How to teach computer courses in primary schools well under the background of new curriculum.

1. What are the problems in computing teaching? What's the main problem?

At present, there are four main problems in computing teaching: the contradiction between creating situations and preparing for exams, the contradiction between intuitive operation and abstract operation, the contradiction between diversified operation and optimization, and the contradiction between skill formation and problem solving.

Let's talk about the general aspects first, and then talk about them in detail later. These four problems are more new problems after the curriculum reform.

2. In the past, computing teaching was mostly introduced by reviewing and paving the way, but now it is more popular to create situations. How to deal with the relationship between bedding and situation so that boring calculation can also arouse students' interest?

Constructivist learning theory holds that learning is always associated with a certain social and cultural background, that is, "situation", and learning in the actual situation is conducive to the construction of meaning. Indeed, a good problem situation can effectively activate students' relevant experiences and experiences. Mathematics Curriculum Standard for Compulsory Education (Experimental Draft) also emphasizes "to further cultivate students' sense of numbers and improve their understanding of the meaning of operation by solving practical problems", "to let students experience the process of abstracting quantitative relations from practical problems and solving problems with what they have learned" and "to avoid the disconnection between operation and application". However, nothing is absolute. Because of the origin of mathematics, firstly, it comes from the development needs of the real society outside mathematics; The second is the contradiction from the inside of mathematics, that is, the need of the development of mathematics itself. These two sources of mathematics may become the background of our teaching. For example, primary schools rarely teach "negative numbers" in traditional textbooks. Now the curriculum standard stipulates that primary schools should introduce negative numbers. There are a lot of quantities with opposite meanings in real life, which can be used as materials to reveal negative numbers; At the same time, starting from mathematics itself, in order to solve the contradiction that "2-3" is not simplified enough, it is necessary to introduce a new number, which is also a problem situation that primary school students can easily perceive. Here, it is appropriate to choose one of the two angles to introduce.

At present, the review foreshadowing in traditional teaching has almost disappeared in computing teaching, and it has been replaced by situational creation. At present, the general teaching process of most computing teaching is: teachers create situational students to ask questions, independent thinking algorithm, feedback communication algorithm, and independent selection algorithm. For this reason, many computing classes either start with "shopping" or end with "shopping". Nowadays, it is difficult to see the common review bedding in the past in computing teaching.

On the other hand, should we "review and pave the way" before computer teaching? In fact, the main purpose of preparing for review before a new lesson is to activate the existing relevant old knowledge in students' minds by reappearing or identifying it, so as to disperse the difficulties in learning new knowledge. The former, as long as necessary, is understandable. The problem lies in the latter. In some computing teaching, in order to make the teaching "smooth", some teachers often design some transitional and suggestive questions, and even artificially set up a narrow thinking channel, so that students can draw conclusions without exploring or trying.

The summary of this problem—

It can be seen that there is no contradiction between creating situations and preparing for review. Not all computing teaching needs to find a "prototype" from life. What kind of import method to choose depends on the content characteristics of computing teaching and the starting point of students' learning.

3. How to deal with the relationship between algorithm diversification and algorithm optimization?

Mathematics Curriculum Standard for Compulsory Education (Experimental Draft) points out in the "Basic Concept" that "due to the differences of students' cultural environment, family background and their own way of thinking, students' mathematics learning activities should be a lively, active and personalized process." In the Content Standard of the first period, it says: "We should pay attention to verbal calculation, strengthen estimation and advocate diversification of algorithms." In the first issue of "Teaching Suggestions", it is pointed out again: "Because students have different life backgrounds and thinking angles, the methods adopted must be diverse. Teachers should respect students' ideas, encourage students to think independently and advocate the diversification of calculation methods. "

"Algorithm diversification" is a hot word in the early stage of new curriculum reform.

At the beginning of the implementation of mathematics curriculum reform, everyone felt very fresh about "algorithm diversification" Computation teaching has changed the mechanical mode of "the teacher explains the algorithm when choosing the algorithm in the teaching material, and the students practice the algorithm by imitating it", and there has been a very gratifying change. "Algorithm diversification" has become the most obvious feature of computing teaching.

[Case] Teaching fragment of "abdication subtraction of two digits minus one digit";

First, the teacher shows examples 23-8 through question situations.

Then, after the teacher's careful "guidance", a variety of algorithms appeared, and the teacher spent nearly a class demonstrating (also demonstrating with animation courseware respectively):

( 1) 23- 1- 1- 1- 1- 1- 1- 1- 1= 15

(2) 23-3=20,20-5= 15

(3) 23- 10= 13, 13+2= 15

(4) 13-8=5, 10+5= 15

(5) 10-8=2, 13+2= 15

(6) 23- 13= 10, 10+5= 15

(7) 23-5= 18, 18-3= 15

……

Finally, the teacher said, "You can use any algorithm you like." (class dismissed)

After class, the author communicated with the class teacher. The teacher said, "Now computing teaching must be diversified, and the more algorithms, the better, reflecting the spirit of curriculum reform." The author also asked the students who came up with the first algorithm in class, "Do you really do this?" The student said, "I don't want to use this stupid method!" " It was the teacher who asked me to say this before class. "I asked several students in succession, and no one subtracted 1 one by one in this way. So are the latter algorithms (especially the sixth and seventh algorithms) really invented by students themselves?

The above cases reflect that a few teachers have a vague understanding of the basic contradiction between algorithm diversity and algorithm optimization in computing teaching. Algorithm diversification should be an attitude and a process. Algorithm diversification is not the ultimate goal of teaching, and formalization cannot be pursued unilaterally. Teachers don't have to painstakingly "demand" diversified algorithms, nor do they have to deliberately guide students to seek "low-thinking algorithms" in order to reflect diversity. Even though it is sometimes the algorithm of textbook arrangement, it does not appear in actual teaching, that is, the "low thinking level algorithm" that students have surpassed, teachers can no longer show it, and there is no need to look back.

4. How does computational mathematics cultivate students' sense of number?

The sense of number is a good intuition of the relationship between logarithm and number. Cultivating students' sense of numbers in computing teaching is mainly manifested in: being able to grasp the relative size relationship of numbers in specific situations; Can express and exchange information with formulas and calculation results; Can choose the appropriate algorithm to solve the problem; Can estimate the calculation results and explain the rationality of the results.

On the cultivation of number sense in calculation teaching. I want to say so much first. This question is more abstract.

5. What are the psychological factors that affect students' calculation? What countermeasures should be taken?

I made a special investigation and analysis on this issue 10 years ago.

The psychological factors that affect students' calculation mainly include: rough perception, attention disorder, memory loss, vague appearance, emotional fragility, strong information interference, and side effects of fixed thinking.

Take verbal calculation as an example-

To do oral arithmetic, we must first perceive the formula composed of data and symbols through the students' sensory organs. Pupils' perception of things is characterized by generality, roughness and non-concreteness, and they often only notice isolated phenomena, but fail to see the connection and characteristics of things, so the impression left in their minds lacks integrity. However, the oral math problem itself has no plot, and its explicit form is monotonous, which is not easy to arouse interest. Therefore, when students do oral calculations, they often only perceive the data and symbols themselves without considering their meanings. For similar and similar data or symbols, they are prone to perceptual distortions and errors. For example, some students often regard "+"as "X", "small" as "+","56" as "65" and "109" as "169".

Attention disorder.

Attention is the direction and concentration of psychological activities on an object. The instability of attention and poor distribution ability are important psychological factors that cause oral arithmetic errors. Primary school students' attention is unstable, not persistent, not easy to disperse, and their attention range is not wide, so they are easily attracted by irrelevant factors and appear "distracted" phenomenon. In the process of oral calculation, we need to pay attention to it often or assign it to different objects at the same time. Because primary school students' attention coverage is not wide, when they are asked to focus on two or more objects at the same time, they often lose sight of one thing and lose sight of another. For example, most students can calculate 6×8 and 48+7 by mouth alone, but when the two questions are combined to calculate 6×8+7, students often get 45, which leads to mistakes.

Memory recovery.

The purpose of memory is not only to store information, but also to extract information accurately. In the process of storing information, due to the influence of physiology, time, review amount and other factors, the stored information disappears or is temporarily interrupted, which leads to forgetting and "forgetting mistakes". Especially for oral arithmetic problems such as addition, subtraction, multiplication and division, the instantaneous memory is large. For example, when calculating 28×3 orally, students are required to temporarily remember the results of each step, that is, 20×3=60 and 8×3=24, and work out 60+24=84 in their minds. The main reason for this kind of oral arithmetic problems is that the storage and extraction of intermediate numbers are incomplete or forgotten.

A vague appearance—

Representation is a bridge from perception to thinking. Judging from the operation form, primary school students' oral arithmetic is a transition from intuitive perception to representation operation and then to abstract operation. Judging from the characteristics of primary school students' thinking, their thinking has great concreteness, and appearances often become the basis of their thinking. Especially in the lower grades, children often make mistakes because of the unclear appearance of oral calculation methods. For example, when calculating the carry addition of 7+6 and 8+5, some first-year students are confused about the appearance of "decomposition" → "rounding up ten" → "merging", and they can't imagine the specific process of "rounding up ten", thus making mistakes.

Emotional fragility—

When doing oral calculations, students all hope to work out the result as soon as possible. Some students are eager to achieve success when doing oral arithmetic problems, and it is easy to have the idea of "underestimating the enemy" when the number is small and the formula is simple; But when the number is large and the calculation is complicated, it shows impatience and produces boredom. Some students often can't read the questions comprehensively and carefully, analyze them carefully and patiently, and can't choose the oral calculation method correctly and reasonably, thus forming the bad habit of writing the questions in a hurry without checking.

Strong information interference-primary school students' visual and auditory perception is selective, and the strength of the information they receive affects their thinking. The enhanced information left a deep impression on students' minds, just like the characteristics of reducing numbers to 0,0 and 1, 25×4= 100, 125×8= 1000 and so on. This kind of strong information comes into view first, and it is easy to cover up other information. For example, students don't know the order of "multiply first, then divide, then add and subtract", but are disturbed by the strong message that "the subtraction of the same number equals 0". Some students first thought of 15- 15 = 0, but ignored the operation order and made mistakes in oral calculation.

The negative effects of mentality-

Stereotype is a kind of "inertia" of thinking and a state of preparation formed by certain psychological activities. This readiness can determine a trend of similar follow-up activities. Naijia? What's the matter with you? Aobao? Is money worthless? Fans rebel? What's a coat? Is the source thin? 40 ÷ 60,450 ÷ 90,360 ÷ 40 and other questions are all followed by a 300-50, and many students often miscalculate 300-50 = 6.

So many psychological factors about interfering with calculation.

6. Please talk about how to solve the contradiction between intuitive arithmetic and abstract arithmetic.

In the past, some teachers thought there was no reason to talk about computing teaching. Students can achieve correct and skilled requirements as long as they master the calculation method and practice it repeatedly. As a result, many students can calculate according to the calculation rules, but because of unclear calculation, the scope of knowledge transfer is extremely limited, and they cannot adapt to the ever-changing specific situation in calculation.

Arithmetic refers to the theoretical basis of four operations, which is the basic theoretical knowledge of mathematics composed of mathematical concepts, properties and laws. Algorithm is the basic procedure and method to realize the four operations, which is usually stipulated by some ideas under the guidance of arithmetic. The algorithm provides theoretical guidance for the algorithm, and the algorithm makes the algorithm concrete. When students learn to calculate clearly, it is convenient to calculate flexibly and simply, and the diversity of calculation is the foundation and possibility. I can't imagine how a student who doesn't even understand the principles and methods of basic calculation can work out flexibly and simply. How can you have the ability to calculate diversity? Therefore, it is a very important subject to attach importance to arithmetic and algorithm in computing teaching.

In teaching, we often see such a phenomenon: under the intuitive stimulation of teaching aid demonstration, learning tool operation and picture comparison, students can understand arithmetic clearly through the combination of numbers and shapes, but the good times are not long. When students are still lingering in intuitive arithmetic, they are immediately faced with very abstract algorithms, and the following calculations are directly calculated by abstract simplified algorithms.

Therefore, I think we should build a bridge between intuitive arithmetic and abstract algorithm and pave a way for students to gradually complete the development process of abstract thinking in action thinking, image thinking and full experience.

In a word, computing teaching needs to let students not only intuitively understand arithmetic and master abstract rules, but more importantly, let students fully experience the transition and evolution process from intuitive arithmetic to abstract algorithm, so as to achieve a profound understanding of arithmetic and a practical grasp of the algorithm.

7. Curriculum reform textbooks clearly put forward "strengthening estimation". How do you cultivate students' estimation consciousness and ability?

To reflect the requirements of "strengthening estimation" in the standard, we can focus on the following two aspects:

(1) Cultivating the sense of number is the basis of making a good estimate. The sense of number is a good intuition of the relationship between logarithm and number. In estimation, the sense of number is mainly manifested in grasping the relative size relationship of numbers in specific situations, choosing appropriate algorithms to solve problems, and explaining the rationality of the results. Estimation can develop students' understanding of logarithm and is of great significance to cultivate students' sense of number. At the same time, a good sense of numbers is the necessary basis for students to estimate. In addition to strengthening the cultivation of number sense in the understanding of logarithm, we should also combine concrete calculation to cultivate students' number sense in the operation of number.

(2) In addition, it is necessary to cultivate students' estimation habits. In teaching, we often find that some students will make some inexplicable mistakes in calculation. In this regard, students should develop the habit of timely estimation and inspection. After completing a topic, we can estimate the numerical value first, and then compare it with the actually calculated answer, so as to find the mistakes and correct them in time.

8. When estimating 19+ 18, many students directly calculate 37. What should teachers do? How to deal with the relationship between estimation and accurate calculation in teaching?

Estimation is a kind of ability to approximate or roughly estimate the operation process and calculation results. At present, international mathematics education attaches great importance to estimation. With the rapid development of science and technology, it is impossible and unnecessary to calculate a large number of facts accurately. Numerous examples show that the number of times a person estimates and multiplies quotient in one day's activities is far more than the number of times he makes accurate calculations.

Accurate calculation ability (including oral calculation and written calculation) is an essential calculation skill for students and should be cultivated in teaching.

Estimation is mainly a calculation method used when it is impossible to calculate accurately or it is not necessary to calculate accurate results in daily life; Actuarial calculation is a method to calculate the results accurately according to needs. Both have their own requirements in teaching. In primary school, it is mainly to cultivate students' ability of accurate calculation, and at the same time let students experience the need of estimation in specific situations.

9. There are no calculation rules in the current textbooks. How should teachers deal with this situation?

Mathematical laws reflect the relationship between several mathematical concepts. Calculation rule is an operation rule expressed in words, and it is a concrete rule to realize the operation process under the guidance of arithmetic, which embodies a standardized operation program.

One of the trends of the new curriculum reform is to dilute the form and pay attention to the essence. Therefore, the current calculation teaching plays down the stylized description of arithmetic and calculation rules, strengthens students' understanding of arithmetic and mastery of algorithms, and strengthens students' experience and active exploration in the calculation process.

For the calculation rules that don't appear in the textbook, just let the students understand the arithmetic and master the algorithm.

As for describing and summarizing the calculation rules, don't be too demanding, especially in the lower grades.

8. When estimating 19+ 18, many students directly calculate 37. What should teachers do? How to deal with the relationship between estimation and accurate calculation in teaching?

Accurate calculation ability (including oral calculation and written calculation) is an essential calculation skill for students and should be cultivated in teaching.

9. There are no calculation rules in the current textbooks. How should teachers deal with this situation?

For the calculation rules that don't appear in the textbook, just let the students understand the arithmetic and master the algorithm.

As for describing and summarizing the calculation rules, don't be too demanding, especially in the lower grades.

10, calculation class, how to effectively improve the speed and accuracy of students' calculation and improve their thinking ability?

The speed and accuracy of calculation are two important dimensions to measure the formation of students' computing ability. The general trend of computing teaching reform is to reduce the requirement for computing speed.

The author thinks that it is very important for students to realize fast and correct oral calculation. That is to say, in the content of primary school oral calculation, the addition of two one-digit numbers in the table and their corresponding addition, subtraction, multiplication and division and their corresponding division are the basic oral calculation in the four operations, commonly known as "four tables of 99", which is the basis of all calculations, so students should be able to achieve the proficiency of "blurting out".

For written calculation, there is no need to set too high a speed requirement. What is important is to let students calculate correctly and gradually improve the speed.

1 1: Can students use calculators when they enter the classroom? How can we solve the contradiction between modern teaching tools and written calculation? Introduce your experience to everyone.

According to the provisions in the Compulsory Education Mathematics Curriculum Standard (Experimental Draft), the second issue pointed out that "you can use a calculator to perform complex operations, solve simple practical problems, and explore simple mathematical laws." Therefore, since the fourth grade, some versions of teaching materials have been introduced into the teaching of calculators to help students calculate and explore laws. As long as it is necessary, students can of course use it in peacetime. But we should also pay attention to guiding students to use calculators reasonably, and we should not rely entirely on calculators.

(1) Handle the relationship between written calculation and calculator operation. For primary school students, mastering some simple written calculation methods is the basic requirement for learning mathematics, so they also need to lay a solid foundation. For some complicated operations, calculators can be used instead.

(2) Cultivate students' habit of using calculators to explore mathematical laws. In some textbooks, arranging some topics for students to explore laws with calculators, and allowing students to calculate, observe, guess and verify with calculators will greatly promote students' inquiry learning.

As for the introduction of calculator into teaching, I haven't taught the fourth grade of the curriculum standard experimental textbook, so I don't have much experience in this field.

12. Do students need to practice more difficult calculation knowledge, such as calculation related to pi?

On the one hand, it is necessary to strengthen targeted exercises for computing knowledge that students are difficult to master. For example, let students remember some multiples of 3. 14, such as 6.28, 9.42, 12.56, 15.7, 18.84, etc. On the other hand, for complex content, students should be freed from the complicated calculation burden, such as the calculation of pi can be helped by a calculator.

13. Not long ago, when you asked students to do vertical calculation in a class in Beijing, you wrote the whole ten on a separate line. For example, the vertical calculation processes of 34×3, 1 1×5 are shown in Figure 1 and Figure 2 respectively. It is certain that you can understand arithmetic better, but can't you understand arithmetic well without writing like this? I feel that you have complicated the simple problem, so I want to hear your analysis of this design.

3 4 1 1

× 3 × 5

1 2 5

9 0 5 0

1 0 2 5 5

On this issue, please look at an essay written by the author-"It seems clumsy, but it is actually clever".

Teaching clips (Grade 3 "One digit times two digits")

Teacher: Students, what mathematical information do you know after reading this picture?

Health 1: There are two monkeys picking peaches.

Health 2: One monkey picked 14, and the other monkey also picked 14.

Raw 3: 14 peaches are all 10, and four peaches are put in one basket.

Teacher: How many peaches did those two monkeys pick? How to solve problems continuously?

Health 1: 14+ 14.

Health 2: 14× 2.

Health 3: 2× 14.

Teacher: Then how did you work out this problem? The same table is negotiable.

(Students whisper to each other to discuss)

Teacher: Who can tell us how you got this result?

Health 1: I use 14+ 14 to get 28.

Health 2: I'm looking at the picture. There are 8 in the right basket and 20 in the left basket, making a total of 28.

Health 3: I think by. 10 times 2 equals 20, 4 times 2 equals 8, and 20 plus 8 equals 28.

Health 4: My idea is different from theirs. 14 is two sevens, when multiplied by two, it is four sevens, and four seven-two-eight.

Teacher: Oh, how kind of you! (The whole class applauds for life. 4)

Teacher (pointing to the screen): Just now, a classmate said that 4 times 2 equals 8. Which part does it actually mean?

Health: There are eight peaches in the two baskets on the right.

Teacher: So what are the peaches in the two baskets on the left?

Health: 10 times 2 equals 20.

Teacher: Just now, we counted the number one and then the number ten. What should we do next?

Health: Add it up.

Teacher: Yes, if you add up the peaches in the right basket and the peaches in the left basket, you can figure out how many peaches there are.

(The teacher writes the following on the blackboard step by step:)

1 4

× 2

8……4×2=8

2 0…… 10×2=20

2 8……8+20=28

Teacher: An algorithm like this is called-

Student (answer): Use vertical calculation.

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