数学教学效率研究

【作者】 王光明；

【导师】 单墫；

【作者基本信息】 南京师范大学 ， 数学课程与教学论， 2005， 博士

【摘要】 教学要为学生的学服务,教学效率不仅体现于学生掌握知识与学好当堂内容的近期学习效果上,还体现于学生获得发展的远期学习效果上,数学教学效率高低不取决于教师打算教给学生什么,而取决于学生实际获得了什么发展。教学效率体现在两个方面:(1)在学生的时间投入方面,指能够充分利用时间,全身心、积极、主动地参与数学学习。(2)在数学教学结果方面,指近期的学习效果——认知成绩与远期的学习效果——理性精神、效率意识、良好认知结构和数学学习能力。教学效率是相对概念。同样的学习效果,学生用时间较少,则教学效率高:同样的学习时间,学习效果好而且多样,则教学效率高。 数学教学效率研究对于数学教育的贡献包括:解决现实问题的需要、比较教育研究的需要、数学教育发展形势的迫切需要。国内学者试图从对教学效率的测量与评价出发,界定教学效率,但不同程度存在试图套用自然科学意义下关于效率的认识,演绎关于教学效率的认识的问题。的确,教学效率是客观存在的,但评价的标准则因依赖教学观念会具有主观性。而且,影响教学效率的因素不仅多,而且错综复杂。因此,教学效率测量与评价不可能达到自然科学意义下完全的客观化,而只能做到尽量科学化。但是,认为只有定量化才是科学化的看法是片面的。教学效率更适宜运用优、良、中差等做评价。 主要结论包括:(1)数学教学效率高低不取决于教师打算教给学生什么,而取决于学生实际获得了什么发展。(2)教学效率思想发展的主线为关注教师教的效率,逐步到关注学生学的效率,而目前更关注促进学生发展的效率。(3)我国学生数学双基与数学认知基础并不厚实。(4)我国数学教学效率亟待提高。(5)理性精神就是对逻辑、自由、普遍法则的追求和超越外在欲望的干扰过程中所体现出来的精神。(6)数学教育让学生形成理性精神是指在数学教学以及数学学习活动中,通过对数学内在理性的感悟以及对数学家的理性精神的感受,学生所获得的精神层面的文化与价值体验。(7)数学教学的应然效果包括塑造学生的理性精神、培养学生的效率意识、帮助学生构建良好的认知结构、促进学生对数学的深刻理解与指导学生学会学习等方面。(8)重视数学的内在价值主要是指在数学学习活动中重视数学对思维的训练。(9)数学教学要培养学生外源建构、内源建构和辩证建构思维能力。(10)数学认知理解分为操作性、关系性和迁移性理解三种水平。(11)在我国中小学数学教学中,虽然学生投入了很大精力,教师费了很大功夫,但学生对知识的理解水平远远没有达到深刻理解。(12)数学教师对数学专业与教育专业的理解各存在操作性、关系性和创造性三种水平。(13)数学教师对数学专业与教育专业的理解水平是影响教师教学效率的重要因素。(14)只有那些自我评价学习效率高的学生对数学与数学教师的评价才高。(15)在高的教学效率评价标准下,数学教学效率同样可以提高。(16)无所不适、无所不能的某种高效率数学教学方式是不存在的。(17)局限于技术思维是教学效率研究的大忌。(18)在认知教学中,高效率教学注重思维的教学,注重数学教学中的理解问题,注意帮助学生构建良好的认知结构。(19)立足教学效率视角,要辩证分析我国数学教育的成绩和不足。(20)既涉及学生情感参与,又涉及学生思维积极参与,才能保证数学教学的高效率。(21)数学教学效率的理论基础并非仅是西方的某些主义,而是那些所有可以为数学教学效率研究带来启迪的国内外的相关理论与相关学科的知识。(22)要用教育中的各种“主义”帮助我们思想和深入思考,而不是僵化我们的思想。(23)提高数学学习效率需要学生有先进的观念和良好的习惯。(24)数学教学与其说激发求知欲,不如说激发求识欲。更多还原

【Abstract】 Teaching should serve for the study. Teaching efficiency not only embodies short-term study result, but also embodies long-term study result. The short-term study result is acquiring and grasping the knowledge. The long-term study result is what student acquires. Mathematics teaching efficiency is not decided by the teacher who wants to teach student what, but decided by the student who acquires something finally. We can understand the concept of teaching efficiency from two dimensions. The first dimension is about the time that student used. This dimension means that the student can make full use of the time and take an active part in mathematics learning. The second dimension means the result ofmathematics teaching, which embodies short-term study result-cognitive score and long-termresult-the spirit of rationality, the consciousness of efficiency, reasonable cognitive structure and theability of mathematics learning. Teaching efficiency is a relative concept. The student who uses less time and has the same result can be called high efficiency. The student who uses the same time and has better and various results can also be called high efficiency.The contribution that mathematics teaching efficiency study to educate for mathematics includes: the need of resolving realistic problem, the need of comparative study and the urgent need of the development of mathematics education. The local scholars try to define the concept of teaching efficiency from surveying and evaluation. This method more or less tries to imitate the view of natural science which about efficiency, and deduce the problem of the cognition concerning teaching efficiency. Really, the concept of teaching efficiency exists objectively, but the standard of evaluation has the subjectivity because of the view of teaching. Moreover, the factors which affect teaching efficiency are not only multiple but also complicated. So, the surveying and evaluation of teaching efficiency is impossible to attain the natural science meaning that is completely objective and pure. We can only make our efforts to make it more scientific. But the view that only quantitative analysis is scientific is one-sided and over-simplified. So we had better use "advanced, high, intermediate, low" to evaluate teaching efficiency.The main conclusion includes: (1) Mathematics teaching efficiency is not decided by the teacher who wants to teach student what, but decided by the student who acquires something finally. (2) Teaching efficiency thought is developed form the concerning about teachers’ efficiency in the process of teaching, then students’ efficiency in the study, and now we pay more attention to students’ development efficiency. (3) Students’ mathematics "double bases" and mathematics cognition base are not solid. (4) Mathematics teaching efficiency should be highly improved in China. (5) The spirit of rationality is the spirit when people can exceed outer-want in the pursuit of logic, freedom and universal principle. (6) That mathematics education makes students develop rationality spirit means that students can feel the inner-rationality of mathematics and rationality spirit of mathematicians and they can acquire the culture on the level of spirit and experience in the mathematics study. (7) The effect of mathematics teaching should include: develop students’ rationality spirit, develop students’ efficiency consciousness, help students construct good cognitive structure, help students have a fundamental understanding toward mathematics and help them learn how to study. (8) We should pay more attention to mathematics inner-value, which means that we should train students’ thought in mathematics study. (9) Teaching of mathematics should develop students’ internal construction, external construction ability and the ability to construct thinking dialectically. (10) Cognitive understanding in mathematics has three kinds: operational understanding, relative understanding and transferred understanding. (11) Although both students and teachers make efforts and use much time, students’ understanding toward knowledge can not attain the fundamental level. (12) The mathematics teachers’ understanding on the mathematics and education has three levels: operational, relative, creative understanding. (13) The mathematics teachers’ understanding level on the mathematics and education is the main factor which affects teachers’ teaching efficiency. (14) Only the students who think their mathematics learning efficiency is high have high appraisal of mathematics and their teachers. (15) With high standard of evaluation about teaching efficiency, mathematics teaching efficiency can also be improved. (16) There is no universal method that can improve the mathematics teaching efficiency. (17) The thought that confine to technology is a big problem in the study of teaching efficiency. (18) In cognitive teaching, high-efficiency teaching attaches importance to thought teaching, understanding and constructing better cognitive structure. (19) From the teaching efficiency point of view, we should analyze the advantages and defects of our country’s mathematics education dialectically. (20) What ensures high-efficiency in mathematics teaching is students emotional and active thinking involvement. (21) The theoretical base of mathematics teaching efficiency is not some doctrine of mathematics education from the west, but some home and abroad related theories and some related subjects knowledge that can help us study the mathematics teaching efficiency. (22) We should use various "doctrines" to help us think deeply, not to rigidify our thought. (23) Students need advanced notion and good habits to improve mathematics study efficiency. (24) Mathematics teaching would rather inspire the want to grasp knowledge than inspire the want to recognize how to do it.更多还原