第1个回答 2009-06-11
Primary Mathematics Teaching Mathematics in the way of thinking which should be infiltrated
Since the ancient times, numerous mathematical way of thinking, each flashing a mathematical way of thinking are the sparks of human wisdom. A
Due to the characteristics of primary school age they decided that some mathematical way of thinking is not easy to accept, the would want so many mathematical
Infiltration to the primary way of thinking is not realistic. Therefore, we should have a choice to infiltrate some mathematical way of thinking.
The author believes that the following types of mathematical thinking of students is not only receptive, but also to improve the mathematical abilities of students have a good
Role.
1. To the ideas of
In the thinking of a practical problem is to through some sort of conversion, reduced to a mathematical problem, to a more complex problem
Conversion, reduced to a simple question. It should be noted that under the thinking is different from that of the general talk about "transformation", "turn
In other words. "It is an irreversible one-way nature.
Example 1 fox and weasel to jump competitions, each time moving fox jumped 4 1 / 2 meters, each time weasel jump forward
2 3 / 4 meters. They only jump a second species. Game on his way from the starting point, at 12 3 / 8 meters with a depression
Well, when one of them falling into the trap when the number of meters of another jump?
This is a real problem, but know that through the analysis, when the fox (or weasel) fall into the trap of the first when it jumped
That is, the distance over which the distance of each jump by 4 1 / 2 (or 2 3 / 4) m in the whole multiple trap spacing is 12 3 / 8 meters
Multiples of the whole, that is 4 1 / 2 and 12 3 / 8 of the "least common multiple" (or 2 3 / 4 and 12 3 / 8 "minimum common multiple
Few "). For the two situations, and then calculated the jump, respectively, several times, to determine who should fall into the trap, the problem is basically solved.
Reflections on the above process, in essence, is a real problem through the analysis of transformation, seeking reduced to a "least common multiple"
Issues, namely the transformation of a real problem, reduced to a mathematical problem, which is oriented to the thinking of the performance of mathematical abilities
One.
2.Number Shape Combination thinking
Number Shape Combinationthinking of making full use of "shaped" the image of a certain number of relations that out. Some, such as through line
Above diagram, tree diagram, map or set a rectangular area to help plan the number of students on the proper understanding of the relationship between simple visual problem.
Example 2 a cup of milk, drank half a second drank the remaining half of each drink on such last
The remaining half time. A total of five times the number of milk to drink?
Figure (Figure)
If this title five times the total milk to drink, that is, 1 / 2 +1 / 4 +1 / 8 +1 / 16 +1 / 32 on the request for, but
This is not the best problem-solving strategies. Let us draw a square, and assuming it as a unit the size of "1", we can see from Figure 1
Request for -1/32, where students not only to infiltrate the Number Shape Combination thinking, but also to students thinking of infiltration of the analogy.
3. Transform thinking
Transformation is a form of thinking into another form of thinking. If the solution of the equation with the solution of the transformation, the law, the formula
Equivalent transformation of the proposition, the geometric shape of the plot, such as transformation, understanding of mathematical problems and so reverse transform.
Example 3 for 1 / 2 +1 / 6 +1 / 12 +1 / 20 + ... ... +1 / 380 and.
Careful observation of these denominator, it is easy to find: 2 = 1 × 2,6 = 2 × 3,12 = 3 × 4, 20 = 4 × 5 ... ... 380 = 19
× 20, and then split ways, to consider and the general type of
a [, n] = 1 / n × (n +1) = 1/n-1/n +1
Thus, the problem is converted to the following summation form:
The original-style = 1 / 1 × 2 +1 / 2 × 3 +1 / 3 × 4 +1 / 4 × 5 + ... ... +1 / 19 × 20
= (1-1/2) + (1/2-1/3) + (1/3-1/4) + (1 / 4-1/5) + ... ... + (1 /
19-1/20)
= 1-1/20
= 19/20
4. Combination of ideological and
Combination of thinking is the object of the research group to carry out the various situations that may arise is neither left nor to repeat
To solve the leakage 11.
4 cases in the following multiplication formula, the same on behalf of the same number of characters and different characters representing different figures
For this formula.
Childhood love of mathematics
× 4
— — — — — —
Learn a few love Xiao Cong
Analysis: As the five digits of the product multiplied by 4 or five digits, so the first multiplicand number "from the" can only be 1 or
2, but if the "from" = 1, "Learning" × 4 bits of the plot should be 1, "learning" no solution. Therefore, "from" = 2.
In a bit, the "study" × 4 bits of the plot is 2, "Learning" = 3 or 8. However, due to "learning" is the first product of the number of
Must be greater than or equal to 8, so "learning" = 8.
In 1000, due to "small" × 4 can no longer binary 10000, the "small" = 1 or 0. If "small" = 0, then
10 on "a few" × 4 + 3 (binary) of a bit is 0, this is not possible, so "small" = 1.
In 10, the "few" × 4 +3 (binary) of a bit is 1, the introduction of "number" = 7.
In 100, the "love" × 4 +3 (binary) of a digital or "love", and 100 to 1000 into 3, so "love"
= 9.
It desires multiplication formula for
21,978
× 4
— — — — — —
87,912
Above, this classification method does not repeat, without omission, reflects the combination of ideas.
In addition, there are symbols of thought, corresponding to thought, the limits of thought, such as collection of ideas in mathematics teaching in primary schools should pay attention to
Purposeful, selective and timely manner to infiltrate.
Third, primary mathematics teaching should be how to enhance the penetration of mathematical thinking
1. To raise the consciousness of infiltration
Mathematical concepts, rules, formulas, the nature of knowledge are clearly written in the textbooks, there is a "shape", and mathematical thinking
Methods of mathematical knowledge implicit in the system, there is no "shape", and the fragmentation of land scattered in various sections of materials. Education
Teachers do not talk about, talk less say more, more arbitrary, often due to tight schedule and will be teaching it as a "soft mandate" squeezed out.
Requirement for students to understand how the number of operators. Therefore, as teachers must adopt new ideas, he kept on from the ideologically
Way of thinking to penetrate the high awareness of the importance of mathematics, mathematical knowledge and mastering mathematical way of thinking at the same time penetrate into the teaching
The purpose of teaching the mathematical way of thinking into the preparation part of the request. Second-depth study materials, the efforts of mining materials can be
Mathematical way of thinking in order to infiltrate a variety of factors, for each section of each chapter, to consider the specific details of how to combine into
Mathematical way of thinking line penetration, which penetrate the mathematical way of thinking, how infiltration, infiltration to what extent there should be a total
Design, the different stages of the specific teaching requirements.
2. To grasp the possibility of infiltration
Mathematical Methods of teaching must be specific to the achievement of the teaching process. Therefore, we must grasp the teaching process
Mathematical way of thinking teaching opportunity - the process of concept formation, the conclusion of the process is derived, and methods of the process of thinking,
To explore the process of thinking, the law of the process reveals. At the same time, the teaching of mathematical thinking should pay attention to the organic combination of
Natural infiltration, have consciously exert an imperceptible influence on students to comprehend the knowledge contained in the mathematical way of thinking among the various mathematical,
Avoid rigid application, a clean breast of everything, from the actual practice, such as counter-productive.
3. Pay attention to the repeated infiltration of
Mathematical way of thinking is thinking in students the process of accumulation and the formation of the progressive. To this end, in teaching, the first special
To solve the problem after another stressed the "reflection", because in this process derives from the mathematical way of thinking, for students
Is easy to understand, easy to accept. Such as through the application of problem scores and the percentage of regular board speech contrast, students in small
Node to answer key questions such applications, to find a specific number of the corresponding sub-rate, so that students experience their own thoughts and the corresponding
Thinking of naturalization. Secondly, attention should be paid to the long-term infiltration, it should be evident to students is not a mathematical way of thinking once the infiltration of a
Xi will be able to improve the mathematical abilities of students to see, but there is a process. Mathematical way of thinking must be gradual and repeated
Training so that students can truly be realized.