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1、浅谈初中数学教学中学生动手操作能力的培养数学知识来源于生活，又应用于生活，这些都是人类在动手操作过程中的沉淀和积累。新的课程标准重视“从学生已有的生活经验出发，使学生获得对数学知识的理解” ，强调以人为本的人文教育。动手操作，是发展学生思维，培养学生数学能力的有效途径，学生通过动手操作可以亲历亲受，提高学习效率，激发在学习过程中主动参与的热情及创新意识，增强求知欲望，优化思维品质。而且符合学生认知事物的心理状态，化抽象为具体。但在过去的教学中往往被忽视。如何在初中数学教学中培养学生的动手操作能力是我们每位初中数学教师必须重视的问题。 一、动手操作可以激发学生学习的兴趣 “兴趣是最好的老师”。兴
2、趣对学生的学习有着巨大的内驱作用。著名科学家爱迪生曾说过:“我从来没有做过一次偶然的发明，我的一切发明都是深思熟虑、严格实验的结果”。教学中多让学生拼一拼，摆一摆，折一折，剪一剪，量一量，画一画，想一想，说一说，给学生提供尽可能多的动手、动脑、动口的机会。动手操作是激发学生学习兴趣行之有效的最好方法。 例如，张文娟老师在讲轴对称时，让学生准备好剪刀、硬纸板等用具，让他们在课堂上自由发挥想象力，折叠剪出自己喜爱的图形，讨论欣赏。然后结合课本理解对称轴、对称点等概念，学生非常轻松地学到了知识。 fitted with exhaust started to thermal cracking. Car
3、efully heat the liquid to make it start to boil until liquid clarified further heated 1h. Liquid cooling in the distillation flask, funnel moving quantitative Samadhi n distillation distillation flask and rinse several times until the total solution volume is about 200mL in the retort. Note that Dis
4、tiller should be distilled in advance, wash the ammonia. Adjusting nitrogen lower end of the condenser of the distillation unit, so that it happens to come across bottom of the flask. This bottle pre 25mL sulfuric acid solution. Sodium hydroxide solution through the funnel 90mL Lysis solution after
5、alkali. Note funnel neck cannot be emptied to ensure sealing. Open the condenser tubes of condensed water, began distilling. In this process, ensure the amount of steam produced is constant. About 150mL 2030min collected the liquid in a volumetric flask, to stop distillation. Lowering of the volumet
6、ric flask, condenser tube left the surface, allow excess condensed water to drip into the bottle, and then rinsing with water condenser tube ends, water drip into the bottle, secured the release of ammonia into the volumetric flask quantitatively. Add water to the flask scale, shake well. Preparatio
7、n of standard curve for a group of at least five per cent of the standard reference solution of known concentration of ammonium group. Each standard solution through a straw draw 50mL respectively into a set of lOOmL in the Erlenmeyer flask. Learn 50mL, lOOmL conical bottle water in the other, for a
8、mmonium on the standard curve .二、动手操作可以使学生体会知识的升华 动手操作既动手又动脑，手脑并用，既开拓了思维想象空间，同时有助于学生从不同角度不同方位理解知识点，深刻体会数学的处处魅力，体会“处处皆学问”的道理。 例如，在学三角形全等时，张文娟和李大兵老师都让学生用两个全等三角形拼成不同的平面图形，观察图形的变化及各种不同的图形，理解全等三角形的性质，非常有效地激发了学生的兴趣，在玩与做的过程中掌握全等三角形的内在联系。总之，从简单到复杂，让学生能主动地进行观察、操作、推理、想象等探索过程，通过这样多次反复的实践探索活动，使学生们真正体会到“知识来源于生活实
9、践”。 当然，巩固练习也是数学教学中的一个重要组成部分。我们在教学中应根据初中学生的认知规律和思维特点培养学生的动手操作能力，让学生亲自动手操作(画标量拼推算猜)，把课堂上学到的数学知识与技巧、数学思想与方法用到解决实际问题当中来。这种方法不仅可以大大节约时间，提高解题效率，特别是在应考当中可给予学生很大的帮助。 三、动手操作可以发展学生思维 思维始于动作，动手操作可以使学生获得感性认识，为学生进行思维提供支柱。学生正处于具体形象思维向抽象思维的过渡时期，对于数学概念、定理、法则等抽象的内容不易理解和掌握，因此教学过fitted with exhaust started to thermal
10、cracking. Carefully heat the liquid to make it start to boil until liquid clarified further heated 1h. Liquid cooling in the distillation flask, funnel moving quantitative Samadhi n distillation distillation flask and rinse several times until the total solution volume is about 200mL in the retort.
11、Note that Distiller should be distilled in advance, wash the ammonia. Adjusting nitrogen lower end of the condenser of the distillation unit, so that it happens to come across bottom of the flask. This bottle pre 25mL sulfuric acid solution. Sodium hydroxide solution through the funnel 90mL Lysis so
12、lution after alkali. Note funnel neck cannot be emptied to ensure sealing. Open the condenser tubes of condensed water, began distilling. In this process, ensure the amount of steam produced is constant. About 150mL 2030min collected the liquid in a volumetric flask, to stop distillation. Lowering o
13、f the volumetric flask, condenser tube left the surface, allow excess condensed water to drip into the bottle, and then rinsing with water condenser tube ends, water drip into the bottle, secured the release of ammonia into the volumetric flask quantitatively. Add water to the flask scale, shake wel
14、l. Preparation of standard curve for a group of at least five per cent of the standard reference solution of known concentration of ammonium group. Each standard solution through a straw draw 50mL respectively into a set of lOOmL in the Erlenmeyer flask. Learn 50mL, lOOmL conical bottle water in the
15、 other, for ammonium on the standard curve .程加强直观演示、动手操作，使学生增加感性认识，在头脑中形成鲜明的表象，有利于他们对抽象数学知识的理解。 如;“角的大小比较”这节课，学生掌握了用量角器量角的度数及画角的一般方法。怎样画120度的角，多数学生都是用量角器和三角板画出来的，老师问:不用量角器，怎么画,学生立即带着问题进入愉快的操作中，很快就发现了两种画法:(1)用三角板的直角和一个30度的角拼起来。(2)用两个60度的角拼起来。学生通过自己的思考找到了方法，得到了成功的喜悦。接着教师再问;还有什么方法?这时学生积极性更高，争先恐后的又开始探究，
16、发现先画一个平角，在平角的基础上用三角板画一个60度的角(即用180度减去60度)。最后问你用三角板还能画出多少度的角(15的整数倍)。如此这样尽可能的给学生提供动手操作的机会，使学生思维得到发展、知识得到升华，学生的实践能力和思维能力都得到发展和提高。 因此在课堂教学中，多给学生提供动手操作的机会，鼓励学生求异创新，进一步开拓学生思路，学生在动手过程中既掌握了知识，也提高思维能力。 (三)实践活动四、动手操作必须使学生养成动手习惯，开发学生“再创造”潜能 定理：在同圆或等圆中,相等的圆心角所对的弧相等、所对的弦相等、所对的弦心距相等。实践出真知，实践是创新的摇篮，学生通过动手操作，既可以培养
17、解决问题的能力，又可以培养创新能力。传统的教学中，基本概念、基本知识常常是要求学生死记硬背。现在我们应积极引导学生通过动手操作，关注概念的实际背景与生成过程，使学生理解概念的来fitted with exhaust started to thermal cracking. Carefully heat the liquid to make it start to boil until liquid clarified further heated 1h. Liquid cooling in the distillation flask, funnel moving quantitative S
18、amadhi n distillation distillation flask and rinse several times until the total solution volume is about 200mL in the retort. Note that Distiller should be distilled in advance, wash the ammonia. Adjusting nitrogen lower end of the condenser of the distillation unit, so that it happens to come acro
19、ss bottom of the flask. This bottle pre 25mL sulfuric acid solution. Sodium hydroxide solution through the funnel 90mL Lysis solution after alkali. Note funnel neck cannot be emptied to ensure sealing. Open the condenser tubes of condensed water, began distilling. In this process, ensure the amount
20、of steam produced is constant. About 150mL 2030min collected the liquid in a volumetric flask, to stop distillation. Lowering of the volumetric flask, condenser tube left the surface, allow excess condensed water to drip into the bottle, and then rinsing with water condenser tube ends, water drip in
21、to the bottle, secured the release of ammonia into the volumetric flask quantitatively. Add water to the flask scale, shake well. Preparation of standard curve for a group of at least five per cent of the standard reference solution of known concentration of ammonium group. Each standard solution th
22、rough a straw draw 50mL respectively into a set of lOOmL in the Erlenmeyer flask. Learn 50mL, lOOmL conical bottle water in the other, for ammonium on the standard curve .推论1: 同弧或等弧所对的圆周角相等。龙去脉，加深对概念的理解，培养学生数学思维的严谨性。每节课，不论是代数还是几何课都有学生动手能力的培养，日积月累学生自然就养成良好的动手习惯。 分析性质定理及两个推论的条件和结论间的关系,可得如下结论:在多姿多彩的图形的
23、教学中，我们可以用三维动画制作成多媒体课件，立体、形象、直观地讲解几何体的各种要素。 （1) 与圆相关的概念：在“无理数”的教学中，用剪拼正方形的方法发现正方形的边长可以用我们没有学过的一种数来表示，从而引出无理数的概念。学生在自我探寻的过程中，同学们对无理数知识有了深刻认识，留下了更深的印象。活跃课堂气氛的同时，让知识真正地成为学生自己的东西。 五、强化学生动手能力，主动获取知识 动手操作会让学生轻松灵活地掌握知识，并学到掌握知识的方法和技能。新的课程标准指出:课堂教学是师生之间多向交流的复杂过程，教师是整个教学过程中的领导者，而学生应该通过老师的启发诱导主动地获取知识，这是提高课堂教学效果
24、的基点，运用学具、教具动手的方法，就是为学生创设一个活动、探索、思考的环境，使全体学生都参与探求新知识的活动。 (3)相离: 直线和圆没有公共点时,叫做直线和圆相离.1.动手目的必须明确 三三角函数的计算学生在动手之前要有明确的指导语，使学生知道要做什么。如:在教三角形的内角和时，先让学生猜想三角形三个内角之和为定值。让学生量出三角形三个内角的度数，然后把它们加起来，发现三角形三个内角之和为180度;再让学生用纸做一个任意形状的三角形，将fitted with exhaust started to thermal cracking. Carefully heat the liquid to m
25、ake it start to boil until liquid clarified further heated 1h. Liquid cooling in the distillation flask, funnel moving quantitative Samadhi n distillation distillation flask and rinse several times until the total solution volume is about 200mL in the retort. Note that Distiller should be distilled
26、in advance, wash the ammonia. Adjusting nitrogen lower end of the condenser of the distillation unit, so that it happens to come across bottom of the flask. This bottle pre 25mL sulfuric acid solution. Sodium hydroxide solution through the funnel 90mL Lysis solution after alkali. Note funnel neck ca
27、nnot be emptied to ensure sealing. Open the condenser tubes of condensed water, began distilling. In this process, ensure the amount of steam produced is constant. About 150mL 2030min collected the liquid in a volumetric flask, to stop distillation. Lowering of the volumetric flask, condenser tube l
28、eft the surface, allow excess condensed water to drip into the bottle, and then rinsing with water condenser tube ends, water drip into the bottle, secured the release of ammonia into the volumetric flask quantitatively. Add water to the flask scale, shake well. Preparation of standard curve for a g
29、roup of at least five per cent of the standard reference solution of known concentration of ammonium group. Each standard solution through a straw draw 50mL respectively into a set of lOOmL in the Erlenmeyer flask. Learn 50mL, lOOmL conical bottle water in the other, for ammonium on the standard cur
30、ve .三个内角撕下来，把三个内角拼在一起，发现所拼成的角是一个平角，接着让学生自己归纳三角形的内角和是180度。学生在轻松愉快的操作中得出结论;任意一个三角形的内角和都是180度。这样学生在动手中发现、思索、领悟、概括，在积极参与中主动获取新识。 2.动手过程中必须有序 在动手过程中要有条不紊、步骤明确、层层推进，这样对形成清晰的思维体系有很大帮助。学生的认知规律是先从图形开始到数的认识，再到符号表达，最后代数式的总结。 （1）二次函数的图象(抛物线)与x轴的两个交点的横坐标x1，x2是对应一沪科版七年级上册阅读与思考归纳推理一节课对正方形个数、表示N个奇数的和以及组成图形线段条数的解释就是
31、如此。(袁超英老师在开渠的走进数学大世界一课中有体现。) 104.305.6加与减（二）2 P57-60总之，动手操作能力的培养是学生学习数学、应用数学、从理论到实践的一个综合素质的实施过程。提高学生的动手操作能力，应培养学生运用“观察有方法、操作有动力、思考有依据”的思维方式深入分析问题、解决问题。这样既有利于把抽象的数学知识形象化、具体化，易于学生接受，又有利于学生自主学习，使其真正成为学习的主人，为学好数学奠定坚实的基础。 fitted with exhaust started to thermal cracking. Carefully heat the liquid to make
32、it start to boil until liquid clarified further heated 1h. Liquid cooling in the distillation flask, funnel moving quantitative Samadhi n distillation distillation flask and rinse several times until the total solution volume is about 200mL in the retort. Note that Distiller should be distilled in a
33、dvance, wash the ammonia. Adjusting nitrogen lower end of the condenser of the distillation unit, so that it happens to come across bottom of the flask. This bottle pre 25mL sulfuric acid solution. Sodium hydroxide solution through the funnel 90mL Lysis solution after alkali. Note funnel neck cannot
34、 be emptied to ensure sealing. Open the condenser tubes of condensed water, began distilling. In this process, ensure the amount of steam produced is constant. About 150mL 2030min collected the liquid in a volumetric flask, to stop distillation. Lowering of the volumetric flask, condenser tube left
35、the surface, allow excess condensed water to drip into the bottle, and then rinsing with water condenser tube ends, water drip into the bottle, secured the release of ammonia into the volumetric flask quantitatively. Add water to the flask scale, shake well. Preparation of standard curve for a group
36、 of at least five per cent of the standard reference solution of known concentration of ammonium group. Each standard solution through a straw draw 50mL respectively into a set of lOOmL in the Erlenmeyer flask. Learn 50mL, lOOmL conical bottle water in the other, for ammonium on the standard curve .