The validity of the cases to talk about the problem of design

The exploratory teaching is under the guidance of the teachers and students to use the method of inquiry learning initiative to acquire knowledge, cultivate the spirit of science, development ability of practical activities. With the deepening of curriculum reform, inquiry teaching the teachers accepted and widely used teaching. I combined the actual teaching, to talk about their understanding of how to design effective inquiry.

First, the creation of foreshadowing problem situations effectively explore

Effective inspired creation bedding scenario for students associative thinking, students are often starting from the original problem, through a progressive approach, and thus their different ways, different levels of Lenovo, changes in the development of a new problem, which broad thinking space for different students, students sensible thinking and reasoning ability. For example, the teaching of the line segment, I made the creation of bedding type scenario as follows:

1. One, there are two points on a straight line, A, B, and there are several segments? With letters.

2. A straight line on the three points, A, B, and C, there are several segments? With letters.

3. A straight line and the four points A, B, C, and D, there are several segments? With letters.

4. Train from station A, the three stations along the way through before reaching the B station, then A, B between the two stations, the number of types of fares? To arrange a number of different ticket?

5. N points in a straight line, A, B, then the number of segments? (Containing the letter n algebraic

Students hands-on practice under the guidance of teachers, self-inquiry, and levels of, find out the law, access to knowledge, meet the requirements of the students to create classroom becomes vibrant.

Second, the creation of regularity type scenario effectively explore

In teaching mathematics, we often encounter some regularity type problems, teachers should actively create problem scenarios, to guide students divergence inquiry learning, guiding students on the basis of independent thinking and make full use of induction, analogy, Lenovo and other methods, in particular should promote mathematical conjecture students starting from a certain basis, using means of non-logical directly conjecture conclusions, so that students experience mathematical inquiry and the joy of creating.

For example, in the study of rational numbers exponentiation, I have the following two questions to let students explore:

1. Students have seen the drama << Journey to the West >> will like the Monkey King Monkey King Bar can easily scalable, assuming it the shortest when only 1 cm, the first changes into 3 cm 9 cm second change, three changes into 27 cm ... the basis of this law changes go to several changes to 243 cm?

2. Observe the following formula: 31 = 3,32 = 9, 33 = 27, 34 = 81,35 = 243 ... you found the law to write 32,005 last digit is the number?


Students through observation, analysis, comparison and conclusion categories such as mathematical conjecture, and gradually find the correct conclusion.

Third, the creation of the game type scenario effectively explore

Psychological characteristics of students in the classroom necessarily appropriate math games, math experiment to create problem scenarios to guide students divergence inquiry learning, so students hands-on brain, actively involved in the learning both stimulate students' interest in learning mathematics, but also cultivate their ability to innovate and satisfy their curiosity.

For example, when learning RATIONAL me out of such a title: "Happy Dictionary" part of CCTV Each issue has a 24.2 "interesting question, I give a natural number between 1-13, you you can take any of four, these four number (four number can only be used once) "+", "-", "×

"÷" computing, brackets, so that the result is 24, learned RATIONAL, you will use this method to solve each of the following?


1, the existing four rational -9, -6,2,7, you can use three different methods was 24?


2, if to you, -5,7, -13, also Couchu 24?


Students through self-exploration, cooperation and exchange, and finally reach the right conclusion. This problem scenarios can improve the student computing power can train students thinking agility help students divergent thinking ability and establish an effective sense of exploration.

Fourth, the creation of a given problem scenarios effectively explore

Need to explore the problem the same open-ended questions, reasonable, divergent profound and different, different designs also bring a different experience to the students.

Such as: "not in the same straight line to a circle defined by three points." Nature of teaching. Usually so several design program.

Program: Students follow the teacher step-by-step painting (1) painting is not in the same line three o'clock, (2) to connect any two points on the line segment was the triangle, (3) draw the Trilateral the vertical bisector intersect at one point, then a question: Why do these three lines intersect at one point. Resolved concludes drawn: not in the same straight line, a circle defined by three points. Then ask students to think: along the same line three o'clock ability to determine a circle? Then the teachers on the
Option Two: directly given practice and graphics (see table below), and then ask questions: meet the requirements of his round for it? Allow students to discuss, exchange concluded, "are not in the same straight line, three points determine a circle."
Option Three: Teachers are given a three-point position known to allow students to try to draw, paint graphics allow students to discuss, exchange concluded, "are not in the same straight line defined by three points of a circle". Then guide the students are not in the same straight line, a circle three are not sure. Links to free papers Download Center http://eng.hi138.com
program: teachers asked the following questions as a guide.
Issues: -: 1, draw a circle, make it known point, you can draw a few this round? 2, think about the center of the circle, whether the location of the regular? Students hands-on practice concluded.


Problems: 1, draw a circle, to make it known points A, B, how do you? You can draw several such round? 2, observe and think about the center of the circle distribution? With segment AB? why? student group collaboration, drawing students, observation, comparison, analysis, discussion, exchange obtained: the center of the circle on the same line, the line is the perpendicular bisector of the segment AB .

Question three: 1, draw a circle, to make it through a known point A, B, C, how you doing? Can you draw a few this round? 2, the center of the circle distribution with line segments AB What? Why?
Program students learn very solid, students learned by imitating painting circumcircle of the triangle, but learn Debu flexible, many students known, however I do not know why the result is that students do title, but less likely to think about, but will not creation. Option Two students in others map is well on the basis of thinking concluded, learn to draw. But students because there is no hands-on experience is not profound, many students learn neither solid, and the lack of just made. Program three with a two-phase system more autonomy through their own analysis, comparison, think, and try to draw graphics, but because of the teachers are given a three-point position, to some extent bound students thinking space, classroom teachers control process carried out smoothly in accordance with the design of teacher scheduled. Program is actually an open experimental exploration activities, due to the teachers in the experimental exploration of the process of the students. Design a series of questions. These problem very level. And there is no lack of openness, teachers teaching activities is neither a mere formality. Lively, and there is no lack of mathematical wisdom. Which 1,2 has a shallow. Poor students the foundation for all students, but also the courage to try, but also provides a guideline for the inquiry to question 3. For the problem (2) Because teachers have no defined point A, B, C of the position. The problem is given a more open more challenging. Left to the students - the vast exploration space of thinking, students not only found in the process of drawing a three-point position of the A, B, C are two possibilities: A, B, and C are not in the same straight line, and in the same straight line, Some students to draw the AB, BC, AC trilateral perpendicular bisector also some students drawn one of the two perpendicular bisectors, but actually only one intersection, by comparison, analysis, discussion found in Paint only allow students to enjoy the joy of discovery in the problem-solving process, the joy of success can be drawn triangle circumcircle. Triangle circumcircle only problem was difficult to understand the problem. Students drawing, observation, comparison, analysis, and solution of the problem was a matter of course, a matter of course.

For the fourth scenario, due to the teachers' problems, designed a series of levels and reasonable open-ended questions. Students in the drawing process, naturally thought of classification thinking, think of the three-point position may be along the same line, may not be in a straight line, a logical solution to a problem that many teachers avoided, but also so that students really understand "is not in the same straight line of the importance of this condition.

In short, the creation of the problem scenario is conducive to effective inquiry learning of the students, to enable every student to be fully developed, to improve their level of thinking, original abstract mathematical knowledge becomes vivid with interest. Links to free papers Download Center http://eng.hi138.com

Mathematical Papers