Talk about the concept of teaching examples common misconceptions and strategy to solve

Since the new curriculum reform, the concept of teaching by more and more concern and attention to let students experience concept was developed in order to emphasize on behalf of the concept of teaching mode continue to appear in various types of teaching seminar in to observe lessons seminars found that the concept of a link is often the main front of the teachers to design teaching, often unique insights. However, I also found that many teachers on the the concept teaching of Example design often failed to arouse enough attention put into due effort, but that relatively simple concept teaching examples, some just scripted, ignoring the example of an exemplary role model, some arrangement for self-learning, completely not able to tap the example contains mathematical ideas, methods, and some do not cut actual blind overstating, from the core of the concept, which would naturally result less effective. Below the author of his own practice, study and reflection on the teaching of the concept of design examples of several common misconceptions and Countermeasures do Reflections, hope share their learning with colleagues.

, The current concept of teaching examples designed several common misconceptions

Re new overstating light materials Example

Provided in the textbook examples, are experts at after due and careful consideration and well-designed, not only has the characteristics of typical, demonstration, scientific, and guidance and in accordance with the law of students' cognitive, step by step, teachers Teaching Reference modeled "and" Master data "but teaching practice, we can easily find that many teachers do not want to use the examples in the textbook, but I found some consider themselves" good title "unrealistic blind overstating counterproductive such as:
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:

Example 1 from math homework in this class of 50 students, was drawn four check how many different election law?

Variant class of 50 students math homework mixed together, and then everyone is free to take from a 48 just to get their jobs this possible?

Just ask 47 people to get their jobs this?

Example 2 In the graph shown in Figure 1, you can find the number of rectangles?

Variant in the graph shown in Figure 2, you can find out how many rectangles?

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.

2 heavy variant training, light the concept of core

"Variant" Example exercises presented by the change in the concept of non-essential characteristics, conditions or conclusions in the transform, transforming the form or content of the problem, can help students understand the concept of the nature of property, easy concept application from a psychological perspective, it is to overcome the mindset of the important measures in the negative factors, the students good quality of thinking also of positive significance in teaching practice, many teachers often focus only on the presentation of variants, ignore the "variant" should expand around the core of the concept, "variant" should strive to prompt the nature of the concept as:
Case 2 in April 2011 a studio teacher activities, Wenzhou, teachers B "combination" first class teaching, design examples of the following variant:

Example plane 10 points to the total number of segments, wherein each of the two points is the endpoint?

Variant 1 round 10 points over every 2 Draw a string, you can draw a total of how many strings?

Variant 2 round on 10 points, 3 Draw a circle inscribed triangle, you can draw a total number of circle inscribed triangle?

Variant 3 convex decagon number of diagonals?

Variant 4 convex n (n> 3)-gon how many diagonals?

10 points within the plane of the variant, wherein the four points in a straight line, in addition to non-collinear points.

① 10 points can be connected into a number of lines?

② three points by 10 points as vertices can be determined by the number of triangles?

Variant examples of the group context and background, but also closely linked to the characteristics of the "portfolio" - has nothing to do with the order of the elements, but as the concept of "fine" in the process of Example only variant in the application environment, not through Example reveals removed from the n different elements of the nature of the combination of k elements "is a collection of n different elements of a k-element subsets" can be described as wonderful Have no regrets.

3 re-solving skills, light mathematical thinking

Example knowledge (concepts), skills, methods and ideas linked bond in the concept of teaching not only help to further understand the concept of connotation and extension at, also charged with the important mission to turn knowledge into ability common myths in Example choice: out of touch with the current contents of the subject too difficult, too trickier. emphasis on mathematical thinking as:

Case 3 in my school teaching seminars, a teacher lesson of the angle of inclination of the straight line and slope design such Examples variants:

Variant slope k, the angle of inclination @, if -1 <k <1, and @ ranges.
Practice the angle of inclination of a straight line known as @, if sin _AT_ = seeking the slope of this straight line.
Exercise 2 known straight line y = xsinθ-1, seeking the tilting angle of the line.
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

Second, the concept of teaching design strategies and principles in Example

1 Example design should pay attention to materials development

Materials is the collective wisdom of many mathematicians, mathematics educators, with strong authority and guidance, but the concept of teaching materials, formulas, theorems, most of them with strong abstract generality academic morphology knowledge presented, in teaching, we have to delve through textbooks, understand concepts, formulas, materials theorem, and translate them into easy to understand students' educational form of "knowledge mining, to develop their potential teaching function. Such as:
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.

Students according to the definition of the parabola, the use of the linear movement of the method, can be quickly obtained trajectory equation:

= 8x (x> = 0).
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.

Ibid trajectory equation can be obtained:

= 8x (x> = 0).
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.

Some students because of the mindset immediately think of the parabola defined concluded:

= 8x (x> = 0).

Can be seen clearly from the image, all points on the x-axis negative Axle satisfy a condition so there are two equations:

= 8x (x> = 0) and y = 0 (x <0).

In fact, by seeking track, column type

Chase Question 1 and Question 2 Why only one equation? Whether leakage is it?

Question 4 in a plane, the distance of the point P and the point F (2,0) than it is to the line x-1 = 0 from the Grand 3, 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.

Example designed to focus on step-by-step

An example are able to stimulate interest of students to enable students to actively participate in, depends primarily on the issues raised by ability to arouse students 'understanding of the conflict, whether caused by ideological resonance of students every problem should be based on the students' prior understanding basis, and they leave room for thinking the saying goes: Reviewing the Old knowledge need to continue to be applied and consolidate learning new knowledge should pay more attention when the echoes and comparison with the old knowledge as:
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:
Question 1 known x, y ∈ [0,6] and x, y ∈ N. demand event "xy> = probability.

Question 2 known x, y ∈ [0,6] and x, y ∈ R, and event xy> = 3 the probability.
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.

3 Example designed to focus the concept of core

Example design to contribute to the understanding of the concept, to help apply the concept, the focal point of the design should be gathered on the core of the concept. Example solution, to help students understand concepts essential purpose as:

Case 6 finished function concept can choose such examples to help students deepen the concept:

Question 1, Table 1 data collected by the students do tap experience the maximum capacity of the measuring cup is 100 ml.

(1) If you continue to test, how many seconds the amount of glass of water full and overflow?

(2) This is a function? Please explain.
Question 2 Zhang and Li together the faucet leaks experiment. They will each collect the data described in the Cartesian coordinate system, shown in Figure 4, is what causes the image they painted? Shown in Figure 5 leaky faucet experimental data on the image, the image show?
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.

Example designed to penetrate way of thinking

Example designed to make the students from the seemingly plain text description, symbol deduction mining its meaning. Comprehend the profound mathematical thinking, if only the example as a model of problem-solving skills, and then teaching the inevitable lack of "mathematical flavor. Such as:

Case 7 In learning arithmetic sequence and its first n and the formula, the teaching materials (PEP compulsory 44) design:

Materials through to solve, and did not elaborate example implication of mathematical thinking in words, but we found from this example design, materials design intent is to guide students to study the series with the idea of ​​the function, that is, from the number of shaped combination of the viewpoint Thought classified using mathematical discussion on the classification obtained expression can be constant (number of columns) from 0, can be a direct proportion function of n (such as number of columns) composed by a non-zero constant, a quadratic function of n (image passes through the origin), so that the students found that the intrinsic link between knowledge, learn to learn mathematics with a contact point of this way of thinking as the main line series design examples, that can really play Example functions and value, we should fully understand the function and value of the examples in concept learning, to grasp the concept of teaching examples key to the design and principles on the basis of a deep understanding of mathematical concepts do layman's language reposted elsewhere in the Research Papers Download http:/ /

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