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 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 Therefore， we should have a choice to infiltrate some mathematical way of 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 R 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 It should be noted that under the thinking is different from that of the general talk about "transformation"， "turn In other "It is an irreversible one-way 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 They only jump a second 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 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 O Number Shape Combination thinking Number Shape Combinationthinking of making full use of "shaped" the image of a certain number of relations that 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 Example 2 a cup of milk， drank half a second drank the remaining half of each drink on such last The remaining half 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 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 Transform thinking Transformation is a form of thinking into another form of 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 Example 3 for 1 / 2 +1 / 6 +1 / 12 +1 / 20 + +1 / 380 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 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 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 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 Therefore， "from" = In a bit， the "study" × 4 bits of the plot is 2， "Learning" = 3 or However， due to "learning" is the first product of the number of Must be greater than or equal to 8， so "learning" = In 1000， due to "small" × 4 can no longer binary 10000， the "small" = 1 or If "small" = 0， then 10 on "a few" × 4 + 3 (binary) of a bit is 0， this is not possible， so "small" = In 10， the "few" × 4 +3 (binary) of a bit is 1， the introduction of "number" = In 100， the "love" × 4 +3 (binary) of a digital or "love"， and 100 to 1000 into 3， so "love" = It desires multiplication formula for 21，978 × 4 — — — — — — 87，912 Above， this classification method does not repeat， without omission， reflects the combination of 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 Third， primary mathematics teaching should be how to enhance the penetration of mathematical thinking 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 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 Requirement for students to understand how the number of 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 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 To grasp the possibility of infiltration Mathematical Methods of teaching must be specific to the achievement of the teaching 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 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- Pay attention to the repeated infiltration of Mathematical way of thinking is thinking in students the process of accumulation and the formation of the 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 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 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 Mathematical way of thinking must be gradual and repeated Training so that students can truly be
Solves mathematics competition topic certain thinking method Take mathematics competition topic as the carrier， elaborated mathematics thinking method implication: Mathematics thought is knew to mathematics knowledge essence that is overweight refines the rise from certain concrete mathematics content and to mathematics understanding mathematics viewpoint， is mathematics knowledge structure essence and the soul， it the command and the control mathematics knowledge It is utilized repeatedly in the understanding activity， has the universal guiding sense， is establishes mathematics and solves the question guiding principle using The mathematical method refers to mathematics， in proposed that the question， solves in the question process， uses each way， method， way and so on; Has enumerated the algebra substitution law， the addition effective condition in mathematics competition in the problem solving application; Has demonstrated mathematics unification beautifully， simple beautiful， symmetrical beautiful， strange beautiful 数学思想；Mathematics thought数学方法；Mathematical method竞赛；Competition代换法；Substitution method增设条件Addition condition
