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Question

函数及函数的思想是贯穿整个高中数学的一条主线，是中学数学教学的重要内容之一。函数是高中数学的一个重要的基本概念，它渗透在数学的各部分内容中，一直是高考的热点、重点内容。函数的思想，就是用运动变化的观点，分析和研究具体问题中的数量关系，建立函数关系，运用函数的知识，使问题得到解决。这种思想方法在于揭示问题的数量关系的本质特征，重在对问题的变量的动态研究，从变量的运动变化，联系和发展角度拓宽解题思路。函数思想是用运动、变化、联系、对应的观点来分析数学和实际生活中数量关系的思想。函数思想的培养是高中数学教学培养目标中的一项重要内容。本文从论述函数概念教学入手，突出以“基础”为起点，注重教学的过程，特别注意结论的发生、发展及应用过程的揭示和理解，强调了思维深刻性的培养是以扎实的基础知识和基本技能为前提的。本文结合教材中各章节教学及高考对函数的考查，论述了函数思想是函数基础理论的升华，是揭示函数意识方法的实质和规律的思维发展结晶。在教学中,教师应使学生在解题过程中不仅限于只简单地模拟、套路，而更多的是创设一个自己去观察、探索、研究问题的情境。在理清思路，搞清原理的基础上，将具体的模式和解题方法上升到一定的思想高度。这样才能使学生的思维得到真正的发展和深化，使数学教育质量得到真正的提高，进而实现函数思想的培养。本文并未对函数意识的培养专门加以论述，而是融合在各个环节的讨论中，体现了数学思想方法与具体的数学知识是有机的整体，它们相互联系，相互依存，协同发展。
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Answer 1

The function and the function thought are to run through a entire mathematic high school mainline, one of the important content being middle school mathematical education. The function is a mathematic important basic concept of high school , it permeates in every mathematics part content, be always the college entrance examination hot spot , priority content. The function thought , the viewpoint being to use motion to change, the relation analysing and studying quantity in concrete problem , the knowledge building function relation , wielding a function's, problem gets a messenger solve. This mentality lies in the intrinsic characteristics revealing the problem quantity relation , the development duplicating each other in the variable to problem studies, the motion from the variable changes, the angle broadens connection and development solving problems train of thought. Function thought is to use motion , change , to contact , to come analyse corresponding viewpoint the thought that quantity concerns in the mathematics and the real life. Function thought culture is that high school mathematical education trains one in target important content. The main body of a book is complied with discussing function concept teaching starting , is lay stress on the process taking "basis" as starting point , attaching importance to teaching , is pay attention to conclusion occurrence , development and revealing applying process's and is understand that specially, have emphasized that thought depth culture is to take solid ABC and basic skills as premise. The main body of a book be hit by every chapters and sections teaching and college entrance examination to the function combining with teaching material examine, having discussed function thought is function basic theory distillation , is that the thought revealing function consciousness method essence and law develops crystal. In teaching, the teacher should make a student be confined to only the simple field simulation , a series of skills and trick in wushu , etc. not only in solving problems in process , be the circumstances creating a self go and observing , probing , studying problem but more much. Reasonable method rises on the basis cleaning up a train of thought , being engaged in clear principle, with concrete pattern with solving problems to certain thought altitude. Such ability makes student's thought develop and deepen really , make mathematics educational quality get real rise, culture realizing function thought then. That the speciality discusses the main body of a book and the culture not having realized to the function additionally, is to fuse in each links discussion but , having embodied mathematics mentality and concrete mathematics knowledge is that the organic entirety , their mutual connection, are interdependent , cooperate and develop.

Answer 2

Function and the idea of function throughout the high school mathematics is the main line, secondary school mathematics teaching is one of the important contents. Function is a high school mathematics an important basic concepts, infiltrated it in the various parts of mathematics, has been a hot college entrance examination, focusing on the content. The idea of function, and that is using the campaign in perspective, analysis and research in the number of specific issues, the establishment of relations function, the function of the use of knowledge so that the problem can be resolved. This way of thinking is that it reveals the number of characteristics of the nature of the relationship, focusing on the issue of the dynamics of the variables, the variables from the campaign changes, contacts and broaden the perspective of the development of problem-solving ideas. Function idea is to movement, change, contacts, corresponding to the view of mathematics and real life relationship between the number of thinking. Thinking of the training function is the objective of fostering high school mathematics teaching in an important part. Based on the concept of teaching function start, focus on the "basis" as a starting point, focus on the process of teaching, with particular attention to a conclusion, the development and application of the process of revealing and understanding, and emphasized the profound thinking of the training is a solid foundation of knowledge and basic skills as the prerequisite. In this paper, teaching materials in the various sections of the college entrance examination and the test function, a function on the basis of theoretical thinking is the function of distillation method is to reveal the real function of the law of thinking and the development of crystallization. In teaching, teachers should allow students in the problem-solving process is not limited to simply simulation routines, it is more related to the creation of its own to observe, explore and study the situation. In straightening out ideas, understand the principles on the basis of specific models and problem-solving methods will rise to a high degree of thinking. Only in this way can the students thinking of real development and deepening of the Mathematics Education real difference to the quality, so as to realize the thinking of the training function. This paper does not function awareness of the specialized training to be addressed, but in the integration of all aspects of the discussion, a mathematical way of thinking and expression of specific mathematical knowledge is an organic whole, they are interconnected and interdependent, and collaborative development.