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1、数学解题能力问题与方法大全1.其他学科中部分教师患有数学解题能力贫乏症 1. Part of the teachers in other subjects suffering from poor mathematics problem-solving ability 在教学实践中，笔者常遇到计算机、物理、化学和地理等学科的教师向数学教师请教一些问题，这些问题看似其他学科的问题，其实都可以转化为数学问题.一些老师不能将问题转化为数学问题;一些老师能转化为数学问题，却不能用数学方法解答.尽管教师常给学生讲“数理不分家”，事实上，数学教师不会解物理题，物理教师不会解数学题在中学很普遍，既能主讲数学又
2、能主讲物理的教师很少.像前面提到的问题，物理教师都知道是二面角问题，却不能求出二面角的大小.原因在于这些教师患有数学解题能力贫乏症，缺乏必要的数学解题能力. In the teaching practice, the author often encounter computer science, physics, chemistry and geography teachers to mathematics teacher consult some problems, these problems seem to other disciplines, actually can be conv
3、erted to mathematical problems. Some teachers cant convert problems into math problems; Some teachers can be converted into math problems, but I cant use mathematical methods to solve. Although teachers often give students speak mathematical separation, in fact, mathematics teachers will not solve p
4、hysics problem, not mathematical problem solving of physics teachers in middle school is very common, both can on mathematics and lectures on physics teachers rarely can. As mentioned earlier, all know is dihedral Angle problem of physics teachers, but cant find out the size of the dihedral Angle. T
5、he reason is that the teachers had poor mathematics problem-solving ability, lack of necessary mathematics problem-solving ability. 2.应试教育使数学教师患有知识狭窄症和思维僵化症 2. The test education makes teachers of mathematics with knowledge narrow and rigid thinking disorder 教师时刻把握高考命题规律，关注各个知识点命题概率的大小，各类考试题得分的难易程度，
6、甚至总结出常见题型的解题方法和解题程序，三面角公式早已忘记，积淀下来的唯一技能就是解高考题，从而患上了知识狭窄症.另外，高考试题中的二面角问题都可以用常规方法解答，考题都给出图形，条件中既有边的数据，也有角的大小.而此问题没有图形，也没有边的数据，仅知两个二面角的大小，和高考试题模型不同，所以，一旦教师患上思维僵化症，精于解高考题的数学老教师就不及年轻的物理教师的思维活跃，固定的高考试题解答模式面对新问题就苍白无力. Moments grasp the university entrance exam proposition rule, teachers pay attention to th
7、e size of the probability of each knowledge point proposition, to the difficulty of the various types of test scores, and sums up the common questions of problem solving method and the problem solving process, three sides Angle formula had forgotten, is the only skill accumulation down solutions for
8、 the college entrance examination questions, so as to develop the knowledge stenosis disease. In addition, the dihedral Angle problem in test solutions, can use the general method of examination questions are given graph, the conditions of both side of the data, also has the size of the Angle. :/ An
9、d this problem not graphics, also does not have the edge data, only two size of the dihedral Angle, and the test model is different, so, once the teacher to develop thinking is rigid, skilled in college entrance examination questions of mathematics old teacher is not as good as young physics teacher
10、s active thinking, test solutions for the fixed mode in the face of the new problem is pale. 3.膜拜教育思想和理念，教研员患有专业知识荒芜症 3. Worship education thoughts and ideas, research staff with professional knowledge and disorder 教研员既是一线教师的指导者，又是教育新思想、新理念的传播者，本是素质教育的急先锋.为什么也不能解答这个问题呢,原因在于只重视教育理论和方针的吸收和传播，忽视了对数学本身的
11、钻研.一些教研员对心理学、教育学和数学教育等理论非常熟悉，甚至能写出诗一般的教育论文，让中学教师赞叹不已.但是，一些教研员和教育专家贫乏的数学素养也让人惊诧，例如，一位小学教研员说“他不会解答初中数学题”，一位知名数学教育专家在报告中竟然说出“直线与双曲线有4个交点”.曾有人问:“你们不懂数学，怎样搞数学教育研究,如何指导一线教师,”他们回答:“数学和数学教育是两个不同学科，不懂数学不会影响搞数学教育研究;足球教练不会踢球，照样当教练，不懂数学难道就不能指导数学教师吗,”可见，他们对教育思想和理念盲目膜拜，完全割裂数学与数学教育的关系.有些教研员过去迷恋目标教学，后来倡导研究性学习，现在又讴歌
12、新课标精神，整天“理论不离口，方针到处吼”，而对数学中的问题漠不关心，甚至不屑或不敢过问数学问题.虽然人们称其为“专家”，其实他们并非数学人. Research staff is both a glimmer of teachers guidance and education new ideas, new ideas, this is the pioneer to quality-oriented education. Why cant solve this problem? Because only attaches great importance to the education th
13、eory and policy of the absorption and transmission, and overlooked the study of mathematics itself. Some research staff on the psychology, pedagogy and theory of mathematical education are very familiar with, even can write poetic education, middle school teachers. However, some research staff and e
14、ducation experts have meager math literacy also let people surprise, for example, a primary research staff said he will not answer the junior high school math problem, a leading mathematics education experts saying in the report and hyperbola has four lines. Once someone asked: how do you dont under
15、stand mathematics, mathematics education research? How to guide a teacher? They said: mathematics and mathematics education are two different disciplines, dont understand the math does not affect the mathematics education research, the football coach wont play, so when the coach, dont understand mat
16、h cant guide the math teacher? Visible, they blindly worship of education thought and concept, fully dissever the relationship of mathematics and mathematics education. Some fascination target teaching research staff in the past, later, advocate the inquiry learning, and now acura curriculum spirit,
17、 all day long theory from mouth, policy roar everywhere, and indifferent to the question in the mathematics, despise or even didnt dare to ask math problems. Although people called it experts, actually they are not mathematics. 解决办法: :/ Solution: 1.改变重教育理论轻专业技能的教师培训观念，实现数学与教育并进 1. Change the light h
18、eavy theory of education teachers professional skills training, to realize mathematics education 目前基础教育培训名目繁多，如国培计划、西部教师培训、特级教师培训、培训者培训、骨干教师培训.笔者有幸参加过一些培训，发现这些培训有一个共同特点重教育理论轻专业技能，培训教师都是大学教授或知名专家，主讲内容通常有三类，第一，国内外教育学或心理学的理论;第二，新课程改革和新课程标准中的思想和理念;第三，课堂教学的有效性策略.偶尔也有课堂教学观摩或高考试题研究，针对学科专业技能的培训很少.事实上，一线教师迫切
19、需要的是学科技能的培训.比如研究性学习，全日制高中课程计划明文提出，要求研究性学习在高中每周平均课时为9课时，而目前的现状是“有教材，无老师;有课表，不上课;口号响，无行动;著作多，无实效”，很多学校的研究性学习成果中没有一个与数学学科密切相关的课题.为什么数学教师和学生不开展数学研究性学习呢,为什么新课标的精神和各种培训在数学研究性学习中没有产生效力呢,原因在于很多教师缺乏数学研究的习惯和兴趣，连解答教学中的难题都很困难，哪有能力指导学生研究性学习.所以，在教师培训中有必要强化教师的专业技能，实现数学与教育并进. Based education training is various, su
20、ch as the top-tier western culture plan, teacher training, teacher training, training of trainers, backbone teachers training. I have taken part in some training, found the training has a common characteristic - heavy theory of education professional skills, training teachers are university professo
21、rs or well-known experts, on the content usually have three categories, first, the theory of pedagogy and psychology at home and abroad; Second, the new curriculum reform and new curriculum standard in thoughts and ideas; Third, the effectiveness of classroom teaching strategies. Occasionally there
22、to inspect or test research of classroom teaching, in view of the subject professional skills training are rare. In fact, frontline teachers urgently need is discipline training. Such as inquiry learning, full-time senior high school curriculum plan definitely put forward that require research learn
23、ing in high school average weekly lesson 9 classes, and the current status is teaching materials, without teachers; schedule, not class; slogan loud, without action; works, no actual effect, a lot of research learning achievements of the school is not a subject closely related to mathematics. Why wa
24、s the math teacher and the student not to carry out the inquiry learning of mathematics? Why the spirit of new and various training in mathematics inquiry learning have no effect? The reason is that many teachers lack the habit of mathematical research and interests, even very difficult to solve dif
25、ficult problems in teaching, which has the ability to guide students research-oriented learning. Therefore, it is necessary to strengthen teacher training in teachers professional skills, to implement mathematical education. 2.开设新型的初等数学研究，提高其他学科教师的数学解题能力 2. The opening of a new elementary mathematic
26、s research, improve other subjects teachers mathematics problem-solving ability :/ 在教学中，有的学生爱问一些问题，个别问题让物理教师和计算机教师为难，他们虽知道是数学问题，却无法解答.这些问题所涉及的都是初等数学知识，而其他学科教师没有学过初等数学研究，所学的高等数学又无能为力.在教学中没有初等数学培训的机会，他们的数学解题能力缺乏锻炼和提高，部分年轻教师的数学解题能力较好，而一些老教师的数学解题能力尚不及优秀的中学生.要提高其他学科教师的数学解题能力，有必要开设初等数学研究课程，这门课既可以在教师培训课程中开
27、设，也可以作为教师的课外读物. In the teaching, some students ask some questions, individual problem embarrassed of physics teachers and the computer teacher, though they know is mathematical problems, but not answer. These problems are involved in the elementary mathematics knowledge, and learning other subjects
28、teachers studies of elementary mathematics, learned of higher mathematics and powerless. No elementary mathematics in teaching training opportunities, lack of exercise and improve their mathematics problem-solving ability, some young teachers mathematics problem-solving ability is better, and some o
29、f the old teachers mathematics problem-solving ability less than outstanding middle school students. To increase the price of other subject teachers mathematics problem-solving ability, it is necessary to set up the study of elementary mathematics curriculum, the course can be opened in the teacher
30、training course, can also be as a teacher of extracurricular reading. 3.加强数学应用与数学建模培训，提高数学教师应用数学的能力 3. Strengthen mathematical application and mathematical modeling training, improve the ability of teachers of mathematics applied mathematics 其他学科学习中学生或教师所问的一些问题，虽然可以转化为数学问题，但数学教师解决这些问题并非得心应手，通常是陌生和茫然
31、.由于数学教师缺乏这些学科知识，对于这些问题的背景生疏，甚至毫无所知，导致即使一个简单问题也需要其他学科教师解释很久才能真正理解问题的含义和实质.显然，数学教师要解答这些问题，必须具备理解问题背景的能力和数学建模的能力.要提高数学教师的这些能力，仅靠教育理论知识和课改精神是不够的，必锐角A的正弦、余弦和正切都是A的三角函数当锐角A变化时，相应的正弦、余弦和正切之也随之变化。须对教师进行数学应用能力的培养和提升，迫切需要编写一部切合中学教学实际的数学建模教材.该教材有别于大学数学建模教材，其内容必须与中学的计算机、物理、地理、化学、3、认真做好培优补差工作。 开展一帮一活动，与后进生家长经常联系
32、，及时反映学校里的学习情况，促使其提高成绩，帮助他们树立学习的信心与决心。生物等学科密切相关，所涉及的问题和难度必须符合中学教学实际. 4、在教师的具体指导和组织下，能够实事求事地批评自己、评价他人。Learning other subjects for middle school students or the teacher ask some of the problems, although can be converted into math problems, but the math teacher isnt handy, to solve these problems are o
33、ften strange and at a loss. Due to the lack of knowledge of these disciplines, mathematics teacher background unfamiliar with these problems, even there is no know, cause even a simple problems also need to other subjects teachers explain a long time to really understand the meaning and essence of t
34、he problem. Obviously, teachers of mathematics to solve these problems, must have the ability to understand the problem background and mathematical modeling ability. To improve the the ability of mathematics teachers, only by the education theory knowledge and the spirit of curriculum reform is not
35、enough, must be conducted for teachers of mathematics application ability cultivation and promotion, the urgent need to write a mathematical 3.余弦：:/ modeling teaching material of middle school teaching practice. The material is different from the university of mathematical modeling teaching material
36、, its content must be with middle schools computer, physics, geography, chemistry, biology and other disciplines closely related to the issues involved and difficulty must conform to the teaching practice of middle school. 4.开发校本课程和选修课，提高教师解决非常规问题的能力 4. The development of school-based curriculum and
37、 elective courses, improve teachers ability to solve the problem of irregular 4.垂径定理：垂直于弦的直径平分这条弦，并且平分弦所对的两条弧。韩愈说:“师者，传道授业解惑也”，这里的“惑”不能局限于教材上的习题和高考试题，应（1）圆周角：:顶点在圆上,并且两边都与圆相交的角,叫做圆周角.该是学生在学习过程中所有与数学相关的问题，既包括其他学科中涉及的数学问题，也包括（2）圆周角定理:圆周角的度数等于它所对弧上的的圆心角度数的一半.生活实践中抽象出来的数学问题，这就要求数学教师具备灵活的数学思维能力和解决非常规问题的能
38、力.要提高教师解决非常规问题的能力，最佳方法是教师主动参与解题的锤炼和课五、教学目标：程的开发.值得一提的是，这里的课程开发不是课堂教学的简单延续和拓展，而是对其他学科问题和生活中的实际问题进行提炼、加工和再创造.笔者在教学实践中发现:多解高考试题可以迅速提高解答与教材相关的问题的能力，而开发数学校本课程和选修课则可以提高教师发现问题和数学建模的能力，也可以提高解决非常规问题的能力. 5、能掌握一些常见的数量关系和应用题的解答方法，逐步提高解答应用题的能力。Han yu said: teachers, a compassso to reassure also, time here cannot
39、 be confined to textbooks high problem sets and exams, students should be all related to mathematical problems in the learning process, both in other disciplines involved in the math problem, also include the life practice of abstracting mathematical problems, which requires mathematics teachers hav
40、e flexible mathematical thinking ability and the ability to solve the problem of irregular. To improve teachers ability to solve the problem of irregular, best method is to teachers actively involved in the problem solving exercise and curriculum development. It is worth mentioning that the curricul
41、um development is not a simple extension and expansion of classroom teaching, but to other discipline problems and practical problems on the life of refining, processing and creating again. The author found that: in the teaching practice more solution test can quickly improve the ability of solve problems related to teaching materials, and the development of mathematics courses and elective courses can improve teachers ability to discover problems and mathematical modeling, and also can improve the ability to solve the problem of irregular.