0 1 A, what is the basic starting point of mathematics curriculum in compulsory education? A: The basic starting point is to promote students' all-round, sustained and harmonious development.

B, what's the difference between numbers and numbers? A: The symbols used for counting are called numbers. There are four commonly used numbers: Arabic numerals, China lowercase numerals, China uppercase numerals and Roman numerals. At present, Arabic numerals are commonly used in the world, including the following ten digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. Numbers are made up of numbers. When counting according to the position principle, one or more of the ten numbers are arranged according to the position principle, indicating the number or order of things. Numbers are the basis of numbers, and together with other digital symbols, they can represent various numbers.

02 A, "Standards" clearly pointed out: Learning mathematics should not only consider the characteristics of mathematics itself, but also follow what? Answer: It is necessary to follow students' psychological laws in learning mathematics, and emphasize that starting from students' existing life experience, students should experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can gain an understanding of mathematics and further develop their thinking ability, emotional attitude and values.

B, analyze and answer the following questions: 105 minus 78 times 15, what is the product? A: We can start with the analysis of the problem. To ask what the product is, we need to know two factors, one is 15 and the other is the difference between 105 and 78, so now we need to calculate the product after the difference, that is, (105-78)× 15.

3a. Would you please talk about what should be highlighted in the mathematics curriculum in compulsory education? Answer: The mathematics curriculum in the compulsory education stage should be basic, universal and developmental, so that mathematics education can face all students and realize:? Everyone learns valuable mathematics; ? Mathematics necessary for everyone's life; ? Different people get different development in mathematics. B. how many quotients are there for the following questions? What are the rules for determining the number of digits on the table?

(Divider is the division of one digit) 2016 ÷ 4 7035 ÷ 5 4543 ÷ 8 90180 ÷ 9 A: The quotients of the above questions are three digits, four digits, three digits and five digits in turn. According to the law of division, we can find the following law: one digit is divided by multiple digits, and if the first digit of the dividend is less than the divisor, then the digit of the quotient is less than the digit of the dividend. If the first digit of the dividend is greater than or equal to the dividend, then the digits of the quotient are the same as those of the dividend.

04 A. What are the requirements of mathematics curriculum standards for students' mathematics learning content? A: Students' mathematics learning content should be realistic, meaningful and challenging, which is conducive to students' active observation, experiment, guess, verification, reasoning and communication. Content should be presented in different ways to meet diverse learning needs.

B, according to the following questions, choose the correct formula from the following categories and describe the rest correctly. What is the quotient of the sum of 252 and 173 multiplied by 8 and divided by 2?

( 1)(252+ 173)×(8÷2)

(2)(2)(252+ 173×8)÷2

(3)(3)(252+ 173)×8÷2

(4)(4)252+ 173×8÷2

(5) Answer: (3) The formula is correct (1) Formula: What is the product of the sum of 252 and 173 multiplied by 8 divided by 2? (2) Formula: What is the quotient of the product of 252 plus 173 multiplied by 8 and divided by 2? (3) Formula: What is the sum of 252 plus 173 multiplied by 8 divided by 2?

05 A. What does the mathematics curriculum standard mean for students to learn mathematics?

A: Effective mathematics learning activities cannot rely solely on imitation memory. Hands-on practice, independent exploration and cooperative communication are the main ways for students to learn mathematics. Because of students' different cultural environment, family background and their own way of thinking, students' mathematics learning activities should be a lively, proactive and personalized process.

B, give an example to illustrate what is the relationship between divisibility and division?

A: divisibility must be divisible, but divisibility is not necessarily divisible. For example, 8÷4=2 means that 8 is divisible by 4, and 2÷0.2= 10. Because 0.2 is a decimal, not a natural number, it can only be said that 2 can be divisible by 0.2, or 0.2 can be divisible by 2, but it cannot be said that it can be divisible.

07 A. What should be paid attention to in the evaluation of mathematics learning required by the standard? Answer: the evaluation of mathematics learning should pay attention to the results of students' learning, and pay more attention to their learning process; We should pay attention to students' mathematics learning level, and pay more attention to their emotions and attitudes in mathematics activities. Help students know themselves and build up confidence. B. "If you rewrite an integer into a decimal, add 0 after the decimal." Is this statement correct? Why? A: No, when an integer is rewritten as a decimal, you must first add a decimal point after the decimal and then add 0. If you don't put the decimal point, just add 0 after the integer, it will enlarge the original number by 10 times, 100 times? This value will change. So this statement is wrong.

08 A, please talk about the great influence of the development of modern information technology on the value, goal, content and the way of learning and teaching of mathematics education. The design and implementation of mathematics curriculum should attach importance to the application of modern information technology, especially the influence of calculators and computers on the contents and methods of mathematics learning, vigorously develop and provide more abundant learning resources for students, take modern information technology as a powerful tool for students to learn mathematics and solve problems, and devote themselves to changing students' learning methods, so that students are willing and have more energy to invest in realistic and exploratory mathematics activities.

B, when learning the divisor, why is 2 different from 2.0?

A: When studying the divisor, we must pay attention to which one is accurate. 2 accurate to one place, 2.0 accurate to ten places; 2.0 is more accurate than 2. Considering the approximate value obtained by rounding method, 2 is different from 2.0. Adjacent number 2 is the closest digit from numbers not less than 1.5 and less than 2.5; The divisor 2.0 is obtained by the tenth place of a number not less than 1.95 and less than 2.05. The range of approximation 2.0 is smaller than that of approximation 2, so approximation 2.0 is more accurate than 2.

09 A "Mathematics Curriculum Standard" specifically divides the nine-year study time into several periods.

A: There are three stages: the first stage (1-3), the second stage (4-6) and the third stage (7-9). B. write two classification methods about decimals.

Answer: (1) classified by integer parts: decimals are divided into pure decimals and those with decimals.

(2) According to the digits of the decimal part, it is classified into finite decimal and infinite decimal.

Pure cyclic decimal system

Mixed cyclic decimal

Acyclic decimal

10 A, "Standards" defined the overall goal of mathematics curriculum in compulsory education stage, and further elaborated it from four aspects. Please name these four aspects. A: Knowledge and skills; Mathematical thinking; Solve problems; Emotions and attitudes.

B, why should we emphasize the word "average" in teaching "fractional meaning"?

A: Fractions are obtained by measurement and equal division. Only by dividing an object into equal parts can a definite number be obtained. Therefore, when teaching "fractional meaning", we should emphasize "average" points. Significance of the score: divide the unit "1" into several parts on average, and the number representing such one or several parts is called the score. If students suddenly drop the word "average" in their narration, that is to say, they only see the side of "score" and suddenly drop the side of how to divide it, then the number may not be a score. Emphasizing "average score" means limiting the score to "equal division", and the score expressed in this way is called score. So in teaching, we should emphasize the word "average".

1 1 A, please name the procedural target verbs that describe the level of mathematical activities in the standard.

A: The standard uses process target verbs such as "experience (feeling), experience (understanding) and exploration" to describe the level of mathematical activities.

B, what is the relationship between fraction and division?

Answer: Fraction has the following relationship with division: m ÷ n = m/n (both m and n are integers, n≠0) Compared with division, the numerator in a fraction is equivalent to the dividend in division, the denominator is equal to the divisor in division, the fractional line is equal to the divisor, and the fractional value is equal to the quotient of division. The difference between fraction and division is that fraction is a number and division is an operation. They are two different concepts.

12 a. Please name the target verbs that describe knowledge and skills in the standard.

A: Target verbs such as "know (know), understand, master and use flexibly" are used in the standard. B, prime number, prime factor, prime number, what's the difference between these three concepts?

A: (1) A prime number is a number, for example, 2 is a prime number and 7 is a prime number.

(2) Although prime factor also refers to a number, it refers to a composite number. For example, 7 is a prime factor of 28.

(3) Prime number does not refer to a number, but refers to two numbers with only one common divisor. For example, 5 and 7 are prime numbers and 8 and 9 are prime numbers.

13 a. What are the four learning areas that the standard divides the learning content into?

A: It is divided into: number and algebra, space and graphics, statistics and probability, practice and comprehensive application.

B, give an example to explain why the sum of the numbers on each digit of a number can be divisible by 3 or 9, and this number can be divisible by 3 or 9?

A: Let's take 8235 as an example.

8235=8000+200+30+5

=8× 1000+2× 100+3× 10+5

=8×(999+ 1)+2×(99+ 1)+3×(9+ 1)+5

=8×999+8+2×99+2+3×9+3+5

=8×999+2×99+3×9+(8+2+3+5)

Because the first part of the previous step (8×999+2×99+3×9) must be divisible by 3 (or 9); It has nothing to do with 8235. So the sum of the digits of a number 8235 is 8+2+3+5. If it is divisible by 3 or 9, then the number 8235 can be divisible by 3 or 9. If it is not divisible by 3 or 9, then this number is not divisible by 3 (or 9).

14 A, the "standard" puts forward that the learning of course content emphasizes students' mathematical activities and develops students' sense of numbers. What are the main aspects of your sense of numbers in the textbook?

A: It is mainly manifested in: understanding the meaning of numbers; Numbers can be expressed in many ways; Grasp the relative size relationship of numbers in specific situations; Able to express and exchange information with numbers; Can choose the appropriate algorithm to solve; Can estimate the operation results and explain the rationality of the results.

B, except that 0 is emphasized in the nature of fraction and ratio, why not put forward 0 except in the nature of constant divisor? Answer: Because the numerator and denominator, and the first and last items are all multiplied or divided by the same number (except 0), it is emphasized that 0 is also a number; However, in the property that the divisor quotient is constant, it is mentioned that the dividend and divisor expand or shrink the same multiple at the same time, and the quotient is constant, so the multiple cannot be 0, so there is no need to make an exception to 0.

15 A, the "standard" puts forward that the learning of course content emphasizes students' mathematical activities and develops students' sense of symbols. What do you think the sense of symbol is mainly manifested in the teaching materials?

Answer: It is mainly manifested in the following aspects: (1) It can abstract the quantitative relations and changing laws from specific situations and express them with symbols; Understand the quantitative relationship and changing law represented by symbols; Will be converted between symbols; Can choose appropriate programs and methods to solve the problem of symbol representation.

B. why do the denominator remain the same and the molecules add up?

Answer: The counting unit of the score is a new unit obtained by averaging the unit "1"; It varies with the denominator. Fractions with different denominators have different fractional units; Fractions with the same denominator have the same units. The numerator of a fraction indicates the number of fractions, not the size of each fraction. It is the addition of denominator fractions, that is, the addition of several fractional units with other fractional units is molecular addition; Obviously, the decimal unit has not changed, that is, the denominator has not changed. For example: 2/7+3/7=(2+3)/7, that is, two 1/7 plus three 1/7 equals five 1/7.

16 A, "standard" puts forward that the learning of course content emphasizes students' mathematical activities and develops students' application consciousness. What do you think the application consciousness is mainly manifested in the teaching materials?

A: It is mainly manifested in: recognizing that there is a lot of mathematical information in real life and that mathematics has a wide range of applications in real life, when facing practical problems, I can actively try to use the knowledge and methods I have learned to seek solutions from the perspective of mathematics; In the face of new mathematical knowledge, we can actively seek the actual background and explore its application value.

B, the similarities and differences of volume, volume and capacity?

A: The definition of (1) is different. Volume is the size of the space occupied by an object; Capacity is the volume of objects that a container can hold. (2) The measurement methods are different. The volume of an object should be measured from the outside of the object and the volume of a container should be measured from the inside of the container. If you calculate the volume of a container, you should measure it both inside and outside.

17 A, the "standard" puts forward that the learning of course content emphasizes students' mathematical activities and develops students' reasoning ability. Where do you think reasoning ability should be mainly displayed in the course content?

Answer: It is mainly manifested in the following aspects: mathematical conjecture can be obtained through observation, experiment, induction and analogy, and further verification, proof or counterexample can be given; Be able to express your thinking process clearly and methodically, and be reasonable and well-founded; In the process of communicating with others, I can discuss and ask questions logically in mathematical language.

B, What's the difference between lateral area and surface area? Transverse area surface area

A: Surface area refers to the size of the surface area of an object, actually refers to the size of the contact surface between the object and the air, and lateral area refers to the size of the side area of the object.

18 A. What is your understanding of the word "flexible application" in the standard knowledge and skills objectives?

Answer: I can comprehensively apply what I have learned, flexibly and reasonably select and apply relevant methods to complete specific mathematical tasks.

B. What's the difference between ratio and simplified ratio?

Answer: To find the ratio is to find how many times (or scores) the former is the latter. The method is to divide the former by the latter, and the result is a numerical value; Simplified ratio refers to the simplest integer ratio by using the properties of ratio to get a ratio.

19 a. How do you understand the word "experience" in the standard process objectives?

Answer: Take part in specific mathematical activities, get a preliminary understanding of the characteristics of objects in specific situations and gain some experience.

B. Is it correct to find the least common multiple as follows? Why?

2 60 18 24

3 30 9 12

10 3 4

The minimum common multiple of ∴60 18 and 24 is 2× 3× 3× 10× 4 = 720.

A: That's not correct. Because short division is used to find the least common multiple of three numbers, it must be divided into three numbers to be pairwise coprime; Only three numbers in the problem are coprime, and then two of them, 10 and 4, have common divisor 2, so the problem is not the least common multiple.

20 A, please briefly talk about the general goals that students can achieve in mathematics learning in compulsory education.

Answer: 1. Obtain important mathematical knowledge (including mathematical facts and experience in mathematical activities) necessary to adapt to future social life and further development, as well as basic mathematical thinking methods and necessary application skills. 2. Initially learn to observe and analyze the real society by mathematical thinking, solve problems in daily life and other disciplines, and enhance the awareness of applied mathematics. 3. Understand the close relationship between mathematics and nature and human society, understand the value of mathematics, and enhance the understanding of mathematics and confidence in learning mathematics well. 4. Have the initial spirit of innovation and practical ability, and can be fully developed in emotion, attitude and general ability.

B. How should teachers deal with the problem of "1/3+3/4=4/7" in students' homework?

A: Students make this mistake because they don't really understand the addition and subtraction of different denominators. This requires teachers to guide students to analyze the differences between 1/3 and 3/4. In teaching, students can draw pictures and intuitively see that 1/3 and 3/4 are different. So you can't add or subtract directly. First of all, we should unify decimal units, and the method of unifying decimal units is general division. After general division, only the numerator is added and subtracted, and the denominator remains unchanged (that is, it is calculated according to the law of denominator addition and subtraction).

2 1 A, please briefly talk about your understanding of the course objectives of "Mathematical Thinking".

A: 1. Experience the process of describing the real world with mathematical symbols and figures, establish a preliminary feeling of numbers and symbols, and develop abstract thinking. 2. Enrich the understanding of real space and graphics, establish a preliminary concept of space, and develop thinking in images. 3. Experience the process of using data to describe information and make inferences to develop statistical concepts. 4. By observing, experimenting, guessing, proving and other mathematical activities, we can develop reasonable reasoning ability and preliminary deductive reasoning ability, and we can explain our views in an orderly and clear way.

B. What kind of mistakes do primary school students easily make when writing numbers within 10?

Answer: The following mistakes often occur: ① Wrong position of up, down, left and right; ; ② The strokes for writing numbers are not in place and the corners are not smooth; 3 strokes are wrong, such as writing 8; (4) the stroke order is wrong, such as writing 8, written in the stroke order; ⑤ The proportion of each part of the character is not well grasped.

In order to let students write numbers correctly, we should first guide students to observe the font: ① Let students realize that the numbers 0, 1, 2, 3, 6, 7, 8 and 9 are all written in one stroke, and the numbers 4 and 5 are written in two strokes. ② 1, 4,7 are composed of straight lines, and 3,0,6,8 are composed of straight lines and curves.

Secondly, the general steps for science professors to write numbers are: watching demonstration writing, stressing the order of strokes, drawing dotted lines and writing independently. You can also use formulas to explain the shape of numbers. 5 like a small hook, 8 like a twist, 6 like a whistle, 9 like a balloon with a floating rope?

22 A, please briefly talk about your understanding of the objectives of the course "Emotion and Attitude".

A: 1. Can actively participate in mathematics learning activities, full of curiosity and curiosity about mathematics. 2. Get successful experience in mathematics activities, exercise the will to overcome difficulties and build self-confidence. 3. Understand the close relationship between mathematics and human society and its role in the development of human history. Experiencing mathematics activities is full of exploration and creation, feeling the rigor of mathematics and the certainty of mathematical conclusions. 4. Form the attitude of seeking truth from facts and the habit of independent questioning and thinking.

B, when talking about the composition of numbers in the first grade, why can't you say 0 and what composition?

Answer: In Senior One, the composition of numbers refers to how many natural units a number contains. Because 0 is not the counting unit of natural numbers and does not contain counting units, the composition of numbers does not contain 0.

23 a. What is the content of statistics and probability research?

A: Statistics and Probability mainly studies data in real life and random phenomena in the objective world. By collecting, sorting, describing and analyzing data, it depicts the possibility of events and helps people make reasonable inferences and predictions.

B, what's the difference between a score and a score?

A: The ratio is the division of two numbers. Of course, the divisor cannot be 0. Therefore, the latter term of the ratio cannot be 0. Ratio refers to the ratio of two numbers (multiple ratio).

Score refers to the result of a game, reflecting the winning or losing score. The last item of the score may or may not be 0.

24 a. How do you understand the relationship between the four learning areas in the standard?

Answer: Numbers and Algebra, Space and Graphics, Statistics and Probability are the basis of practice, which are comprehensively applied. "Practice and comprehensive application" will help students to comprehensively use the existing knowledge and experience, and solve challenging comprehensive problems closely related to life through independent exploration and cooperation and exchange, so as to develop students' problem-solving ability, deepen their understanding of "number and algebra", "space and graphics" and "statistics and probability" and realize the connection between various parts.

B, how to teach the meaning of decimals?

Answer: When teaching "the meaning of decimals", we can generally do it from the following three aspects:

① Let students understand the meaning of decimals by explaining the generation of decimals. ② Explain from the relationship between decimals and fractions. ③ Understand the meaning of decimals further by mastering the numerical sequence table of integers and decimals. Let's make it clear to the students here: ① The basic unit of integer and decimal is "1". Whether it is an integer or a decimal, it should be expressed. ② The position of each digit and the function of decimal point. ③ Count the units of each number and the ratio relationship between units.

25. The new curriculum requires teachers to play a role in many aspects. Please briefly talk about the main changes in the role of teachers. A: 1. The transformation from traditional knowledge giver to knowledge giver under the new curriculum conditions. 2. Teachers become promoters of students. 3. Teachers become researchers.

B, when teaching "1 1-20 understanding of each number", students often mispronounce 12 as 2 1. How do you prevent this from happening to students?

A: In teaching, we should emphasize the meaning of numbers. According to the characteristics of junior students, we can make the grid diagram in the book into a teaching aid, which can be illustrated by the number of squares placed on the left and right sides. In addition, students need to further consolidate their initial understanding of numbers through the operation of learning tools.

26 A, teachers are the "promoters" to promote students' autonomous learning. Please talk about the characteristics of the role of "facilitator".

A: (1) Look positively. (2) Give students psychological support. (3) Pay attention to cultivating students' self-discipline.

B, how to teach reading and writing numbers within 10,000?

Answer: The key to teaching reading and writing numbers within 10,000 is memorizing numbers, so we must firmly grasp this key in teaching. When teaching reading and writing numbers within ten thousand, students must understand the concept of numbers and memorize the counting unit and its position of each number. When organizing students to practice reading and writing numbers, we should pay special attention to students' mastery of reading and writing methods of numbers with zeros in the middle and at the end, and correct students' mistakes in time.

27 A. In the content standard, the standard only stipulates the level that students should reach during the corresponding study period (), and at the same time, it does not stipulate the presentation methods of content () and (), and the teaching materials can be arranged in various ways.

A: Basic level; Order; Form.

B, how to teach simple "division with remainder"?

A: The focus of this part is to let students master the method of trial quotient and calculate quickly. Take 43÷5 as an example, the mistakes that students are prone to make when trying quotient are: quotient 7 is greater than 8, and some quotient 9. The root cause of this error is that students do not pay enough attention to "the remainder must be less than the divisor", so teachers must repeatedly emphasize and explain the truth that "the remainder must be less than the divisor" in teaching. In addition, targeted exercises should be designed to cultivate students' ability to try business.

28 a. What are the common teaching methods in primary schools?

Answer: 1, teaching method 2, heart-to-heart talk method 3, discussion method 4, observation and demonstration method 5, experiment method 6, visit method 7, practice method 8, review method 9, and guide primary school students to learn by themselves.

B, 0 means no? To what extent can the teaching of grade 0 in primary school be talked about?

Answer: 0 has many important functions besides indicating that there is no object: ① indicating numbers. If there are spaces when writing numbers, it must be 0; ② indicates the starting point. For example, the scale of a ruler starts from 0; ③ indicates the boundary. For example, 0 on the number axis indicates the boundary between positive and negative numbers; ④ indicates accuracy. Such as 3 and 3.0, these two numbers are equal in size, but different in accuracy. ⑤ Used for numbering. Such as the license plate number 00487, this license plate number is 487, and the maximum size is five digits.

29 A what is the basis for choosing teaching methods?

Answer: The following aspects should be considered when choosing the teaching method: 1, starting from the teaching content. 2. Starting from the age characteristics and reality of students. 3. Starting from the characteristics and experience of classroom teaching.

B, how to help students establish and understand the unit "1" in teaching?

Answer: The following four links should be grasped in teaching: ① Prove with examples that the unit "1" is anything that can be divisible. It can not only represent a thing, a unit of measurement, but also an object. ② The number in the unit "1" can be arbitrary. (3) Combining the set diagram in the textbook, let students further clarify the relationship between the part represented by the score and the unit "1", and explain that the unit "1" and the part can be transformed, and the key is to see who is regarded as the unit "1". ④ Ask students to do the practice of finding the company "1".

30 A, the whole process of teaching work including those links:

A: The whole teaching process includes five links: first, preparing lessons; Second, attend classes; Third, the arrangement and evaluation of homework; Fourth, extracurricular tutoring; V. Assessment and evaluation of achievements.

B.hongxing village built a highway. It was originally planned to build 20 meters a day and complete it in 30 days. The result was completed six days in advance. How many meters are actually built every day? A student solved the equation like this:

Solution: Suppose that X meter is actually being repaired every day. According to the meaning, X=20×30÷(30-6) X=600÷24 X=25. How to evaluate?

Answer: Solve problems with equations. From the perspective of thinking, it can play a role in simplifying the complex. However, if we just put "X=" on one side of an arithmetic formula and make it a formal equation, then it is essentially an arithmetic solution, which not only gives full play to the advantages of understanding the equation, but also adds some trouble to the original complex arithmetic solution. In teaching, students must be guided to find other solutions instead of simply saying them.