初中数学中的数学思想与方法的教学实践
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摘要
相对于数学知识的呆板而言，数学思想方法更富有生命的味道，数学知识是结果，而数学思想方法关注结果的形成过程；相对于数学知识的以文字、符号、图形等外显的形态直接记录下来的存在方式，数学思想方法则常常以内隐的形式存在于概念、公式、法则、定理的形成过程和问题解决的过程之中；数学思想方法是比数学知识处于更高层次上的知识，如果用把知识比作钥匙，那么，数学知识开启的是某一领域的大门，而数学思想方法可以开启不同领域的大门，比数学知识更富有指导意义。学习数学思想和方法使得学科更容易理解，学习数学思想和方法有利于记忆，学习数学思想和方法有利于促进学生的数学认知结构的发展与完善，数学思想、方法是联结中学数学与高等数学的一条红线。
初中数学中的重要数学思想与方法包括化归思想与方法，符号化、方程与函数思想，数形结合思想，分类讨论思想。影响初中数学中的数学思想与方法的形成因素有知识因素、思维因素、心理因素等。初中数学中数学思想与方法的形成包括以下渠道：在概念产生中体验，从结论推导中体验，从问题发现中体验，从方法思考中体验，从规律揭示中体验。
本文指出渗透是数学思想和方法教学的主要方式，分析了不同阶段的渗透教学，并列举了两个案例：剖析有理数一章的数学思想和方法，及其渗透方案；分析学生从感悟数形结合的思想方法，到灵活运用的过程中的教学措施。在此基础上，本文总结了初中数学中的数学思想与方法渗透的基本原则：揭示渗透，“潜”“显”结合的原则，循序渐进，螺旋上升的原则，注重过程，适时渗透的原则，及时小结，系统归纳的原则，问题解决，突出深化的原则，尊重差异，分层教学的原则，源于知识，回归知识的原则。
Mathematics method of thinking opposite to starched mathematics knowledge is fuller of vitality, mathematics knowledge is a result, but mathematics method of thinking pays attention to the formation of the result; mathematics knowledge is recorded down with letter, sign, sketch...etc explicit esse,but mathematics method of thinking usually tacitly exsits in the formation of concept, formula, rule, axioms and the process of problem-solving; mathematics method of thinking is the knowledge to be placed in the higher than mathematics knowledge, if we assimilate knowledge to a key, then, mathematics knowledge opens the door of a certain realm, but mathematics method of thinking could open the door of the different realm. Studying mathematics method of thinking could make course comprehended more easily, studying mathematics method of thinking could be beneficial to the memory, studying mathematics method of thinking could be beneficial to promote the developing and perfect of students' cognitive structure, mathem
atics method of thinking is a red line that coupling high school mathematics and advanced mathematics.
Important mathematics method of thinking of junior high school include with transform, symbolism, equation and function, numeral-form combination, classification discussion. The cause of affecting formation of junior high school mathematics method of thinking include with knowledge factor, thought factor, mentality factor etc.. In junior high school mathematics, the formation of mathematics method of thinking includes with the below outlet:experiences in concept producing, experiences from the conclusion deducesing, experiences from the problem discovering, experiences from the method considering, experiences from the regulation announcing to public.
This text considers that permeation teaching is the main way of mathematics method of thinking's teaching,and analyzes permeation teaching of the different moment, particularizes two individual cases example: anatomizes mathematics method of thinking of the chapter cleping "rational number" , and the project of its permeation teaching; anatomizes the teaching measure of making students from
feeling numeral-form combination method of thinking, to agile using it. On this foundation, this text sums up the basic principle of permeating mathematics method of thinking in junior high school mathematics: Announce to public and permeate," show"and " hidden" combinative, follow the sequence and advance gradually, spiral raising, make a point of the process, permeat on time, sum in time, system induce, problem solving, outstanding and deep, respect difference, layering teaching, come from knowledge, return to knowledge.
初中数学中的重要数学思想与方法包括化归思想与方法，符号化、方程与函数思想，数形结合思想，分类讨论思想。影响初中数学中的数学思想与方法的形成因素有知识因素、思维因素、心理因素等。初中数学中数学思想与方法的形成包括以下渠道：在概念产生中体验，从结论推导中体验，从问题发现中体验，从方法思考中体验，从规律揭示中体验。
本文指出渗透是数学思想和方法教学的主要方式，分析了不同阶段的渗透教学，并列举了两个案例：剖析有理数一章的数学思想和方法，及其渗透方案；分析学生从感悟数形结合的思想方法，到灵活运用的过程中的教学措施。在此基础上，本文总结了初中数学中的数学思想与方法渗透的基本原则：揭示渗透，“潜”“显”结合的原则，循序渐进，螺旋上升的原则，注重过程，适时渗透的原则，及时小结，系统归纳的原则，问题解决，突出深化的原则，尊重差异，分层教学的原则，源于知识，回归知识的原则。
Mathematics method of thinking opposite to starched mathematics knowledge is fuller of vitality, mathematics knowledge is a result, but mathematics method of thinking pays attention to the formation of the result; mathematics knowledge is recorded down with letter, sign, sketch...etc explicit esse,but mathematics method of thinking usually tacitly exsits in the formation of concept, formula, rule, axioms and the process of problem-solving; mathematics method of thinking is the knowledge to be placed in the higher than mathematics knowledge, if we assimilate knowledge to a key, then, mathematics knowledge opens the door of a certain realm, but mathematics method of thinking could open the door of the different realm. Studying mathematics method of thinking could make course comprehended more easily, studying mathematics method of thinking could be beneficial to the memory, studying mathematics method of thinking could be beneficial to promote the developing and perfect of students' cognitive structure, mathem
atics method of thinking is a red line that coupling high school mathematics and advanced mathematics.
Important mathematics method of thinking of junior high school include with transform, symbolism, equation and function, numeral-form combination, classification discussion. The cause of affecting formation of junior high school mathematics method of thinking include with knowledge factor, thought factor, mentality factor etc.. In junior high school mathematics, the formation of mathematics method of thinking includes with the below outlet:experiences in concept producing, experiences from the conclusion deducesing, experiences from the problem discovering, experiences from the method considering, experiences from the regulation announcing to public.
This text considers that permeation teaching is the main way of mathematics method of thinking's teaching,and analyzes permeation teaching of the different moment, particularizes two individual cases example: anatomizes mathematics method of thinking of the chapter cleping "rational number" , and the project of its permeation teaching; anatomizes the teaching measure of making students from
feeling numeral-form combination method of thinking, to agile using it. On this foundation, this text sums up the basic principle of permeating mathematics method of thinking in junior high school mathematics: Announce to public and permeate," show"and " hidden" combinative, follow the sequence and advance gradually, spiral raising, make a point of the process, permeat on time, sum in time, system induce, problem solving, outstanding and deep, respect difference, layering teaching, come from knowledge, return to knowledge.
引文
[1] 袁小明．数学思想发展简史．北京：高等教育出版社，1992．
[2] 解恩泽，赵树智．数学思想方法纵横论．北京：科学出版社，1987．
[3] 黄翔．数学方法论选论．重庆：重庆大学出版社，1996．
[4] 郑毓信．数学方法论．广西：广西教育出版社，1991．
[5] 朱成杰．数学思想方法教学研究导论．上海：文汇出版社，1998．
[6] 徐利治．数学方法论选讲．武汉：华中理工大学出版社，1988．
[7] 张奠宙，过伯祥．数学方法论稿．上海：上海教育出版社，1996．
[8] (美)莫里斯·克莱因．古今数学思想．上海：上海科学技术出版社，2002．
[9] 李继闵．东方数学典籍《九章算术》及其刘徽注研究．西安：陕西人民教育出版社，1990．
[10] 王培德．数学思想应用及探究——建构教学．北京：人民教育出版社，2003．
[11] 梁法驯．数学解题方法．武汉：华中理工大学出版社，1995．
[12] 李文林编．数学史教程．北京：高等教育出版社，1999．
[13] 郑毓信，肖柏荣，熊萍．数学思维与数学方法论．成都：四川教育出版社，2001．
[14] 中华人民共和国教育部．全日制义务教育数学课程标准．北京：北京师范大学出版社，2001．
[15] 朱成杰．关于数学思想方法教学的几点思考．数学通讯2004(9)．
[16] 路莎·彼得．无穷的玩意．南京：南京大学出版社，1985．
[17] (日)米山国藏．数学的精神、思想和方法．成都：四川教育出版社，1986．
[18] 钱佩玲，邵光华．数学思想方法与中学数学．北京：北京师范大学出版社，1999．
[2] 解恩泽，赵树智．数学思想方法纵横论．北京：科学出版社，1987．
[3] 黄翔．数学方法论选论．重庆：重庆大学出版社，1996．
[4] 郑毓信．数学方法论．广西：广西教育出版社，1991．
[5] 朱成杰．数学思想方法教学研究导论．上海：文汇出版社，1998．
[6] 徐利治．数学方法论选讲．武汉：华中理工大学出版社，1988．
[7] 张奠宙，过伯祥．数学方法论稿．上海：上海教育出版社，1996．
[8] (美)莫里斯·克莱因．古今数学思想．上海：上海科学技术出版社，2002．
[9] 李继闵．东方数学典籍《九章算术》及其刘徽注研究．西安：陕西人民教育出版社，1990．
[10] 王培德．数学思想应用及探究——建构教学．北京：人民教育出版社，2003．
[11] 梁法驯．数学解题方法．武汉：华中理工大学出版社，1995．
[12] 李文林编．数学史教程．北京：高等教育出版社，1999．
[13] 郑毓信，肖柏荣，熊萍．数学思维与数学方法论．成都：四川教育出版社，2001．
[14] 中华人民共和国教育部．全日制义务教育数学课程标准．北京：北京师范大学出版社，2001．
[15] 朱成杰．关于数学思想方法教学的几点思考．数学通讯2004(9)．
[16] 路莎·彼得．无穷的玩意．南京：南京大学出版社，1985．
[17] (日)米山国藏．数学的精神、思想和方法．成都：四川教育出版社，1986．
[18] 钱佩玲，邵光华．数学思想方法与中学数学．北京：北京师范大学出版社，1999．