解決問題中數(shù)量關(guān)系模型教學(xué)的有效策略

1、在小學(xué)六年級分?jǐn)?shù)乘法教學(xué)時，筆者整理了這樣一組題：5 10 3 支水筆要多少元？45 頁，已經(jīng)看了 3/5。已經(jīng)看了多少頁？題整個長方形表示 15，陰影局部表示多少？25 5 3 認(rèn)真閱讀分析之后，我們不難得到這組題的解答分別是：1053，4553，1553，2553。這里有整數(shù)的解決問題、分?jǐn)?shù)的解決問題甚至還有圖形題，為什么四個不5 3？其實(shí)，這組題我們都可以用以下圖來解釋，都是先求1 份再求 3份。其實(shí)這就是模型化的思想。生理解解決問題的方法，從而提高教學(xué)效益。用生活閱歷理解問題，將分析數(shù)量關(guān)系作為解決問題策略的關(guān)鍵。 =單價數(shù)量、路程=速度時間，并能解決簡 =程=速度時間”這種針對數(shù)量相

2、依關(guān)系，承受形式化的數(shù)學(xué)符號和語言，概括性地表述出 來的數(shù)學(xué)構(gòu)造化語言公式，就是數(shù)學(xué)模型化。一、加強(qiáng)運(yùn)算意義教學(xué)，建立根本模型含圖形與幾何方面的主要問題。因此，筆者認(rèn)為在教學(xué)過程中，應(yīng)當(dāng)加強(qiáng)運(yùn)算意義的教學(xué)，以理解運(yùn)算意義模型，提高學(xué)生分析數(shù)量關(guān)系的力量。 算，這種運(yùn)算叫做加法運(yùn)算。如一年級下冊有這樣一道題目：一件上衣50 元、一條裙子40 元、一條褲子0 買一件上衣和一條褲子多少錢？付給售貨員0 元，應(yīng)找回多少錢？3你還能提出什么數(shù)學(xué)問題？教師可以在學(xué)生認(rèn)真讀題之后幫助學(xué)生這樣理解 數(shù)量關(guān)系：衣服的價格+褲子的價格=總價；在具體情境中屢次體驗(yàn)、感悟“數(shù)學(xué)模型”典型實(shí)例的根底上，理解、建立它們之

3、間的數(shù)量關(guān)系模型就是“局部數(shù)+局部數(shù)=35 2 35 20 1還剩多少本故事書？2-借出的故事書=-借出的動漫書=目的數(shù)量關(guān)系模型就是“總數(shù)-分?jǐn)?shù)=就是“大數(shù)-小數(shù)=高學(xué)生解決問題的力量奠定根底。二、結(jié)合情境教學(xué)，建立常見模型概括與應(yīng)用，以數(shù)量關(guān)系的有效構(gòu)建提升學(xué)生分析問題和解決問題的力量。比方，有這樣一道題目：有兩個人在相距72 千米的兩個地點(diǎn)同時相向而行，第一個人的速度是 4km/h，另一個人的速度是8km/h，有一只狗原來與第一個人在一起，與兩個人同時動身，向其次個人的方向跑去，當(dāng)他追上這個人時，馬上向相反方向跑，去追另一個人， 這6km/h，問這 只狗跑的距離。 s=vt，要 了。兩個

4、人同時用的時間與狗跑的時間相等！人所用時間：728+4=6 小時，狗跑的距66=36 思考、分析問題，看的不同了，境地也就不一樣了！=價數(shù)量=總價”演繹出“總價數(shù)量=單價、總價單價=數(shù)量”等。這些根本關(guān)系式具有導(dǎo)學(xué)生將建立的數(shù)學(xué)模型遷移到他們不生疏的情境中，作為實(shí)現(xiàn)解決問題的方法和措施。三、依據(jù)根本關(guān)系，以模型化繁為簡關(guān)系模型，以模型化繁為簡。300 +褲子的價格=認(rèn)真讀題我們還會覺察：褲子的價格=上衣的價格。讓學(xué)生對兩個數(shù)量關(guān)系進(jìn)展分析，覺察3 2 5 1 份再求上衣和褲子的價格就可以了。1 學(xué)生思考與解決問題的力量。 到抽象概括，把解決問題從閱歷式逐步提升到用數(shù)學(xué)方法解決問題。無論用等式

5、象過程，體驗(yàn)提煉、運(yùn)用策略的全過程，在經(jīng)受建模、策略應(yīng)用的過程中，逐步提高學(xué)生數(shù) 力的進(jìn)展，進(jìn)而有效地促進(jìn)學(xué)生思維品質(zhì)的進(jìn)展，到達(dá)教育教學(xué)的目的。In the sixth grade scores multiply teaching, the author compiled a set of questions like this:Problem (1) to buy five pen need 10 yuan, according to this calculation, buy 3 pen how much yuan?a book on 45, has looked at 3/5. Hav

6、e looked at how many s?the whole rectangle said 15, the hatched section shows how much?the strawberry unit price is $25, 5 times that of bananas. Lemon”s price is 3 times of banana, lemon unit price how many yuan?Read carefully after analysis, it is easy to get this problem set solutions are: 10 pre

7、sent 5 x 3, present 5 * 3, 15 members present 5 * 3, 25 members present 5 x 3. There is an integer problem solving, scores of problem solving and even graphics, why four different questions are divided by 5 by 3? In fact, this set of questions we all can be explained by the image below, is the first

8、 1 to 3.In fact this is modeling.Problem solving teaching is the key to training students” problem solving strategy, its characteristic is to use the students rich life experience, to help students understand the methodsto solve the problem, so as to improve teaching efficiency.Curriculum reform in

9、the elementary school mathematics word problems before teaching, we attach great importance to analyze relationship between number in the subject. With the implementation of the curriculum reform, many front-line teachers gradually weakening even marginalized, quantitative relationship between the t

10、eaching and the students to solve practical problems tend to be carried out with the support of life experience or intuition. Students in the process to solve the problem, therefore, the lack of conscious experience, is not conducive to thestudents to form problem solving strategies. With the deepen

11、ing of the curriculum reform, theauthor thinks that we should departure from the students of the existing knowledge, guide the student to use life experience understand problems, analysis of quantitative relation as the key tothe problem solving strategy.2022 edition of the compulsory education math

12、ematics curriculum standards “clearlypointed out:“ to understand some basic methods of analysis and solve problems “. “In a specific situation, understand the relationship between the number of common: total price = unit price * time, quantity, distance = speed and can solve simple practical problem

13、“. Successful absorbs the class changes before the successful practices of traditional teaching of word problems. Like “total price = unit price * number“ and “distance x = speed time“ this number for dependency relationship, using the formal mathematical symbols, and language, a general expression

14、of mathstructured language (formula), is the mathematical modeling.A teaching, strengthening the operation significance, basic model is set upElementary school mathematics problem solving involves knowledge, mostly boils down to is arithmetic model (including graphics and geometric aspects of the ma

15、in problems). Should, therefore, the author thinks that in the process of teaching, strengthen the operation significanceof the teaching, on the basis of understanding operation significance, lets the student carries on thepreliminary experienceandinduction,theproblem ofcomputingandmathematics commu

16、nication, establish the number of the most basic relational model, to improve students” ability to analyze related quantities.For example, in first grade students to understand the meaning of an addition operation, teachers can help students understand addition: combined with the specific situation

17、according to the known two different part Numbers, what is the total demand, is to put the two part number together operation, this operation is called additive operation. Grade as part ii has such a title: 50 yuan a jacket, a skirt for 40 yuan, 30 yuan, a pair of trousers (1) how much money to buy

18、a jacket and a pair of pants? (2) pay the salesman 100 yuan, how much money should be recovered? (3) what you can put forward the math problem? Teachers can help students after thestudents read the questions carefully so that understand number relationships: clothes price + pants price = total price

19、; Many times on the specific situation experience, feeling “mathematical model“, on the basis of typical examples, understanding, establishing the quantitative relation model between them is “part number + = total“.Know subtraction problem in teaching, teachers can help students understand subtracti

20、onsignificance, combined with the specific situation if there is such a title: 35 this story book lend 2, 35 out 20 cartoon books. How much is left (1) this story book? (2) how much is left in this comic book? Teachers can guide students to understand the number of such relationships: “the total sto

21、ry book - lend storybooks = the rest of the story book“ and “a total of anime books - lendanime = the rest of the comic book“. In fact the number of the subject relation model is “- score =another part of the total number.When comparing the size of two quantities, teachers can make students with the

22、 specific situation, can use subtraction operation than their size, which is out of large Numbers and the decimal part of the same, the rest of the is part of the much larger comparing Numbers, isrelatively less decimal is large part, is the larger and smaller Numbers differ parts, thequantitative r

23、elation model is “= a few larger - Numbers“.When teaching multiplication, division, of course, also should pay attention to the teaching of operation significance. Anyhow when solving practical problems, to solve the problem and themeaning of mathematics closely linked, subtly see quantity relations

24、hip, to establish a basicmathematical model, lay a foundation for improving the students” ability to solve the problem.Second, the situational teaching, establish a common modelTo strengthen the guidance of the quantity relationship analysis, in the process of using mathematical method to solve the

25、problem, pay attention to the common quantitative relation of abstract, generalization and application are made valid by means of the quantitative relation ofconstruction of improve students” ability to analyze and solve problems., for example, there is such a topic: there are two men in the 72 km a

26、way from the two sites at the same time each other, the first one is the speed of 4 km/h, the speed of another person is 8 HYPERLINK “ :/ km/h, HYPERLINK “ :/ there was a dog originally with the first one, with two people at the same time, ran to the direction of the second man, when he catch up wit

27、h the person, we immediately to run in the opposite direction, go after another person, repeat,constantly in motion between two people, until two people meet. If the dog is the speed of 6 km/h, ask the dog run.Subject in the elementary school higher grades, but in fact this stumped a lot of high sch

28、ool students, some adults also helpless! The reason is that the students constantly scrutinize the dog every movement, work out every time want to run away together again feel it is very difficult. At this time, as a whole to analyze and ponder over a problem is easy: according to the relationship o

29、f distance, time, speed, the three s = vt, request the dog ran away, in fact as long as know the dog”s speed and time. Have the speed, just know the dog run time. Both at the same time, in time with the dog running time is equal! People use time: 72 present (8 + 4) = 6 hours, dogs run distance is 6

30、x6 = 36 km! What a thought-provoking ideas! We should give students moreopportunities, let them from the overall thinking and problem analysis, look different, state isdifferent!In fact in the teaching, we abstract the quantitative relation model, should also makestudents learn to apply, do the line

31、s, such as according to “speed x time = journey“, change the “distance present time = speed, distance present speed = time“; According to the “unit price * number = total price“ to interpret a “total number of members present = unit price, total price present price = number“, etc. These basic formul

32、a has a high degree of generality and extensive application, we can use the general language and symbol, mathematical model is set up, helps to cultivate students” abstract, general thinking ability, feel the beauty of mathematics abstraction. After the construction of the mathematical model, of cou

33、rse, the teacher should guide students to establish the mathematical model of migration to they are not familiar with the situation, as the methods and measures to solve the problem.Three, based on the basic relations, in order to model change numerous for brief Relationship between the number of pr

34、imary school teaching, both the simple quantitativerelationship between the basic teaching, and also has a complex compound teaching quantity relations. Quantitative relationship between composite teaching is an important content in the elementary school higher grades, and the quantitative relations

35、hip between primary school teaching difficult point and the core. As a result, students in mastering basic quantitative relation model, on the basis of must understand and learn to construct the complex relationship betweenthe number of models, in order to model change numerous for brief.New teachin

36、g material, for example, grade six top volume fraction division unit new topics: atotal of 300 yuan, a set of clothes pants price is the coat. How much is the jacket and pantsmoney respectively? Quantitative relation is the price of the coat + pants price = total price. But we also find carefully re

37、ad the topic: the price of the pants = x coat price. Ask students to analyzethe quantitative relationship between the two, find jacket price is 3, pants price is 2, then the price of a complete set of clothes is five copies. First to 1 again for the price of the coat andtrousers.In this way, the subject back to solve the problem sets at first, this paper fir