research. The teaching knowledge is the important sign to measure the degree of specialization of Teachers. It is significant to study the relationship between the teacher education course and teachers'teaching knowledge. The research on the relationship between the course of the history of mathematics and preservice teachers'teaching knowledge. Focus on the following two aspects:(1) After learning the history of mathematics, what has changed in preservice teachers' teaching knowledge?(2) In learning the history of mathematics, preservice teachers' teaching knowledge is how to change? Among them, each problem is divided into two small question to study.
This research is based on the theory of MKT, study the changes of preservice teachers' teaching knowledge including subject content knowledge and pedagogical content knowledge. This study is divided into two parts of quantitative research and qualitative research. In quantitative research, the researcher developed the teaching knowledge questionnaire, and test the research and the control calss'preservice teachers, in before and after the term. In qualitative research, the researcher asked11preservice teathers to carry on the simulation teaching on a certain knowledge. In the history of mathematics course, the research interduced the history of the certain knowledge. Then, the researcher asked the preservice teachers to reflect on the previous simulation teaching. Through interviews, the researcher know what changed of the preservice teachers'simulation teaching, and know what the changes are caused by the factors of the history of mathematics. The researcher also analyzed the change of preservice teachers'teaching knowledge in different types of the history of mathematics content and different teaching methods.
Conclusions of the research are as follows:
(la) After the history of mathematics course, preservice teachers'subject matter knowledge and pedagogical content knowledge have been improved, and the degree of the pedagogical content knowledge to improve larger than the subject matter knowledge,(lb) The history of mathematics improve class A (normal) preservice teachers'teaching knowledge more than class B (non normal), especially in the pedagogical content knowledge.
(2a) The change of preservice teachers' subject matter knowledge are not directly linked to the order of learning the history of mathematics, but relate to richness and types of the history of mathematics. The change of preservice teachers' pedagogical content knowledge not only relate to richness and types of the history of mathematics, but also relate to the order of learning the history of mathematics.(2b) The type of evolution history is the biggest change preservice teachers' teaching knowledge, the type of enumueration history is the smallest change. Preservice teachers the most welcome the history of mathematics content of both knowledge and fun, and the history of mathematics content combine to HPM teaching case will the most suitable for preservice teachers'learning. Discuss integrating the history of mathematics into mathematics teaching in the history of mathematics course can improvement preservice teachers'teaching knowledge effective. Assign appropriate homework help to enhance preservice teachers on mathematics history and mathematics education understanding. The video cases can help preservice teachers to better translate the history of mathematics into teaching knowledge.
According to the study of revelation, the researcher have proposed some suggestions on construction of the history of mathematics course and teaching design process of integrating the history of mathematics into mathematics teaching. After discussion of the shortcomings of the research, the researcher puts forward some prospects for future research.
本研究的教师教学知识以MKT理论框架为基础,从学科内容知识和教学内容知识两个方面,分析职前教师在学习数学史的过程中教学知识的变化情况。研究分为量化研究和质性研究两个部分,在量化研究中编制了教学知识问卷在学期前后对研究对象和控制班的职前教师进行了测量；质性研究则选取了11位职前教师,要求他们先对某知识点进行模拟教学,然后在数学史课程中听取了与该知识点相关的数学史内容后,对之前的模拟教学进行反思。研究者通过访谈,了解在数学史课堂后,职前教师在教学上出现了什么变化,哪些变化是由于数学史的因素引起的；并分析不同的类型的数学史内容和教学方式,对职前教师教学知识的影响有什么区别。
研究发现：(1a)数学史对职前教师的学科内容知识和教学内容知识都产生了影响,从总体上说在学科内容知识方面影响程度小于教学内容知识。(1b)数学史对A类职前教师(师范类)教学知识的影响大于B类职前教师(非师范生),尤其在教学内容知识方面。
(2a)在学习数学史的过程中,职前教师学科内容知识的变化是不连续的,与学习数学史的时间长短没有直接的联系,而与数学史内容的类型,以及史料的丰富程度有关；而教学内容知识的变化则存在连续性,不但与数学史内容有关,还与学习数学史时间的长短有关。(2b)演进史类型的数学史内容对职前教师教学知识变化最大,枚举史类型的内容对职前教师的教学知识变化最小；知识性和趣味性兼具的内容最受职前教师欢迎；数学史内容与HPM教学案例结合的方式最适合职前教师学习。课堂中组织讨论的教学方式有利于职前教师教学知识的提升；布置适当的作业有助于职前教师加深数学史与数学教育联系的理解；视频案例的教学方式可以帮助职前教师更好的将数学史内容转化成教学知识。
根据研究所获得的启示,研究者在基于教师教学知识的数学史课程建设和数学史融入数学教学的教学设计流程这两个方面提出了一些建议。在探讨了研究的不足之处后,对后续研究提出了若干展望。
In teacher education, the curriculum's setting are more on experience, but not on empirical research. The teaching knowledge is the important sign to measure the degree of specialization of Teachers. It is significant to study the relationship between the teacher education course and teachers'teaching knowledge. The research on the relationship between the course of the history of mathematics and preservice teachers'teaching knowledge. Focus on the following two aspects:(1) After learning the history of mathematics, what has changed in preservice teachers' teaching knowledge?(2) In learning the history of mathematics, preservice teachers' teaching knowledge is how to change? Among them, each problem is divided into two small question to study.
This research is based on the theory of MKT, study the changes of preservice teachers' teaching knowledge including subject content knowledge and pedagogical content knowledge. This study is divided into two parts of quantitative research and qualitative research. In quantitative research, the researcher developed the teaching knowledge questionnaire, and test the research and the control calss'preservice teachers, in before and after the term. In qualitative research, the researcher asked11preservice teathers to carry on the simulation teaching on a certain knowledge. In the history of mathematics course, the research interduced the history of the certain knowledge. Then, the researcher asked the preservice teachers to reflect on the previous simulation teaching. Through interviews, the researcher know what changed of the preservice teachers'simulation teaching, and know what the changes are caused by the factors of the history of mathematics. The researcher also analyzed the change of preservice teachers'teaching knowledge in different types of the history of mathematics content and different teaching methods.
Conclusions of the research are as follows:
(la) After the history of mathematics course, preservice teachers'subject matter knowledge and pedagogical content knowledge have been improved, and the degree of the pedagogical content knowledge to improve larger than the subject matter knowledge,(lb) The history of mathematics improve class A (normal) preservice teachers'teaching knowledge more than class B (non normal), especially in the pedagogical content knowledge.
(2a) The change of preservice teachers' subject matter knowledge are not directly linked to the order of learning the history of mathematics, but relate to richness and types of the history of mathematics. The change of preservice teachers' pedagogical content knowledge not only relate to richness and types of the history of mathematics, but also relate to the order of learning the history of mathematics.(2b) The type of evolution history is the biggest change preservice teachers' teaching knowledge, the type of enumueration history is the smallest change. Preservice teachers the most welcome the history of mathematics content of both knowledge and fun, and the history of mathematics content combine to HPM teaching case will the most suitable for preservice teachers'learning. Discuss integrating the history of mathematics into mathematics teaching in the history of mathematics course can improvement preservice teachers'teaching knowledge effective. Assign appropriate homework help to enhance preservice teachers on mathematics history and mathematics education understanding. The video cases can help preservice teachers to better translate the history of mathematics into teaching knowledge.
According to the study of revelation, the researcher have proposed some suggestions on construction of the history of mathematics course and teaching design process of integrating the history of mathematics into mathematics teaching. After discussion of the shortcomings of the research, the researcher puts forward some prospects for future research.
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