初中数学函数图象的教学策略研究
发布时间：2019-05-18 21:30
【摘要】：函数是研究变量问题的工具,初中生学习函数对其逻辑思维能力和抽象思维能力的培养发挥着至关重要的作用。函数的学习贯穿于数学学习的始终,在数学的学习中占据有至关重要的地位。由于函数的学习对初中生的逻辑思维和抽象思维要求较高,这使得初中生在函数学习的时候感觉十分的困难。函数是现实生活中许多抽象问题的概括和描述,必须深刻的理解函数的内涵,才能更好的掌握函数学习的有效方法。函数图象是学习函数的又一途径,本文针对初中数学函数图象的教学策略问题进行了研究。首先给出了一次函数、二次函数以及反比例函数的图象和性质,指出了一次函数的图象是一条直线,二次函数的图象是抛物线,反比例函数的图象是双曲线,同时对一次函数、二次函数以及反比例函数的各参数对函数图象的影响规律进行了分析,给出了使用描点法进行绘图的过程中需要科学的选择函数图象上的点,这样才能更好的通过函数图象去反映函数的性质。然后分析了如何有效的借助于函数图象去解决实际的问题,实际生活中的最值问题常常需要借助于二次函数的性质,对于二次函数而言,其在对称轴的左侧和对称轴的右侧有截然相反的性质,对于函数的面积问题需要有效的借助数形结合思想,通过数形结合思想使得代数问题几何化,不断的加深对代数和几何关系的理解,同时许多实际问题借助于函数图象可以更加直观的表现出来。最后指出在初中函数图象教学的过程中应该充分的利用多媒体教学,如使用几何画板或者借助EXCEL来描点绘图,不断的培养初中生的数形结合思想,使得初中生养成一种借助函数图象去解决问题的意识和能力,将函数图象和实际问题紧密的联系起来,通过对实际问题的函数化描述,这样更加有利于去发现实际问题的变化规律,有效的结合函数图象去理解函数的性质。函数图象使得抽象的函数问题变得具体化和形象化,借助于函数图象来理解函数的性质有助于加深初中生对于函数的理解,不断的培养初中生对函数学习的兴趣,同时通过函数来研究自然界中的各种变化量的关系。本论文的研究对于更加科学、有效的利用函数图象去实施初中函数的教学具有一定的参考价值。
[Abstract]:Function is a tool to study variable problems. Junior high school students' learning function plays an important role in the cultivation of their logical thinking ability and abstract thinking ability. The learning of functions runs through the learning of mathematics and occupies an important position in the study of mathematics. Because the learning of function requires high logical thinking and abstract thinking of junior high school students, it makes it very difficult for junior high school students to learn functions. Function is the summary and description of many abstract problems in real life. It is necessary to deeply understand the connotation of function in order to better master the effective method of function learning. Function image is another way to learn function. This paper studies the teaching strategy of mathematical function image in junior high school. Firstly, the images and properties of the primary function, the quadratic function and the inverse proportional function are given. It is pointed out that the image of the primary function is a straight line, the image of the quadratic function is a parabola, the image of the inverse proportional function is a hyperbolic, and at the same time, for the primary function, The influence of the parameters of quadratic function and inverse proportional function on the function image is analyzed, and the points on the function image need to be selected scientifically in the process of drawing by using the tracing point method. Only in this way can we better reflect the properties of the function through the function image. Then it analyzes how to effectively solve the practical problems with the help of function images. The most valuable problems in real life often need the help of the properties of quadratic functions. For quadratic functions, It has diametrically opposite properties on the left side of the symmetry axis and the right side of the symmetry axis. For the area problem of the function, it is necessary to effectively make the algebra problem geometric with the help of the combination of numbers and shapes, and the idea of the combination of numbers and shapes makes the algebra problem geometric. The understanding of algebra and geometric relations is deepened, and many practical problems can be expressed more intuitively by means of function images. Finally, it is pointed out that multimedia teaching should be made full use of in the process of function image teaching in junior high school, such as using geometric drawing board or EXCEL to draw points, and constantly cultivating the thought of combining numbers and shapes of junior high school students. So that junior high school students develop a kind of consciousness and ability to solve problems with the help of function images, which are closely related to practical problems, and through the functional description of practical problems, In this way, it is more helpful to find out the changing law of practical problems and effectively combine the function image to understand the properties of the function. The function image makes the abstract function problem concrete and visualization. Understanding the properties of the function with the help of the function image is helpful to deepen the junior high school students' understanding of the function and constantly cultivate the junior high school students' interest in function learning. At the same time, the relationship between various changes in nature is studied by function. The research of this paper has certain reference value for more scientific and effective use of function image to implement junior high school function teaching.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
本文编号：2480351
[Abstract]:Function is a tool to study variable problems. Junior high school students' learning function plays an important role in the cultivation of their logical thinking ability and abstract thinking ability. The learning of functions runs through the learning of mathematics and occupies an important position in the study of mathematics. Because the learning of function requires high logical thinking and abstract thinking of junior high school students, it makes it very difficult for junior high school students to learn functions. Function is the summary and description of many abstract problems in real life. It is necessary to deeply understand the connotation of function in order to better master the effective method of function learning. Function image is another way to learn function. This paper studies the teaching strategy of mathematical function image in junior high school. Firstly, the images and properties of the primary function, the quadratic function and the inverse proportional function are given. It is pointed out that the image of the primary function is a straight line, the image of the quadratic function is a parabola, the image of the inverse proportional function is a hyperbolic, and at the same time, for the primary function, The influence of the parameters of quadratic function and inverse proportional function on the function image is analyzed, and the points on the function image need to be selected scientifically in the process of drawing by using the tracing point method. Only in this way can we better reflect the properties of the function through the function image. Then it analyzes how to effectively solve the practical problems with the help of function images. The most valuable problems in real life often need the help of the properties of quadratic functions. For quadratic functions, It has diametrically opposite properties on the left side of the symmetry axis and the right side of the symmetry axis. For the area problem of the function, it is necessary to effectively make the algebra problem geometric with the help of the combination of numbers and shapes, and the idea of the combination of numbers and shapes makes the algebra problem geometric. The understanding of algebra and geometric relations is deepened, and many practical problems can be expressed more intuitively by means of function images. Finally, it is pointed out that multimedia teaching should be made full use of in the process of function image teaching in junior high school, such as using geometric drawing board or EXCEL to draw points, and constantly cultivating the thought of combining numbers and shapes of junior high school students. So that junior high school students develop a kind of consciousness and ability to solve problems with the help of function images, which are closely related to practical problems, and through the functional description of practical problems, In this way, it is more helpful to find out the changing law of practical problems and effectively combine the function image to understand the properties of the function. The function image makes the abstract function problem concrete and visualization. Understanding the properties of the function with the help of the function image is helpful to deepen the junior high school students' understanding of the function and constantly cultivate the junior high school students' interest in function learning. At the same time, the relationship between various changes in nature is studied by function. The research of this paper has certain reference value for more scientific and effective use of function image to implement junior high school function teaching.
【学位授予单位】：华中师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
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