解决问题中数量关系模型教学的有效策略

1、在小学六年级分数乘法教学时，笔者整理了这样一组题：5 10 3 支水笔要多少元？45 页，已经看了 3/5。已经看了多少页？题整个长方形表示 15，阴影局部表示多少？25 5 3 认真阅读分析之后，我们不难得到这组题的解答分别是：1053，4553，1553，2553。这里有整数的解决问题、分数的解决问题甚至还有图形题，为什么四个不5 3？其实，这组题我们都可以用以下图来解释，都是先求1 份再求 3份。其实这就是模型化的思想。生理解解决问题的方法，从而提高教学效益。用生活阅历理解问题，将分析数量关系作为解决问题策略的关键。 =单价数量、路程=速度时间，并能解决简 =程=速度时间”这种针对数量相

2、依关系，承受形式化的数学符号和语言，概括性地表述出 来的数学构造化语言公式，就是数学模型化。一、加强运算意义教学，建立根本模型含图形与几何方面的主要问题。因此，笔者认为在教学过程中，应当加强运算意义的教学，以理解运算意义模型，提高学生分析数量关系的力量。 算，这种运算叫做加法运算。如一年级下册有这样一道题目：一件上衣50 元、一条裙子40 元、一条裤子0 买一件上衣和一条裤子多少钱？付给售货员0 元，应找回多少钱？3你还能提出什么数学问题？教师可以在学生认真读题之后帮助学生这样理解 数量关系：衣服的价格+裤子的价格=总价；在具体情境中屡次体验、感悟“数学模型”典型实例的根底上，理解、建立它们之

3、间的数量关系模型就是“局部数+局部数=35 2 35 20 1还剩多少本故事书？2-借出的故事书=-借出的动漫书=目的数量关系模型就是“总数-分数=就是“大数-小数=高学生解决问题的力量奠定根底。二、结合情境教学，建立常见模型概括与应用，以数量关系的有效构建提升学生分析问题和解决问题的力量。比方，有这样一道题目：有两个人在相距72 千米的两个地点同时相向而行，第一个人的速度是 4km/h，另一个人的速度是8km/h，有一只狗原来与第一个人在一起，与两个人同时动身，向其次个人的方向跑去，当他追上这个人时，马上向相反方向跑，去追另一个人， 这6km/h，问这 只狗跑的距离。 s=vt，要 了。两个

4、人同时用的时间与狗跑的时间相等！人所用时间：728+4=6 小时，狗跑的距66=36 思考、分析问题，看的不同了，境地也就不一样了！=价数量=总价”演绎出“总价数量=单价、总价单价=数量”等。这些根本关系式具有导学生将建立的数学模型迁移到他们不生疏的情境中，作为实现解决问题的方法和措施。三、依据根本关系，以模型化繁为简关系模型，以模型化繁为简。300 +裤子的价格=认真读题我们还会觉察：裤子的价格=上衣的价格。让学生对两个数量关系进展分析，觉察3 2 5 1 份再求上衣和裤子的价格就可以了。1 学生思考与解决问题的力量。 到抽象概括，把解决问题从阅历式逐步提升到用数学方法解决问题。无论用等式

5、象过程，体验提炼、运用策略的全过程，在经受建模、策略应用的过程中，逐步提高学生数 力的进展，进而有效地促进学生思维品质的进展，到达教育教学的目的。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