数学教学方法改革的总结与认识

（一）各种数学教学方法改革出发点相同，以先进的教学思想为依据 (a) a variety of mathematics teaching method reform, a common starting point based on the advanced teaching thought 自 20 世纪 80 年代起，新型数学教学方法频繁出现，它们看似形异，但背后有着共同的出 发点，即实现数学基础教育的目的，更好地为教学服务，实现有效教学，使学生获得全面 发展.研究者普遍认为，教学方法要实现革新，不只是形式的改变，更重要的是教学思想的 革新，否则只能“换汤不换药”.因此，在积极进行教学方法改革的同时，教育界也更加重 视教育理念的更新与完善，在吸收中国传统启发式教学思想的同时，借鉴西方先进的教学 理念与模式，走上符合中国实际的教学方法创新之路. Since the 1980 s, the frequency of new mathematics teaching method, they seem different, but behind have a common starting point, namely the realization of the aim of mathematics elementary education, better service for the teaching, realize the effective teaching, make students get all-round development. Researchers generally believed that teaching methods to achieve innovation, not only the form change, more important is the innovation of teaching ideas, otherwise only “in its form. Therefore, while actively reforming teaching methods, education also pay more attention to the update education concept and perfect, while absorbing Chinese traditional heuristic teaching thought, draw lessons from western advanced teaching concept and mode, to comply with Chinas actual teaching method innovation. 探究发现法是在布鲁纳的“发现学习”理论基础上进行的创新；问题式教学方法是以建构 主义学习理论作为支撑，并对“支架式教学模式”和“问题情境教学模式”进行本土化改 造而形成，如今已成为课堂教学方法的重要组成部分，在丰富教学内容、启迪学生积极思 维方面具有重要意义.合作学习、小组讨论等新型学习方式也对国内的数学教学方法改革产 生了影响，新课程改革倡导探究性学习，国务院颁发的关于基础教育改革与发展的决定 也专门提及了合作学习，并指出应“鼓励合作学习，促进学生之间相互交流、共同发展， 促进师生教学相长”8. To explore the discovery method is based on bruners “discovery learning“ theory on innovation; Problem-based teaching method is based on constructivism learning theory as the support, and the “scaffolding instruction model“ and the “problem situation teaching model“ to carry on the localization and form, has now become an important part of classroom teaching methods, in rich teaching contents, enlightening students positive thinking is of great significance. Cooperative learning, group discussion and new learning style has made an impact on domestic mathematics teaching method reform, new curriculum reform advocates inquiry-based learning, and the state council issued “on the decision of the basic education reform and development“ also singled out the cooperative learning, and points out that should be “encourages cooperative learning, promote the exchange between students and common development, to promote the teachers and students teaching is learning“ 8. 可以看出，国内新型的数学教学方法以先进的教学思想作为指导理念，在注重学生的主体 地位，促进学生的智能和情意发展，培养学生的参与、探究、合作意识，面向全体与针对 / / / 个体的协调等方面进行了不懈的努力，为实现培养全面发展的人作出了突出贡献. As you can see, the new mathematics teaching methods in advanced teaching thought as the guiding ideology, in pays attention to students main body status, promote the development of the students intelligence and emotion, cultivate the students consciousness of participation, explore, cooperation, coordination, etc, for the and for the individual has carried on the unremitting efforts, in order to realize cultivate has made a great contribution to the all-round development of people. （二）数学教学方法多样化的局面日渐形成 (2) the situation of mathematics teaching method diversification is formed 目前的数学教学方法种类众多，名称各异，有研究者提到了 24 种常用的数学教学方法，笔 者认为远不止这些.关于教学方法的多样化，笔者有如下几点认识. Many mathematics teaching method at present and different names, there are researchers mentioned 24 kinds of commonly used mathematics teaching method, the author thinks that is far more than that. About the diversification of teaching methods, the author has the following points. 1.教学方法是由八种基本教学方法构成，基本教学方法经过恰当组合即可成为一种新型教 学方法，这是教学方法多样性的物质基础 1. The teaching method is composed of eight basic teaching method, combination of basic teaching method properly can be a new type of teaching method, which is the material basis for the diversity of teaching methods 这八个要素是具体的数学教学方法，课堂上使用的多是这八种基本教学方法的组合排列.笔 者认为，一般教学方法即为对这八种基本方法有针对性的组合，这是教学方法多样性的客 观基础. The eight elements is concrete mathematics teaching method, classroom use is the eight basic arrangement of teaching method. The author thinks that, in general teaching methods is the basic methods of the eight kinds of targeted combination, it is the objective basis diversity of teaching methods. 这种观点首先能够帮助我们分析各种新型教学方法的实质，把握方法的核心及重要环节， 如，讲授法即由讲述法、练习法等基本方法构成；自学辅导法是以自学法、辅导法为主的 一种综合性的教学方法.其次，这种观点能够帮助我们更清楚地理解“教有法，无定法”的 道理，树立多样化及优化意识，创建符合实际的教学方法，避免陷入照搬照抄的误区.另外， 此种观点在构建教学方法体系方面也提供了可借鉴的思路. This point of view, first of all, can help us to analysis the essence of all kinds of new teaching methods, grasp the method of core and important link, such as, namely from teaching method, practice method and so on basic method; Self-study tutoring method was mainly used for self- / / / study, coaching method in a comprehensive teaching method. Secondly, this view can help us understand more clearly the word of “teach mechanically, wuding method“, sets up the diversity and optimization consciousness, create a practical teaching method, avoid copying the erroneous zone. In addition, this view in constructing teaching method system also provides a reference for train of thought. 2.教学方法的多样性体现了教学理论的多样性，是教学理论争鸣与变迁的结果，这是教学 方法多样性的理论基础 2. The diversity of teaching methods reflect the diversity of teaching theory, is the result of the teaching theory schools of thought contend and change, this is the diversity of teaching methods of theoretical basis 教学方法都以一定的教学思想作为依据，其本身并无价值，先进、落后与否在于其背后的 指导思想.如果指导思想先进，此法即先进，符合教育规律；反之则落后，违背教育规律.因 此，教学思想改革是深化教学方法改革的内在动力之一.这一点我们可从对讲授法的争鸣中 得以领会.讲授法本身并无问题，奥苏贝尔以其理论作为支撑，他认为学生的接受学习同样 可成为有意义的学习.教师运用讲授法时如能贯彻启发式教学思想的要求，注意与学生的思 维与情感交流，同样可以取得奇效；如果教师“满堂灌” ，搞“一言堂” ，忽视学生真正的 学习需要，此时讲授法就应摒弃.因此，要实现教学方法的先进性，就必然要实现教学思想 的先进性，两者是互为表里的关系.从这个意义来讲，教学方法的表面繁荣反映了教学理念 的争鸣与完善. Teaching methods with a certain teaching ideas as the basis, its itself has no value, advanced and backward or not lies in its guiding ideology behind. If advanced guiding ideology, this method is advanced, conform to the law of education; Behind conversely, contrary to law of education. Therefore, teaching reform is one of the inner motive power of deepening the reform of teaching methods. As we can from the teaching method in the schools of thought contend to grasp. Teaching method itself is no problem, ausubel with its theory as the support, he think students accept learning can also be meaningful learning. When the teacher USES the teaching method can implement the heuristic teaching idea, pay attention to the thinking and emotional communication with students, also can get surprise effect; If teachers “cramming education“, “, neglecting the students real learning needs, the teaching method should be rejected. Therefore, in order to realize the advantage of teaching methods, they can expect to achieve advanced teaching ideas, the two are mutually exterior-interior relationships. Will tell from this meaning, reflects the teaching methods of the surface prosperity of schools of thought contend and improvement of the teaching idea. 有研究者指出，教学方法研究中争鸣不够，笔者对此稍有异议.教学理念实现了从以教师 为中心到以学生为中心的突破，教学方法必然发生变革.从以前强调使用讲授法到现在对多 种教学方法的探究就是例证.为实现学生的全面发展，数学教育界在不同层面进行了努力， 如，为培养学生探究发现能力提出的发现探究式教学方法；为培养学生分析与解决实际问 题的能力，树立生活处处有数学的意识提出的问题解决式教学方法；为培养学生的数学思 想方法意识，提高解题技巧及灵活性提出的 MM 教育模式，还有旨在培养学生反思能力的 / / / 反思式教学方法，等等.因此，笔者认为，承认教学方法的多样性也就承认了教学理论的多 样性，而接受教学理论的多样性势必也就要接受教学方法的多样性，两者互为表里，这是 教学方法多样性的理论基础. Researchers pointed out that the teaching method research in schools of thought contend is insufficient, the author was slightly. teaching idea realized from teacher-centered to student- centered, teaching methods is bound to change. Emphasis on using the teaching method from before to now explore is one example of a variety of teaching methods. In order to achieve the comprehensive development of students, the mathematics education at different levels, such as, to cultivate students exploring discovery discovery of exploratory teaching method is put forward; To cultivate students ability to analyze and solve practical problems, set up the life everywhere has the consciousness of mathematics is put forward the question solution type teaching method; To cultivate the students consciousness of mathematics thought method, improve the problem solving skills and flexibility of MM education pattern, and aimed at training students reflection ability of reflection type teaching method, and so on. Therefore, the author thinks that, to recognize the diversity of teaching methods is the diversity of the teaching theory, and to accept the diversity of teaching theory is bound to accept the diversity of teaching methods, each other, this is the diversity of teaching methods of theoretical basis. 另外，教学作为一个开放式系统，是培养人的实践性活动，必然受到多种因素的影响与制 约，教学活动的不可复制性成为教学方法多样性的实践基础. As an open system, in addition, the teaching is to cultivate peoples practical activities, inevitably influenced by various factors and restriction, no copy of teaching activities become the basis of the practice of diversity of teaching methods. （三）数学教学方法的开放性成为必然 (3) the openness of mathematics teaching methods become inevitable 教学要考虑到各种教学方法的功能及利弊，考虑到教学活动的主客体条件，再加上教学过 程的不可预知性，使得采用多样的教学方法，并要根据客观条件适时调整教学方法已成为 大家的共识.数学教学方法的开放性成为必然. Teaching should take into account the functions and advantages and disadvantages of all kinds of teaching methods, considering the teaching activity of subject and object conditions, coupled with the unpredictability of the teaching process, adopting diverse teaching method, and according to the objective conditions timely adjust teaching method has become the consensus of people. The open method of mathematics teaching become inevitable. 21 世纪后的研究并没有提出多少新型数学教学方法，而是努力寻找已有数学教学方法的优 化组合，利用其各自特征来实现高效率教学与有效教学.目前，学者对于高效率教学与有效 教学仍在积极探索，这些研究并没有提出具体的、带有个性色彩的数学教学方法，而重在 对现有数学教学方法的深入挖掘与功效开发，旨在走上“广积粮”而不是“广撒网”的道 / / / 路.从系统的观点来看，数学教学是一个开放的体系，只有保持数学教学方法的开放性，才 能符合数学教学的实际，避免流于形式、陷入机械性的误区，对于提升数学教学质量，实 现有效教学至关重要. After study didnt ask how much the new 21st century mathematics teaching method, but tried to find out the optimum combination for mathematics teaching method, using their own characteristics to achieve efficient teaching and effective teaching. At present, scholars for effective teaching and effective teaching are still in the positive exploration, these studies did not mention a specific, with a personality color math teaching methods, and focuses on the existing mathematical teaching method effect of in-depth mining and development, and aimed at the “wide accumulate grain“ where not in the way of “the wide net“. From the system point of view, mathematics teaching is an open system, only keep the open method of mathematics teaching, in order to conform to mathematics teaching actual, avoid to become a mere formality, mechanical traps, for improving the quality of mathematics teaching, realize the effective teaching is very important. （四）数学教学方法的理论研究采用“理论思辨+实践研究”相结合的模式日渐明显，研究 方法日趋科学 (4) mathematics teaching method theoretical research by speculative “theory + practice research“ combined pattern of increasingly obvious, increasing scientific research method 数学教学方法的传统理论研究一直采用理论思辨加上经验总结的方法，通常意义上的献计 献策往往停留在一般层面上的讨论，没有给出明确的教学步骤与程序，使一些先进理念在 运用中并没有找到生存的土壤，理论研究与实际教学的鸿沟依然存在， “理论一回事，实际 又是一回事”成为理论研究被诟病之处. Mathematics teaching method of the traditional theory research has been the theoretical speculation and experience summary method, usually in the sense of zhenhai tend to stay in the general level of discussion, no clear teaching steps and procedures, make some advanced concepts in use and could not find the survival of the soil, the theory research and practical teaching gap still exists, “theory is one thing, actually is one thing“ as was worst in theory research. 目前出现的实践研究为我们寻求理论研究的突破提供了重要的思路借鉴.实践研究多在硕士 毕业论文中出现，往往从两个角度进行研究：一种是探究课堂常用的数学教学方法，指出 其弊端，给出建议，但文献不多，如陈海娃的研究；多数是针对具体的数学教学方法（如 探究式、启发式教学方法）进行实践研究，旨在分析其在具体应用中存在的不足，给出改 进建议，如崔丽琴的研究.这种研究模式在一定程度上弥补了理论研究的缺陷，具有实际价 值，但也因研究本身的方法问题，使得结果并不是很深入、具体，需要有所改进.行动研究 的呼声日起，一线数学教师能否反思自己教学中的不足，并根据相关研究提出具体的、有 操作性意义的数学教学方法，我们拭目以待. The practice of the present study to seek theoretical research breakthrough for us to provide the important ideas for reference. The practice research in the masters thesis, often study from two / / / aspects: one is to explore the classroom mathematics teaching methods, and points out its defects, Suggestions, but few literature, such as Chen Haiwa research; Mostly for specific math teaching methods (such as inquiry, heuristic teaching method carries on the practice research, aiming to analyze the shortcomings in the course of practical application, Suggestions for improvement are given, such as Cui Liqin research. This research model to some extent make up for the shortcomings in the theoretical research and practical value, but also for research method itself, the result is not very thorough, concrete, needs to be improved. The call for action research, a line of mathematics teachers can reflect on their teaching the insufficiency, and according to the related study and put forward specific and operational significance of m