Case 1 in April 2011 a studio teacher activities, Wenzhou, A teacher in teaching the first class of the "portfolio", set aside the textbook example, the design of the following examples:

These two examples, Example 1 variant and asked the students just contact counting principle and arrangement, the combination of knowledge, apparently thinking span is too large, potentially also dilutes the core of the concept of this lesson; while Example 2 flexible application of the design is a combination of knowledge, the students' knowledge of migration is too high, can not play the role of the delicate concept.

Case 2 in April 2011 a studio teacher activities, Wenzhou, teachers B "combination" first class teaching, design examples of the following variant:

Not difficult to find examples and exercises designed too difficult, too skill examine is the the trigonometric tangent image and nature, out of touch with the content of this lesson, did not grasp the lesson concept core idea and essence (coordinates of), making the core concepts of the lesson to be marginalized, easy to give students an illusion: the learning of mathematics learning problem-solving skills. Reposted elsewhere in the Research Papers Download http://eng.hi138.com

Case 4 the Jiang Xin Yi teacher in a class of Professor "parabolic" textbook examples of secondary development, design the following examples, and received good teaching results:

Question 1 in a plane, the distance of the point P and the point F (2,0) than it is to the straight line x +4 = 0 the distance is small, find the equation of the locus of the point P.

Question 2 in a plane, the distance of the point P and the point F (2,0) than it is to the straight line x +1 = 0 large distance 1, find the point P, the equation of the locus.

Question 3 in a plane, the distance of the point P and the point F (2,0) than it is to the y-axis the distance is 2, find the equation of the locus of the point P.

This problem is the use of column-determined trajectory equation: = 8x (x> = 1) = -4 (x-3) (x <1) has no difficulty; move straight key is in the process of using the geometric method In order to allow the fixed point to the straight-line distance to the point of equal distance, in addition to considering the straight line out x-1 = 0 left shift of three units, three units to the right straight track to meet the conditions, track image in Figure 3 , the trajectory parabola superimposed into two parts.

From the point of view of the classroom effect, the design of this Example stimulate the students a great deal of enthusiasm for learning through self-exploration, students not only to the definition of the parabola have a deeper understanding, and the shape of the number of missing is less intuitive, shaped Missing with a deeper understanding the difficult nuanced "Shuxingjiege of thinking, strengthen the awareness of students to form the number of help, want to shape number.

Case 5 after learning "Geometric Probability Model" concepts and formulas, in order to highlight the probability model comparison and selection of classical probability and geometry, can design the following examples:

Example design focuses on the prominent contact with the difference between the old and new knowledge, before and after the echo, step by step, highlights from the classical probability to geometric probability model, from the finite to the infinite extension of the original boring explanations preaching is the title of this word changes, self-evident.

This example, the function of taste is very strong, "variable" a volume change with the changes in the amount of a correspondence between the "variation", have been fully reflected. Problem focus on the understanding and application of the concept, as long as understanding of the concept will be able to answer, rather than to the students set a "trap" to make trouble, not so much the concept of function such examples to help students understand the nature of the concept, allow students to experience the role of mathematics ability is more comprehensive.

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