从获得知识到拥有智慧From knowledge to wisdom.docx

1、从获得知识到拥有智慧From knowledge to wisdom从获得知识到拥有智慧（From knowledge to wisdom）From knowledge to wisdomExploration and practice of inquiry learningZhao Xin, the Second Affiliated Middle School of Beijing Normal UniversityKey words: mathematics education; learning style; information technology; inquiry learni

2、ngFirst, the question raised(1) the basic purpose of mathematics education;After many students go to work, not directly used many middle school mathematics knowledge and the people, are often able to use mathematical knowledge in middle school and even fewer people. So we think of the famous mathema

3、tician Mr. Hua Luogengs words: what is the number? From the specific definition, its formula and theorem, the rest is the number. The plain language contains a profound philosophy. We put this sentence to migrate to the secondary school mathematics teaching, can say: what is mathematics? From the sp

4、ecific definition, its formula and theorem, the rest is the middle school mathematics. Based on the idea, teachers should create a learning environment for students to explore Math: when they entered the world of mathematics, can see the graphic beauty, symmetrical beauty, of beauty, of beauty,. And

5、 for these beauty and admiration; when they are out of the mathematical world, there will be a method of exploring science, the courage to conquer the difficulties, firm and indomitable quality of life - which may accompany them, should be the fundamental purpose of mathematics teaching.In fact, the

6、 new curriculum reform advocates the construction of learning, students are constructors of knowledge. Learning is re organized and re experience the process of understanding. To achieve the purpose of mathematics teaching, we need in the process of teaching, let the students under the guidance of t

7、eachers, independent inquiry, found to complete the learning of new knowledge the process of teaching. This will not only enable students to master the knowledge more firmly, more thorough understanding, more importantly, in the learning process of students thinking ability training and improve. Stu

8、dents learn through the process not only to acquire knowledge, but more importantly, have the wisdom of long-term development(two) students learning style;Improving students mathematics learning method is a reform goal advocated by the new curriculum standard. The new curriculum standard clearly poi

9、nts out that effective mathematics learning activities can not rely solely on imitation and memory. Hands-on practice, independent exploration and cooperation and communication are important ways for students to learn mathematics. Obviously, this way of learning is beneficial for students to experie

10、nce the formation of mathematical knowledge, help to restore the true features of mathematical knowledge, and also help to achieve the basic goal of mathematics education. Therefore, teachers should make great efforts to promote the change of students learning style, and the change of students learn

11、ing style depends on the change of teaching methods and the richness of teaching methods.(three) the continuous development of information technology;With the rapid development of society, various means of information technology are constantly enriched. The rational application of these information

12、technologies can effectively promote classroom teaching and provide a broader space for students to explore independently.The graphic calculator is developed after the scientific calculator, it has very strong drawing function, except conventional mapping, but also dynamic demonstration, graphical e

13、xploration; symbolic computation symbolic algebra system can algebra, calculus; data processing system, to explore the data of regression analysis; transmission between graphic calculator and the graphic calculator and computer can carry data, image and program, easy to communicate, modify file and

14、output. These features make the graphic calculator become students in class and outside of self learning inquiry.Based on the above several aspects of thinking, I believe in the concept of the new curriculum, the change of learning style is the inevitable trend of the inquiry learning to make studen

15、ts learn how to find the problem, from the point of view of mathematics to solve problems in the learning process, the construction of complete sense of their own cognition, develop exploration and innovation consciousness. The abundance of information technology enables students to have more extens

16、ive space for self exploration,Therefore, I have carried on the beneficial exploration to the teaching content, the teaching object and the teaching pattern of inquiry learning supported by the information technology, and has formed some conclusions which have the popularization valueTwo, concrete p

17、ractice(1) the role of inquiry learning in different classroom teaching contents1, the role of inquiry learning in conceptual TeachingThe traditional concept of teaching mainly teachers teach mainly passive acceptance of students, students have no space to think, no doubt, each concept as input to t

18、he computer in order to transfer to the students as stiff. Some teachers used to quickly explain the concept after a lot of practice at all levels to cope with the examination, which is obviously contrary to the goal of mathematics education. The students do not get the exercise of thinking in the p

19、rocess of learning concepts, and understanding of the concept is scanty, often the past, students develop the concept of learning is not considered habits, become aware of the serious gap between the machines, concept and problem solving, and problem solving on the back questions the form of memory,

20、 only knowing but not the why,Therefore, the concept of teaching, students should be in the current level of knowledge on the formation process, let students experience mathematics concept, through the students self exploration, the formation of a new concept. The graphic calculator make students in

21、dependent inquiry as possible, can be carried out on concrete analysis of the phenomenon and to abstract mathematical concepts by graphic calculator students the process of teaching, the concept of students into the process of active construction of knowledge. So in order to maximize the concept of

22、teaching to improve the level of students thinking, to enable students to understand the concept correctly and thoroughly.Typical case: the unified definition of conic curvesteaching process(a) create situations and ask questionsThe definition of analogy questions: what is the parabolic geometry mea

23、ning of ellipse and hyperbola in line?Elliptic and hyperbolic, students call program for a given input a, b values, and then enter freely in the range of x value, calculator will automatically calculate the y value and the ratio of line to point to focus and distance.Through the research and demonst

24、ration of computer students can get on the properties of ellipse, hyperbola, ellipse and hyperbola on point to focus and to the centrifugal rate curve alignment distance.Parabola, ellipse, hyperbola has many common areas, such as satellite to orbit at a rate different range when are ellipse, hyperbo

25、la and parabola; they can be cut. The conical surface whether there are similarities in the way of trajectory formation?(two) observation experiment and reasonable conjectureThe properties of the above elliptic and hyperbolic points and the definition and the conjecture of the analogical parabola:Th

26、e ellipse and hyperbola can be regarded as the locus of the point whose distance is fixed to the fixed lineThe derivation of the standard equation for Parabolic Equations remains:The trajectory of the distance between the fixed point F and the fixed line L is constant e ()Set the distance from F to

27、P, establish the Cartesian coordinate system, and make F (straight line):The trajectory of any point (x, y) (projection) according to the geometric conditions listed algebraic formula:Simplify and arrange,In this way, we obtain the trajectory equation of the point at which the distance between the f

28、ixed point and the fixed line is the constant e. We find that it is not the standard equation of the ellipse and hyperbola. What curve does this equation represent?Because the equation is complicated, its difficult for students to recognize it. We can use graphical calculators to help us analyze. We

29、ll call the program in the calculator belowAs long as the students take a group of E and P graphics calculator will automatically draw the curve. The equation that you can try for a given p, enter a different E; and then given a e, enter a different P, see what different results. Students are found

30、by running the program: e1 that is e=1, is a hyperbola; parabola; 0e1, an ellipse. Through the dynamic demonstration of geometric sketchpad,Students are observed to change the curve from hyperbola to parabola and then to ellipseFrom this conjecture:The trajectory of the point at which the distance b

31、etween the point to the point and the distance to the line is constant is zero(three) reasoning, demonstrating, and revealing the principles1, teachers guide students to explore the above conclusions of the mathematical proofAfter the formulation of the equation, combined with the standard equation

32、of conic curve, the type of the curve represented by the equation can be explained. Thus, the unified definition of conic curve is obtained:The trajectory of the point at which the distance between the point to the point and the distance to the line is constant is zero2, a further understanding of the definition:The teacher guides the students to think more deeply about the second definition of ellipse and hyperbola:(1) the first definition and the second definition of ellipse and hyperbola recognize the formation of curves from different angles;(2) the definition of conic