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1、1In a mathematical way of thinking about teaching functionThe so-called mathematical way of thinking is understanding the nature of mathematical knowledge, from some of the specific mathematical content knowledge of mathematics and refining the process of increasing mathematical point of view, he wa
2、s repeatedly raising activities to use with the general guidance is the establishment of mathematics and mathematical problem-solving guidelines; is to ask questions in mathematics teaching, problem-solving process, using a variety of ways, means, ways, etc. to grasp mathematical way of thinking, is
3、 to grasp the essence of mathematics, so make students to comprehend, to master and skilled use of mathematical thinking, teaching is not mechanical. Here I was in a function used in teaching mathematical thinking what to talk about some of the practices of individuals: A way of thinking Shuoxingjie
4、ge “Number of invisible, less intuitive, form numerous, difficult nuanced”. “Shuxingjiehe” is the most important in mathematics, but also one of the most basic way of thinking, is to solve many mathematical problems and effective ideas. Use 2“Shuoxingjiege” allows to study the issue of Aesthetic, to
5、 simplify, to make the abstract become intuitive, such as: a function of y =- x +5 image without which quadrant? Solution 1: According to the nature of the image, k 0 over one hundred twenty-four that more than three quadrants. Solution 2: If the image of nature forgot to a function, this function c
6、an make the image, the problem is solved this way of thinking is the use of Shuoxingjiehe. Third, the classification of thinking When a problem because the amount of a different result might cause problems is not the same, the need for this amount of discussion to classify various situations, such a
7、 function y = kx + b image after which several quadrants, which When will discuss four categories: (1) When k 0, b 0, the image after one hundred twenty-three quadrant, (2) When k 0, b 0, the image after one hundred thirty-four quadrant, (3) When k 0, the image through one hundred twenty-four quadra
8、nt, (4) When k 0, b 0, the image through two hundred thirty-four quadrant. Third, a whole way of thinking The whole idea is to 3proceed from the overall nature of the problem, highlighting the overall structure of the problem analysis and transformation, identify problems and the overall structure,
9、good at “integration” perspective, certain formulas or graphics as a whole, to grasp them association between, for a purposeful, conscious of the overall process. the whole way of thinking in algebraic simplification and evaluation, solution of equations (group certificates and other aspects of geom
10、etry to solve a wide range of applications, the overall substitution, superimposed fold by treatment , the overall operation, the overall design element, the overall handling is a whole way of thinking in solving mathematical problems in the specific application, such as: Given y + b and x + a (a, b
11、 is a constant proportional, (1 Explain y is a function of x: (2 case x = 3 时, y = 5, x = 2 时, y = 2, find y and x as a function of style. to solve this problem (1, we take y + b and x + a are as a whole, set y + b = k (x + a draw y = kx + ak-b, which can show that y is a function of x, solve the pr
12、oblem (2, when we take two values into analytic y = kx + ak-b in the quadratic equation obtained after a triple group, obviously can not find the value of each unknown, 4but we can put ak-b as a whole, we can find k = 3, ak-b = 4, y and x to find the function relationship is y = 3x-4, use twice in t
13、his matter to a whole way of thinking. Links to free download http:/www . .com Fourth, the model of thinking When a problem may be associated with a particular equation, the equation can be constructed to study the nature and equations to solve this problem, such as if you want to find a function y
14、= kx + b with the x-axis, y-axis intersection, according to the point axis features, x-axis point vertical axis is 0, that is, when y = 0, x =- b / k, that is the intersection with the x-axis is (-b / k, 0.y horizontal axis point coordinates 0, that is, when x = 0, y = b, so the intersection with th
15、e y-axis is (0, b. This equation of the model used in the way of thinking. Fifth, an analog way of thinking When we need to find a function y = kx + b image and its variation, due to a function y = kx + b is the image can be seen as directly proportional to the image of the function y = kx translati
16、on | b | units length obtained, which can be used directly proportional to learn before the function y = kx 5image and its variation analogy drawn a function y = kx + b image and its variation. Sixth, special and general way of thinking Direct proportion to study the function y = kx image and its variation, let the students draw a direct proportion function y = 2x and y =- 2x image, compare these two functions the same and differences,
