Present situation and improvement measures of estimation teaching

Daxi Erxiao Xu Lizhai

Abstract: The teaching of estimation makes us feel a lot of confusion, for example, students "calculate before estimating" and "the estimation speed is slower than the accurate calculation".

And the phenomenon of "indecision of estimation methods" shows that our estimation teaching needs to be improved.

To study law, we should change teachers' ideas and attach importance to estimation teaching; Cultivate the awareness of estimation according to the specific situation; Teaching evaluation

Strategies for improving evaluation ability.

Keywords: teaching effect evaluation, teachers' evaluation ability, ideas and consciousness

With the birth of the new curriculum, estimation teaching has become one of the focus issues discussed by teachers. It is not difficult to find that although we are actively discussing estimation teaching, it still makes us feel a lot confused. For example, students' "calculation before estimation", "estimation speed is slower than accurate calculation" and "uncertain estimation method" all indicate that our estimation teaching needs to be improved. So, what makes the teaching of estimation ineffective, and what can we do to improve it?

Change teachers' concept and attach importance to estimation teaching

analysis of existing circumstance

Judging from the current situation, teachers pay less attention to estimation teaching than curriculum standards. There are three reasons:

1. Teachers are influenced by traditional teaching concepts. Estimation teaching is optional in the old textbook, compulsory in the new textbook and compulsory in all books and chapters of the textbook. However, influenced by the traditional teaching concept, teachers do not regard estimation teaching as a kind of computing ability, and often teach textbooks with arrangements, but not without arrangements. They didn't insist on training from beginning to end, and didn't equate estimation teaching with accurate calculation at all.

2. Teachers don't know the teaching function of estimation clearly. I found from individuals and peers that many of our teachers think that the function of estimation is to act as a simple calculation method when accurate calculation is not needed, or as a test method to test whether accurate calculation is correct. Many teachers don't realize that apart from the above two functions, the more important function of estimation is to cultivate students' sense of numbers and mathematical literacy.

3. The evaluation status of estimation teaching makes teachers pay insufficient attention to estimation teaching. Because estimation teaching is not arranged as an independent unit, the evaluation of estimation teaching effect is not independent and significant, and only a few estimation questions are added in the paper-and-pencil test. Compared with a test paper, the scores of several questions are not very different, so it is estimated that the teaching effect is not valued by teachers.

(2) Improvement measures

1. Get out of the radiation circle of traditional teaching concepts. Teachers should get out of the old textbooks, read the new curriculum standards and understand the estimated teaching objectives; Teachers should also look at the new textbooks, sort out the whole textbook arrangement system, and understand the arrangement of estimation teaching in the whole textbook system; Make it clear that the new textbook attaches importance to estimation teaching and should not be influenced by traditional teaching concepts. Teachers should understand that oral calculation, written calculation and estimation are three basic calculation skills. Oral computing ability, written computing ability and estimation ability constitute a person's complete computing ability. These three skills are indispensable to cultivate students' mathematical ability. Therefore, we should pay attention to estimation in the usual teaching, and now we should focus on spending time to make up for it.

2. Understand the role of estimation teaching. Estimation is a calculation method, its basic function is to use it to calculate quickly when accurate calculation is not needed; Estimation often plays the role of checking calculation. In addition to these two functions, estimation has another important function, which can cultivate students' sense of numbers and mathematical literacy. For example, through the estimation of logarithm and quantity, students can experience the size and quantity of the numbers and quantities they have learned. For example, after learning the natural number 1- 100, students can estimate how many soybeans there are in a handful and how many people there are in a classroom. After estimating the result, calculate it accurately, look at the gap between the two, and get an idea of the number of 1- 100. Isn't this the embodiment that the new curriculum standard requires students to learn mathematics through experience? Through estimation teaching, students can also establish the consciousness of using mathematics and improve their ability to use mathematics. For example, when shopping in a supermarket and estimating how much fruit you need to buy, you feel how much a bag of fruit weighs. These problems can make students turn book knowledge into real life problems and strengthen the connection between book knowledge and life problems. Therefore, we say that estimation teaching is necessary and teachers need to pay enough attention to it.

3. Change the evaluation mechanism and evaluate the teaching effect. Changing the evaluation mechanism to estimate the teaching effect, students should avoid the simple paper-and-pencil method of evaluating the estimation ability, and pay attention to the examination of the estimation process [1]. The following measures can be taken:

(1) Write the estimation process, such as 49× 3 ≈ 50× 3;

(2) Write the approximate range of the estimated results. 49 × 3,300 people. A: They can't get on the boat at the same time. "Seeing this situation, I had the following conversation with the students:

Teacher: "Does this question have to be accurate?"

After a moment of silence, you get 1: "No need."

Teacher: "Why?"

Health 1: "Because 100 plus 200 equals 300."

Teacher: "How did he work it out? What do you think of this method? "

Health 2: "He used the estimation method, which is relatively simple. He can write 138+202 > 300. "

Teacher: "Then why don't you do it?"

The students were speechless.

This case reminds me, what happened to our students? Don't everyone like to write more when writing questions? Then why would they rather write a few more words than use estimation? Isn't what we have been trying to teach an "armchair strategist"? Is it still meaningful to learn to estimate like this?

2. habit. Another current situation is that students are not aware of the estimation. Students are used to calculating accurately when they see problems, without thinking about which method is more suitable first.

(2) Improvement measures

1. To improve the estimation ability of primary school students, we should first let students know the meaning of estimation, so as to improve their enthusiasm for learning estimation [2]. This requires us to create specific situations and cultivate students' estimation consciousness in combination with specific situations. If it is not in a specific situation, it is empty to talk about cultivating the awareness of estimation. For example, in the estimation class of Professor Wu Zhengxian, a famous special-grade teacher, she created a situation before class. Qingqing and her mother go shopping in the supermarket. After selecting the goods, her mother's question is: Does her mother have enough money with 200 yuan, so that students can judge whether it is meaningful to use the estimate in the following situations: a. Her mother considers whether 200 yuan is enough; B, when the salesman wants to input the price of each commodity into the cash register; When mom was told how much to pay.

Here, Mr. Wu did not ask "how much does it cost to buy these items" but designed such multiple-choice questions, obviously from the perspective of cultivating students' awareness of estimation. Like Mr. Wu, before teaching estimation, let students judge when to estimate and when to calculate accurately, so that students can understand why we should learn estimation. Isn't the mathematics curriculum standard that "everyone should learn useful mathematics"? This is more useful than we always tell students that estimation is very useful.

Of course, the specific situations mentioned here do not all refer to the above-mentioned shopping environment, but also include other specific problems, such as

Among the following formulas, the formula with a number greater than 800 is ()

a，462+335 B，397×2 C， 1000-209 D，2 15×4

Obviously, problems like this can be solved quickly through estimation, so by comparing the speed of solving this problem, students' estimation consciousness can also be cultivated.

2. To cultivate students' awareness of estimation, we should not only let students know when to use estimation, but also develop the habit of estimation. It takes time and perseverance to cultivate the habit of estimation. For example, before calculation, estimate the approximate range of the estimated number, and after accurate calculation, estimate whether the estimated value is within this range. There are many requirements in class, such as "please estimate" and "tell me how you estimate" After a period of such training,

Third, teach estimation strategies and improve estimation ability.

(A) analysis of the status quo

1. The status quo of "calculate first and then estimate" exists. It is not difficult to find that some students (especially poor students) will calculate the results accurately when they encounter the estimation problem, and then get the approximate value of the accurate results. This situation was quite common in the first few years of the new curriculum reform, and it still exists partially at present. The main reason is that students' estimation speed is slower than accurate calculation, and their estimation ability is not strong.

2. The estimation method is "indecision". According to my teaching experience and survey results, I found that some students prefer accurate calculation to estimation, because the answer to accurate calculation is unique, the method is often unique, and the estimation methods and results are diverse, so students feel lack of confidence when using estimation methods and hesitate when their estimation ability is not strong.

3. One-sided training under the teaching mode of "estimate first, then calculate". In estimation teaching, teachers often attach great importance to estimation and calculation, that is, let students calculate after approximation. This is also one-sided. Some topics can be estimated without approximate figures, which shows that the estimation strategy is very important.

(2) Improvement measures

Although the estimation methods are flexible and diverse, and the answers are not unique, the estimation is not without rules, and general estimation strategies can be summarized. In order to enable students to use estimation flexibly and actively, we must teach students the strategies and skills of estimation and improve their estimation ability.

1. Familiar with approximate method. Approximation is the basis of estimation teaching, which requires us to design more questions like "how close is this number", "how big is this number" and "what number do you think of when you see this number", so that students can reflect its approximation in their minds when they see a number. When students take an approximate value, such as 378, different results will appear. We should all make appropriate evaluations instead of denying students' ideas with satisfactory answers in the teacher's mind. Students should be encouraged to take approximate values and express their ideas, so that their sense of numbers will be gradually enhanced and the speed of estimation will be improved.

2. Learn to adjust strategies and cultivate awareness of optimization. Estimation is a very strategic calculation method. Students should fully experience the process of diversification and optimization of estimation methods and give them the experience of choosing their own estimation strategies. For example, Wu Zhengxian, a famous special-grade teacher, attached great importance to the adjustment strategy of estimation in the lesson Estimation. She first draws the conclusion that "it is best to use the method of intermediate estimation, adjustment estimation or size estimation" through the students themselves, and then arranges the following two exercises to realize the estimation.

(1) The school organized 350 students to go for a spring outing and rented 7 cars with 56 seats each. Is one seat enough for everyone?

(2) A truck, with its own weight of 986kg, carrying 6 boxes of goods, each with 285kg, can successfully cross a bridge with a weight limit of 3 tons?

Teacher Wu organizes students to discuss: "Which estimation method is better, big estimation or small estimation?" "Is the big estimate sure or the small estimate sure?" "When you want to estimate in the future, is it a big estimate or a small estimate, or ..." Students want to know for themselves. "。

Problems like this that need to be estimated by adjusting strategies are the weaknesses of students, especially poor students. Therefore, it is necessary to strengthen the training of estimation adjustment strategies at ordinary times, so that students can flexibly use estimation skills with the support of experience.

3. Flexible use of strategies for evaluation.

(1) Flexible use of mathematical laws and properties for estimation [3]. Using mathematical laws and properties to estimate, the approximate step can be omitted, which makes the estimation more concise and fast. If a number other than 0 is multiplied by a pure decimal and the product is less than this number, it can be determined that the product of 4.9×0.6 must be less than 4.9. When it is zero, you can think >; Therefore, mastering mathematical laws and properties can make the estimation faster.

(2) Select the estimation method according to the actual needs. Approximation is not always needed for estimation, and in some cases, the step of seeking approximation can be omitted. For example, when we teach "understanding of tons", we only need to let students feel the weight of 50 kilograms. Imagine 1 ton, that is, 1 000 kg, and there are 20 50 kg. In fact, this is also the process of estimation. In some life examples, sometimes we don't need to get an approximation. For example, when estimating the number of people in a venue, we don't take one person as the unit, and then think about how many such people there are. But first think about how many 50s there are in our class. Of course, you can also think about how many 100 before thinking about how many 100.

References:

[1] Zhang Junying, Reflections on the Teaching of Mathematical Estimation in Primary Schools, Primary School Teaching Research, 2008(6)

[2] Zhang Lizhen, the cultivation of estimation ability in primary school mathematics teaching, Gansu Education, 200 1(9)

[3] Zhou Hao, estimation of primary school students' ability, primary school teaching reference, 200 1(3)

Elementary school mathematics thesis

Development and Utilization of "Scenario String" Teaching Resources in Computing Teaching

Wenling henghu primary school baomiao

[Abstract] Play a guiding role in the calculation class from beginning to end, so that students can trigger the learning of mathematical calculation by solving the problems in the "scenario string", closely combine problem-solving with computational learning, let students experience the formation process of computational knowledge and skills, and use the learned computational knowledge as a problem-solving tool to cultivate application awareness throughout the whole process of mathematical learning, which is the core connotation of "scenario string" teaching. Teachers should find the right fulcrum. Only by creating a "scenario string" with "mathematical charm" can it really play its due value in the calculation class. This paper expounds the development of "scenario string" teaching resources from the following aspects: first, dynamic scenario string comes from static theme scenario diagram; Second, the dynamic scene string comes from the close life practice; Third, the dynamic scene string comes from vivid animated stories; Fourth, the dynamic scene string comes from interesting game activities.

[Keywords:] dynamic scene string static theme map life practice animation story game

Text: The National Committee of the United States pointed out in the report "Everyone cares about the future of mathematics education": "Today, a person whose mathematics skills are limited to calculation has little contribution to today's society, because cheap calculators can do things better." If the goal of computing teaching is to remember computing rules and form computing skills, it is obviously meaningless. Teachers should use the carrier of computer teaching to guide students to actively participate. Actively explore, so that they can get the harmonious development of emotion, attitude and values while gaining computing knowledge. Therefore, the goal of computing teaching should not only be satisfied with letting students master methods and learn to calculate, but also focus on letting students experience the needs of computing learning, let students experience the exploration of computing strategies, appreciate the charm of computing thinking, truly give play to the educational value of computing teaching, and let students obtain the harmonious development of emotions, attitudes and values while gaining computing knowledge.

Mathematics class requires students to be highly focused and active in thinking in order to complete their learning tasks. For primary school students, the time of concentration in class is relatively short, not to mention the relatively boring calculation class. If we link the whole class into a "scene string" by creating a set of related scenes, that is, the whole class is organized around a big scene with a theme. Teaching content design leads to a series of relatively independent questions with a certain logical relationship in each link of related scenes, that is, each scene string, forming a "question string", calculating the teaching background in real life, and strengthening the communication between the "book world" and the students' "life world", which will undoubtedly greatly increase the interest and attraction of the learned knowledge and prevent students from "attention fatigue" and.

First, the dynamic scene string comes from the static theme scene.

The implementation of situational teaching is not water without a source, but a tree without a root. The new textbook obviously lacks text narration in typesetting, which is followed by vivid, interesting and colorful thematic maps embedded in our teachers' and students' horizons, which deeply attracts us. It is these thematic maps that integrate knowledge, thoughts and emotions into our classroom teaching, providing rich resources for our teaching design and giving fresh life to boring mathematics. Let our scene series teaching become the source of water and the tree of roots. Fully tap the theme map, interpret the "theme map" scenario with relatively independent stories or activities that students are interested in, and organically combine rich scene pictures with specific mathematical knowledge, so that rich scene settings can play a guiding role in students' learning process from beginning to end, helping students learn knowledge in a happy atmosphere.

For example, in the first lesson of Volume 4, "Division in Table (2)", the example 1 gives the theme pictures of students celebrating festivals, while the theme pictures of exercise 1-4 are monkeys climbing poles, rabbits picking mushrooms, birds delivering letters and pigs blowing bubbles respectively. However, junior students' interest in the static information window is too short, and the relatively independent theme picture makes the classroom seem too sloppy. In the second half of the class, the students were lifeless and step by step, so I tried to turn several static and relatively independent information windows into a dynamic and coherent scene string. The whole class focuses on students' favorite "Celebrating June 1st", through "arranging the venue for the party" (such as 1 teaching content)-"participating in the Happy Garden activities" (exercise 65438+).

Scene 1: Setting up classrooms for festivals (teaching example 1). "Today is a happy Children's Day. Are you happy? The children will decorate the classroom to celebrate their festival. Let's go and have a look! " (Courseware demonstration) The design purpose of this link is to put forward a question string according to the information window and explore the calculation method, so that students can realize that calculation is only for solving problems, and calculation is accompanied by solving problems.

Scene 2: Garden Activity "The Blind Ask the Way" (Exercise 1) The teacher is going to take you to the garden activity on June 1. Do you want to join? The rules of the game for blind people to ask for directions: one person points out the problem blindfolded and other students participate in the calculation.

Scenario 3, Scenario 4 and Scenario 5 are garden activities such as "catfish", "fishing for the moon in water" and "blowing bubbles", corresponding to Exercise 2- Exercise 4.

Through the effective adjustment of teaching materials, the static information window is turned into a dynamic scenario string, and the calculation skills of multiplication formula quotient are subconsciously passed on to students in the form of pictures, operations and languages, so that students can calculate with interest in intuitive and vivid game situations, let them realize that multiplication formula quotient is a tool to help people solve practical problems, and let students find that mathematics is around and feel close to mathematics.

Second, the dynamic scene string comes from the close life practice.

Choose the life scenes that students are familiar with. You can directly select familiar daily life scenes provided by students in textbooks for processing or create real life scenes that students are interested in, and run through the scenes of life practice activities that students are interested in and arrange them into a "scene string".

For example, the practice class of the fourth volume of multiplication and division, I designed it like this: scene string background: On Sunday, the teacher led the students to play in the amusement park. Scene 1: Before leaving, the monitor counts the number of people. Teacher: I asked the monitor to count several groups (6 groups) of friends who came today and see how many people (4 people) there are in each group. Teacher: blackboard writing: 6 groups. There are four people in each group. Teacher: Who can ask a question based on these two pieces of information (how many people are there? * *) Who can solve this problem? Scene 2: Start, how to rent a car. Courseware picture: There are 8 cars in the parking lot, and each car can only carry 3 people. Scene 3: Come to the gate of the garden and get ready to buy tickets. Courseware picture: There are tourist information and ticket price (2 yuan per person) at the gate of the amusement park. Scene 4. Design entertainment projects and tourist routes. Courseware picture: the price and related regulations of amusement facilities in amusement parks. Scene 5: Have a rest and go shopping in the food supermarket in the amusement park. Courseware picture: In the food supermarket of amusement park, there are 2 bottles of mineral water, 2 bottles of 6 yuan and 4 yuan for each bottle of soda.

In the above-mentioned series of related scenes, there are bright lines and dark lines. The bright lines are sightseeing, and the dark lines are "observing the picture, collecting information-asking questions according to the obtained information-cooperating and communicating, calculating and solving problems". In the whole learning process, students are enthusiastic, active in thinking and actively participating. In the process of seemingly playing, they not only consolidated their proficiency in multiplication and division in the table, but also cultivated their ability to apply knowledge to solve practical problems. Around the scene of "sightseeing" all the time, teachers have created one scene after another for students, causing one problem after another, providing an effective platform for students to study independently and explore independently, prompting students to think deeply, experience and feel at different levels, and letting students consciously and wholeheartedly devote themselves to computational learning activities, and sincerely discover, think and communicate. Complete the construction of knowledge independently in the ups and downs of emotional experience, creatively construct situational strings, and integrate the calculated content, knowledge and skills into colorful, vivid, interesting and concrete life scenes, thus activating students' learning enthusiasm; Activate the flexibility of students' thinking; Activate students' question consciousness and form a question string; It changes students' learning style, allowing students to apply mathematical ideas in real "scenario series", find problems, ask questions and explore and solve problems independently; Cooperation and communication in "scenario string" can experience the fun of learning mathematics and promote the development of students.

Thirdly, the dynamic scene string comes from vivid animated stories.

It is difficult to create a scene that interests students by relying on a picture and a paragraph of text. Animation stories are pupils' favorite. Pupils are interested in animation stories, and their thinking is easy to be inspired, developed and activated. Scenario strings derived from animated stories will generate sustainable motivation, which is a catalyst to make computing teaching jump out of the old road of skill training only for computing, let students learn mathematics in vivid and concrete situations, and combine computing with application to make the classroom full.

For example, when I was teaching the first book "Applied Mathematics", I used the beautiful picture of "forest morning" to attract children's attention and make them feel as if they were there. In the whole class, I designed a series of story strings to guide a series of students to go for an outing in the big forest, and organically linked the examples and exercises in the textbook, so that students seemed to be in a happy journey and let them play and enjoy middle school. Learning is very interesting. The abstract knowledge is concretized, and the static picture is dynamic, so that students' various senses can participate in learning activities, forming a vivid and interesting learning atmosphere and promoting the exploration, dynamics and emotionalization of cognitive activities. For example, in Unit 6 of Book 5, "A factor has a multiplication of 0", I tried to replace the static and relatively independent information window with a dynamic scene string with the fairy tale of Journey to the West that students like as the main line. Scene 1: (Example 5 Theme Map) The Queen Mother is going to celebrate her birthday. She sent seven fairies to the Flat Peach Garden to pick peaches to celebrate her birthday. When the fairies came to the Flat Peach Garden, they were surprised to find that the Monkey King was sitting on a peach tree, munching on peaches, and there were no peaches on the tree. The fairies hurried back to report to the Queen Mother: "All the peaches were eaten by the Monkey King, but none were picked." Ask the students to list the formulas of addition and multiplication, and discuss that 0 multiplied by any number is 0. Scene 2: (Example 6 Theme Map) Can children really live long after eating flat peaches? (No) Yes, life lies in exercise. We should keep doing physical exercise every day like this birthday girl. Can you figure out how many meters the old birthday girl walks every day? Think about how many meters the old birthday girl walks every day. How to calculate the formula? Students explore the algorithm and come to the conclusion that whether there is zero in the middle of the factor or not, you should multiply each digit with this single digit, even if there is a zero in the ten digits. If there is no carry, the ten digits of the product should be occupied by a zero. Scene 3: (Consolidate and deepen, expand application) Now is the growth of children. So we must take part in physical exercise. You see, Cong Cong is going to take part in the intellectual long-distance race. Shall we join in? (The specific exercises are omitted, and the basic questions, improvement questions and expansion questions are infiltrated in the later exercises. )

The creation of this scene string is friendly, simple and natural, which allows students to ask related calculation problems in familiar animation story scenes. Students practice in stories and learn knowledge in stories, which not only makes them feel relaxed and happy, but also unconsciously learns the knowledge of a class until the class is over.

Fourthly, the dynamic scene string comes from interesting game activities.

Scenes from lively and interesting game activities are especially suitable for calculation practice classes and review classes. In the review class of computing practice, everyone was at a loss. Either one question after another, or classification. It's really boring, and unconsciously it becomes a permanent pain in our math teacher's heart. For students, especially the primary school students in the middle and lower grades, it will be boring to simply take out the exercise review materials and let students practice directly, just staying in the simple knowledge melting pot. However, if they follow the routine, they will get bored.

For example, I designed three step-by-step situational games to run through the whole class in the revision class of Unit 2 of Mathematics in Book 3, Addition and subtraction of numbers within 100. Game 1: "See who gets more harvest", you are required to fill in any harvest card and stick it on the blackboard. The winner is king, mainly by summarizing the calculation rules of adding and subtracting two digits within 100. When adding manually, when the () bit reaches ten, enter1in the () bit; ; If the () position is not reduced enough, it is necessary to retreat from the () position; When solving a problem, when the result does not need to be very accurate, you can find a number close to the result by the method of (). Game 2: "Please raise your hand" and calculate each question in your favorite vertical way. Each student gets a question card, and the winner is the person who answers correctly within the specified time. The main test is the accuracy and speed of calculation. Game 3: "Take the treasure chest by intelligence". Cong Cong and Mingming, the elves, see that children are so capable and want to invite you. There are two treasure boxes in the smart house, which are filled with many wisdom stars and wisdom beans. Do you want them? If you want to get the wisdom star and wisdom bean, you should solve the problem card on the treasure chest quickly. The problem card design combines real life and real situations, including shopping estimation and solving mathematical problems in life. Winners are clear expressions of ideas and correct solutions. This design makes students feel refreshed and overcomes the disadvantages of monotony, boredom and topic-oriented.

The creation of "scenario string" should fill the whole time and space of computing classroom. As long as there is computing activity, there will be a corresponding computing background. It should be multi-dimensional and all-directional, and should play a guiding role in the whole learning process of computing for students from beginning to end, so as to promote students' independent and effective learning. To stimulate students' interest in computing as the pillar, to cultivate students' awareness of mathematical problems as the guide, and to promote the effective achievement of teaching objectives, we strive to create a "suitable" scenario string. Let the situation string have the support of "mathematics", make the situation string more "mathematical flavor", let our math class not lose the "mathematical flavor", and let our calculation class not lose the "life flavor"!

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