【作者】 柴俊；

【导师】 王建磐；

【作者基本信息】 华东师范大学 ， 课程与教学论， 2008， 博士

【摘要】 数学教师教育实行多元化、分层次培养,是时代进步和社会发展的必然结果,也是我国数学教师教育50多年发展的经验总结。本文通过文献研究,历史考察,国际比较,特别是运用2003-2007届华东师大数学系的实施样例,以及四校大样本的实证调查,全面研究高等师范院校数学专业的“多元化、分层次”培养方案,力图为21世纪高师院校数学教师教育的未来发展,提供理论依据和实践案例。“多元化”与“多层次”观念的出现,有其深刻的社会背景。改革开放30年来,就业市场化的改革必然导致就业的多元化。中学数学教师来源不再局限于高师数学系,而高师数学系毕业生也可以离开教育单位,从事其他工作。重点高中、普通高中、和职业高中对数学教师的学科背景的要求有许多差别。同时,中学数学新课标的实施,校本课程的推广以及各类选修课的开设,需要数学教师群体中存在不同的知识结构和专业背景:有些教师强于数学理论,有些善于建模和应用,还有一些则专长数学教育的理论。另一方面,高等教育扩招,入校学生数量猛增,导致学生个体素质的差异不断扩大。为了尊重学生的差异,在基础课程的教学中,对不同层次的学生按不同要求分层次授课的教学模式成为必然选择。本文提到数学教师培养的“多元化”,是指在打好数学基础的前提下,通过为学生设置多个不同目标的系列课程(称“目标选修课”,有基础系列、应用系列、数学教育系列),让学生根据自身的目标选择某个系列修读,适应社会发展和数学知识爆炸性增长对数学背景多元化的要求。“分层次”是指对于不同对象,基础课程按照基本要求、较高要求分不同层次实施教学(如华东师大数学系的理科基地班学生按较高要求教学,普通班学生以及地方高师学生按基本要求教学)。相对于过去的单一培养方案,“多元化”代表宽度,而“分层次”则表示课程的深度,即分别在横向和纵向上进行改革和发展。本文通过对50年来我国师范教育历史的回顾,特别是华东师大数学系50年来不同时期4份培养方案的解读,看到了“多元化、分层次”培养形成的历史轨迹。20世纪下半叶进入信息时代以后,数学科学本身的进步引起数学知识的爆炸,数学课程的内容更加多元化。数学教育发展使得师范生的学习具有更多的自主性。因此,提供多种系列的选择性课程成为一种自然的发展趋势。本文收集了美国“数学科学学校”、AP课程,以及俄罗斯“数学物理学校”等相关情况,并且于2003年直接考察美国Arcadia大学和Sworthmore学院,看到了国外在教育普及过程中,学校的水平和任务自然地发生多样化,数学教师教育也相应地出现了不同的模式。其中美国和俄罗斯重视优秀生的数学教育,使我们进一步认识到培养具有高度数学专业知识水平的数学教师,是一个重要的战略决策,它将关系到我国在国际间未来尖端人才创新竞争的成败。本文的核心部分是关于“多元化、分层次”培养方案实证研究,借助案例和大样本调查,为今后实施的必要性和可行性,提供了客观的依据。华东师大2003级(2007年毕业)数学与应用数学专业,完整地实施了“多元化、分层次”培养方案。这届学生共招收137人,进入理科基地班42人。137人中选择数学教育系列+基础系列的71人,数学教育系列+应用系列的59名,基础系列7人。毕业时在有去向的123名学生中,54人进入普通中学,4人到高职和中职任教;到非教育单位工作的17人,包括IT企业、银行、保险、证券、咨询等;38人就读研究生,10人出国深造。所占比例分别为普通中学43.90%,职业学校3.25%,非教育单位13.82%,读研30.89%。在直接就业的学生中,到教育单位的比例高达72%,重点中学尤其欢迎具有较强数学背景(甚至数学专业硕士生)的学生担任教师。总之,就业是“多元化”的,而更重要的是“多元化、分层次”的培养方案给中学数学教师队伍带来了多元化的数学背景。基础、应用、数学教育三个不同目标的“多元化”培养模式适应了中学和社会对高师数学系需求。关于“多元化、分层次”的设计,我们在2001-2003年间进行了四次较大规模的测试和调查,目的是为了回答“大学扩招”后数学基础课程是否能够保证基本的教学质量,如何设置体现“多元化”思想的课程系列。参加的高师院校是华东师大,杭州师院,南通师院,四川师院,代表两个不同的层次;参加的学生人次(样本)为:华东师大517,杭州师院249,南通师院402,四川师院167。四次调查的内容分别是1.华东师大学生关于课程设置和分层次的问卷调查;2.两校《数学分析》课程第二学期末统一考试;3.四校2001级基础课较高理解水平测试;4.高考成绩与大学基础课成绩的相关性调查。问卷调查为“多元化、分层次”培养方案及体现“多元化”的“目标选修课”提供了支持。测试结果表明,数学基础课程的基本要求在大规模扩招后基本能够基本达到,在较高要求上面四个学校差距较大,华东师大明显好于另外三所学校。由此说明了基础课程的“分层次”教学是必要的。本文最后讨论了长期争论不休的“师范性”问题,对如何将数学的“学术形态”转变为学生容易接受的“教育形态”进行了重点的研究,同时也对包括华东师范大学在内的国内一些重要的师范大学数学系的数学教育课程的设置进行了一些分析和评述。本文尚有以下的不足之处。一是在研究“多元化”问题时,缺乏对职业中学数学教师的状况进行详细分析。二是在分层次调查中没有收集和使用边远少数民族地区数学教师教育(师专层次)的资料。希望将来能有机会继续研究,为我国的数学教师教育的发展提供进一步的实践和理论。更多还原

【Abstract】 Mathematics teacher education implements training in a diversified and multi-level’s way, which is the progress of the times and an inevitable result of social development, and also the summary of Chinese 50 years’ experience of mathematics teacher education development. This paper aims to conduct a comprehensive study of mathematics’ "Diversification and Multi-level" training programmer at Normal University through literature review, history study and international comparisons, particularly use the sample of 2003-2007 Department of Mathematics at East China Normal University （ECNU） and also the empirical survey of large samples from four universities, with the soul purpose of providing the theoretical basis and practical case for the future development of mathematics teachers education of 21^st universities.The emergence of the two concepts "Diversification" and "Multi-level," has a profound social background. With the reform and opening up for over 30 years, the employment in market will inevitably lead to the diversification of employment. The source of middle school math teacher no longer confined to mathematics department, and graduates of mathematics can engage in other work instead of staying in the education unit. Key high schools, ordinary high school and vocational high school pose different requirements for the background of the math teachers. At the same time, math teachers need to diversify in knowledge structure and professional backgrounds because of the implementation of new curriculum standards for mathematics, promotion of school-based curriculum and establishment of the optional courses. In this case, some teachers need to be good at theory of mathematics, some modeling and applications, and still others theory of mathematics education. On the other hand, increasing enrollment of higher education and increasing number of students lead to diversification in the quality of individual student. In order to respect the differences of students, the model of teaching different levels according to different requirements becomes the inevitable choice in the basic courses."Diversification" of math teacher training mentioned in this paper refers to setting a series of courses （called "the goal of elective courses", including base series, application series and Mathematics’ education series） on the premise of a good foundation for mathematics. Students can select a series of studies with accordance to his/her own characteristics so as to adapt oneself to the diversified requirements caused by social development and explosive growth of mathematical knowledge."Multi-level" refers to different requirements according to the different objects. Basic courses are divided into two levels of basic requirements and higher requirements which are implemented according to different levels （such as the Department of Mathematics at ECNU, Science Base Classes are taught according to higher requirements, regular classes of students and students of local normal university to basic requirements）. Compared to the past single training programmer, "diversification" is on behalf of the width, while "multi level" is on behalf of the depth, which is the horizontal and vertical reform and development.In retrospect to the past 50 years’ history of China’s Teacher Education Review, in particular to interpretations of four training programmers in the past 50 years of the Department of Mathematics at ECNU, we can see the trace of formation of "diversification, multi-levels". In the second half of the 20th century into the information age, the progress of the Mathematical Sciences leads to the explosion of mathematical knowledge, which causes the diversification of mathematics courses. Development of Mathematics Education makes the study of students at normal university more flexible. Therefore, to provide a wide range of optional courses is becoming a natural developing trend.The data are collected from "the school of Mathematical Sciences" of the United States, AP courses, and the Russian "school of mathematical physics". In 2003, I also paid a visit to Sworthmore College and Arcadia University in the United States. We could see that the level and task of university diversified and different models of mathematics teacher education emerged. The United States and Russia attach great importance to the top students in mathematics education, which enlightens us that it is of great importance to train mathematics teachers of highly professional knowledge and improve the overall international competition of our innovative talents.The core of this paper is about the empirical study of training programmers "diversification and multi-levels". It provides an objective basis for the implementation of the necessity and feasibility through case studies and a large sample survey.The "diversification and multi-levels" training programmer was implemented at the 2003 （graduated in 2007） students majoring mathematics and applied mathematics at ECNU. A total number of 137 students had enrolled in 2003, and 42 of them had entered Science Base Class. 71 chose teacher education series and base series, 59 chose teacher education series and application series, 7 chose based series. Among 123 graduates who found jobs, 54 entered ordinary schools, 4 entered vocational schools, 17 were in the non-educational units, including: IT companies, banks, insurance, securities, and consulting, 38 pursued further study, 10 went abroad. The proportion for ordinary schools was 43.9%, vocational schools 3.25%, non-education unit 13.82%, further study 30.89%. Students with good math background （esp. students with master’s degree） are very popular in key schools. In short, the employment situation is "diversified". The training model with three different objectives （basis, application, teacher education） meets the social requirements for the math department of normal university.As for the problem of "multi-levels", we conducted four large-scale testing and investigation from 2001 to 2003 with the purpose of answering whether the "University Expansion," can guarantee the basic quality of math teaching. The universities participated were: ECNU, Hang Zhou Teachers College, Nan tong Teachers College and Sichuan Teachers College, which represented two different levels. The numbers of samples respectively were: ECNU 517, Hang Zhou Teachers College 249, Nan Tong Teachers College 402, and Sichuan Teachers College 167. Four investigations were about: 1. Questionnaire on the curriculum and the level at ECNU; 2. Examination of "mathematical analysis" at the end of the second semester from 2 universities; 3. Test of higher levels of understanding of students enrolled in 2001 from 4 colleges; 4. Survey on relevance of the result of college entrance examination and grade of basic courses at university.The survey was about the "diversification and multi-levels" training programmer and embodied "diversification" of the "the goal of elective courses." The results showed that the basic requirements of mathematics base courses can be basically met after the large-scale expansion. However, there was great gap between the colleges at the higher level, ECNU was much better than the other three, which could serve as an evidence of the essentiality of the "different levels" of teaching.Finally, the paper discussed the long-term dispute over the "normal" issue, especially on the problem of how to transform the "academic form of mathematics" to "form of education" which can be easily accepted by students. Besides, it made analysis about the arrangement of the curriculum of math education at some famous normal university in China, including ECNU.Of course, there are lots of deficiencies in this paper. For example, it lacks a detailed analysis of the condition of teachers at vocational high school. It doesn’t contain the data of Mathematics Teacher Education （Junior college level） in remote ethnic minority areas. I hope that more researches will be conducted in this area, so as to provide further practice and theory for the development of teacher education.更多还原