（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xx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 China's 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 bruner's "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 student's 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

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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.