1. Summary of primary school mathematics knowledge points

1. Numbers and algebra: understanding of numbers, operations of numbers, formulas and equations, ratios and proportions.

2. Space and graphics: lines and angles, plane graphics, three-dimensional graphics, graphics and transformation, graphics and position. 3. Statistics and possibility: measurement, statistics and possibility of quantity.

4. Practice and comprehensive application: Exploration rules, general compound application problems, typical application problems, fractions and percentage application problems, ratio and proportion problems, problem-solving strategies, comprehensive application problems.

Extended information: Integers 1. The meaning of integers:...numbers like -4,-3,-2,-1,0,1,2,3,...are called integers.

2. Natural numbers: When we count objects, the 1, 2, 3, 4... used to express the number of objects are called natural numbers. There is not an object, represented by 0, which is also a natural number.

3. Counting units One (one), ten, one hundred, one thousand, ten thousand, one hundred thousand, one million, ten million, billion... are all counting units. The advance rate between each two adjacent counting units is 10.

This counting method is called decimal notation. 4. Digits Counting units are arranged in a certain order, and the positions they occupy are called digits.

5. Divisibility of numbers: Integer a is divided by integer b (b≠0). The quotient of the division is an integer without a remainder. We say that a can be divided by b, or that b can divide a. . If a number a is divisible by a number b (b ≠ 0), a is called a multiple of b, and b is called a divisor of a (or a factor of a).

Multiples and divisors are interdependent. Because 35 is divisible by 7, 35 is a multiple of 7 and 7 is a divisor of 35.

7. What is ratio: The division of two numbers is called the ratio of two numbers. For example: 2÷5 or 3:6 or 1/3. The first and last terms of the ratio are multiplied or divided by the same number (except 0) at the same time, and the ratio remains unchanged.

8. What is proportion: The formula that expresses the equality of two ratios is called proportion. For example, 3:6=9:189. The basic property of proportion: In proportion, the product of two external terms is equal to the product of two internal terms.

10. Solving the proportion: Finding the unknown items in the proportion is called solving the proportion. Such as 3: χ=9:18 The basis for solving the proportion is the basic properties of proportion.

11. Direct proportion: Two related quantities. If one quantity changes, the other quantity will also change. If the corresponding ratio of the two quantities (that is, the quotient k) is certain , these two quantities are called directly proportional quantities, and their relationship is called a proportional relationship. For example: y/x=k (k is certain) or kx=y12. Inverse proportion: two related quantities. When one quantity changes, the other quantity also changes. If the two corresponding quantities of the two quantities If the product of numbers is constant, these two quantities are called inversely proportional quantities, and their relationship is called an inversely proportional relationship.

For example: x*y=k (k is certain) or k/x=y Percent: A number that expresses how many percent a number is of another number is called a percentage. Percentage is also called percentage or percentage.

13. To convert a decimal into a percentage, just move the decimal point two places to the right and add a percent sign at the end. In fact, to convert a decimal into a percentage, just multiply the decimal by 100%.

To convert a percentage to a decimal, just remove the percent sign and move the decimal point two places to the left. 14. To convert a fraction into a percentage, usually first convert the fraction into a decimal (when division cannot be completed, usually keep three decimal places), and then convert the decimal into a percentage.

In fact, to convert a fraction into a percentage, you first need to convert the fraction into a decimal and then multiply it by 100%. To convert a percentage into a fraction, first rewrite the percentage into a fraction, and then reduce the ratio to the simplest fraction that can be reduced.

15. Learn how to convert decimals into fractions and fractions into decimals. 16. Greatest common factor: Several numbers can be divisible by the same number at once. This number is called the greatest common divisor of these numbers.

(Or the common divisor of several numbers is called the common divisor of these numbers. The largest one is called the greatest common divisor.)

17. Reciprocally prime numbers: common Two numbers whose factors are only 1 are called coprime numbers. 18. Least common multiple: The common multiple of several numbers is called the common multiple of these numbers, and the smallest one is called the least common multiple of these numbers.

19. Common fraction: converting fractions with different denominators into fractions with the same denominator that are equal to the original fraction is called a common fraction. (Use the least common multiple for common fractions) 20. Reduction: Turning a fraction into a fraction that is equal to it but with smaller numerator and denominator is called reduction.

(Use the greatest common factor for reduction) 21. Simplest fraction: A fraction whose numerator and denominator are relatively prime numbers is called the simplest fraction. At the end of the fraction calculation, the number must be converted into the simplest fraction.

Any number whose units digit is 0, 2, 4, 6, or 8 can be rounded by 2, that is, it can be reduced by 2. Any number whose units digit is 0 or 5 can be divisible by 5, that is, it can be reduced by 5.

Pay attention to the use when making reservations.

22. Even and odd numbers: Numbers that can be divided by 2 are called even numbers.

A number that is not divisible by 2 is called an odd number. 23. Prime number (prime number): If a number has only two divisors, 1 and itself, such a number is called a prime number (or prime number).

24. Composite number: If a number has other divisors besides 1 and itself, such a number is called a composite number. 1 is neither a prime number nor a composite number.

28. Interest = principal * interest rate * time (time is generally in years or months, which should correspond to the unit of interest rate) 29. Interest rate: The ratio of interest to principal is called the interest rate. The ratio of one year's interest to the principal is called the annual interest rate.

The ratio of one month’s interest to the principal is called the monthly interest rate. 30. Natural numbers: Integers used to represent the number of objects are called natural numbers.

0 is also a natural number. 31. Repeating decimal: A decimal, starting from a certain digit of the decimal part, one number or several numbers appear repeatedly in sequence. Such a decimal is called a recurring decimal.

32. The time of a day: There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in 1 minute. Baidu Encyclopedia - Primary School Mathematics Knowledge Baidu Encyclopedia - Primary School Mathematics.

2. What knowledge should be mastered in the first grade of primary school mathematics?

In order for students to achieve the best results in mastering learning methods, they must find a method that is consistent with children’s age characteristics, personality characteristics, knowledge levels and learning methods. content path. Such approaches urgently need to be studied, explored, and summarized in practice. According to the experiences of some teachers, the usual ways for primary school students to master learning methods in classroom teaching can be summarized into three types.

1. Specify - try

Specify is the teacher's active guidance, prompt, and explanation; try is the student trying to do what the teacher specified.

The mastery of learning methods, like the acquisition of knowledge, has a development process from scratch to something, from less to more, and never to perfection. In the beginning, a large part of the process depends on the teacher's active and clear guidance in the process of teaching knowledge. For example, how to speak and answer questions, how to write, how to spell syllables, how to observe illustrations, how to memorize glyphs and understand word meanings, how to read words and sentences, how to form words and sentences, how to speak complete sentences, etc., all require teachers to teach students While putting forward learning requirements, - explain the learning methods. Not only do students who are new to school need to be informed in advance, but students in middle and upper grades who have already mastered some knowledge and learning methods also need to be informed in advance when entering more difficult learning content. For example, the method of using the central sentence to make a paragraph; the method of connecting the paragraph to summarize the main content of the article; the method of summarizing the main content of the article and analyzing the author's writing purpose, etc., etc., should also be exposed to these for the first time. The method shall be specified by the teacher in advance.

But only the teacher’s instructions will not work without the students’ attempts and application. Only when combined with learning practice, using the specified learning methods, practicing many times, and receiving the expected results, can we say that we have mastered this learning method.

2. Demonstration - imitation

Demonstration is when the teacher uses teaching methods to set an example for students to learn; imitation is when students understand the essence and use it to learn New knowledge of the same kind.

For primary school students to master learning methods, based on the psychological characteristics of children who are good at imitating, teachers need to intentionally, accurately and clearly demonstrate to students whether they are in the early stages of school or entering middle and senior grades. The methods and steps used to understand a certain type of text, a series of thinking questions designed to understand someone, something, or something, and the process of breaking through a certain difficulty and guiding students to analyze and reason are displayed in front of students. , allowing students to get inspiration from the teacher's teaching methods, understand the essence of the teaching method, stimulate imitation psychology, and then use the teacher's demonstration method to learn new and similar knowledge, which can play the role of "teaching methods are taught one way, and learning methods are inverted." role.

What is different from "demonstration" to "imitation" and from "indicating" to "trying" is that this is an invisible guidance and an internal process of students' psychology from perception to understanding. It is achieved through invisible and intangible thinking activities.

3. Review - Summary

Review is self-discovery, self-experience, and reflection on the learning methods you have used; summary is to learn similar knowledge based on review. The used learning methods are evaluated, processed, and incorporated into the overall structure of the learning method system.

Students master learning methods. Some are specified by the teacher and then tried, some are demonstrated by the teacher and then imitated. Some are neither specified, tried, nor demonstrated and imitated, but are left to the students themselves to explore and imitate. create. Even if the teacher has pointed out and demonstrated it, sometimes students will modify some parts and create methods suitable for their own characteristics. A student's knowledge base, personality development, and brain function are all different. Students should be encouraged to seek different methods suitable for their own characteristics based on their own characteristics. Learning has rules but no fixed methods. Learning methods that suit students' individual characteristics are often explored by students themselves in practice. The reason why some students have particularly good learning results is that, in addition to being diligent and hardworking, they have created effective learning methods that suit their own characteristics. The learning method of creation and discovery is much more effective than the learning method of teaching.

Many students have indeed created many good learning methods. They should choose the opportunity, arrange time, guide students to review the learning process, reflect on the learning methods used, analyze and compare one by one, eliminate learning methods that have been proven to be ineffective, and summarize the methods that are suitable for learning. The scientific method of objective laws, after being sorted out, enables some creative and correct methods to be determined.

From "review" to "summarization", it is also a complete process of mastering learning methods. It must be summarized in time on the basis of review. Only "reviewing" without "summarizing" cannot gradually form a well-structured method learning system, and fragmented methods cannot achieve effective transfer.

Review - Summary is generally arranged as a link in teaching. Sometimes it can also be carried out in the form of opening-of-school method exchange meetings, "Learning Method Collection" columns, etc. Using the form of group activities to implement multi-directional communication among classmates can not only encourage students to summarize their own learning methods, but also promote students to continuously explore learning methods in depth.

From "specifying" to "trying", from "demonstration" to "imitation", from "review" to "generalization", it is a dialectical and unified development process of mastering learning methods. They are interdependent and inseparable. Specifying - trying, demonstrating - imitating, reviewing - summarizing are three different levels and levels of approaches, from low to high, from shallow to deep. It should be selected according to different learning contents and the specific situations of students at different levels. Sometimes they can also penetrate each other and cooperate with each other.

3. How to teach first-grade children to recognize the greater than sign and less than sign

The mouth of the greater than sign is thinking about the left hand (the hand that does not write), and the mouth of the less than sign is facing the right hand (the hand that writes). hand)

A big apple is bigger than a small apple; a small apple is smaller than a big apple; two apples of equal weight or apples of the same size.

Dear parents, children will encounter the problem of learning mathematical symbols in the first-grade mathematics course. Those symbols are rigid, and children must not be allowed to memorize them by rote. Today I will talk about the greater than and less than signs that give children headaches.

1. First of all, let’s recognize which one is the greater than sign and which one is the less than sign: >; Take a look at it, the opening is facing the left and the sharp corner is facing the right. The overall symbol looks like the left one is bigger. The right side is small. The big side is directly read as big, and the small side is directly read as small. According to our reading habits, we generally read from left to right, so this is read as a greater than sign. Once you understand the less than sign, just reverse the process.

2. Now look at the application of these two symbols. For example: should 20○30 be filled in with a greater than sign or a less than sign? You can use imaginative techniques to help children remember and stimulate their interest. . Tell the children that the ends that are larger than the size and smaller than the size can be seen as the big mouth of the crocodile. Crocodiles are very greedy and only like to eat the big ones, not the small ones, so the big mouth of the crocodile faces that side when counting the big ones. So in this question, 20 is on the left and 30 is on the right. The crocodile's big mouth on the right should be to the right.

4. What is the primary school mathematics knowledge?

1. A conical grain pile is 2 meters high and covers an area of ??10 square meters. If every cubic meter of millet weighs 500 kilograms, this pile will How many kilograms of millet are there? 2. Master Li is going to make a pair of iron chimneys. Each section is 80 cm long and the bottom diameter is 10 cm. How many square meters of iron sheet is needed at least? The volume of a cylinder is 48 cubic centimeters. How many cubic centimeters is the volume of this cylinder larger than that of a cone with the same base and height? 4. A conical iron barrel is 15.7 decimeters high and its side area is exactly a square. How much iron is needed to make such a tin oil barrel? 5. The volume and height of a cone and a cone are equal. It is known that the circumference of the base of the cylinder is 18.84 cm. What is the base area of ??the cone? 6. Cut a 2-meter-long cylindrical wood into two sections. If the surface area increases to 6 square meters, for example, what is the volume of the wood in cubic decimeters? 7. Adding one part, the time ratio of A, B and C is 6:7:8.

There are currently 3650 parts to be processed. If 3 people are required to complete the task in the same amount of time, how many extra parts should each be added to? 8. For a piece of alloy, the ratio of copper to zinc is 2:3. Now add 120 grams of copper and 40 grams of zinc to get 660 grams of alloy. What is the ratio of copper to zinc in the new alloy? 9. Two alloys are of the same weight. The ratio of copper to zinc in one alloy is 2:5, and the ratio of copper to zinc in the other alloy is 1:3. The two alloys are now combined into one. Find the ratio of copper to zinc in the new alloy.

10. When two workers, A and B, go to work, A walks longer than B, and B walks less time than A. What is the ratio between A and B? 11. As a fraction, after adding m to the numerator and denominator, the ratio of the numerator to the denominator is 19:7. What is m? 12. A piece of wood is 2.5 meters long. If it is cut into sections of 0.5 meters each, it will take 1 hour. Now according to the needs, this piece of wood needs to be sawed into several sections of 15 cm and 14 cm long.

It is necessary to make as many 15 cm long pieces as possible, and no leftovers are allowed. How many hours will it take? Example 7: Hard candies are 5.1 yuan per kilogram, and soft candies are 8.9 yuan per kilogram. The mixed sugar price is now required to be 5 per kilogram.

4 yuan, what is the appropriate weight ratio between hard and soft candies? Example 8 The ratio of early fields to paddy fields in Xinguang Village was 5:3 in 1989. After converting 2,800 hectares of early fields into paddy fields last year, the ratio of dry fields to paddy fields was 1:2. How many acres of paddy and dry fields did Xinguang Village have? .

5. What mathematical knowledge should be mastered in the first grade of primary school

1. Understanding numbers

(1) Interesting "0"

"First grade 0" can mean nothing, "0" can participate in calculations, "0" plays a placeholder role in numbers, "0" can represent the starting point, and represents 0 degrees.

(2) Cardinal numbers and ordinal numbers

When expressing the number of objects, cardinal numbers are used; when expressing the order in which objects are arranged, ordinal numbers are used.

Cardinal numbers are different from ordinal numbers. Cardinal numbers represent the number of objects, and ordinal numbers represent the order in which objects are arranged.

2. Counting

(1) Counting simple shapes

When counting scattered objects or counting the number of certain types of shapes, you should First, mark all objects with serial numbers in order. You can observe them in sequence according to the serial numbers and count the specified graphics. Note that for the same object, if you observe it from different angles, the observation results will be different. Therefore, when counting simple graphics, you must be good at observing and analyzing problems from different angles.

6. First-grade mathematics stories should be relatively simple and easy to recite.

Number songs one, two, three, climb up the mountain, four, five, six, somersault, seven and eight 9. To shoot the ball, stretch out two hands and ten fingers.

Counting methods There are many counting methods, it depends on who is more flexible. You can count correctly and quickly, and you can count without making mistakes.

Two two-digit numbers, two, four, six, eighty, five five-digit numbers, one, five and ten. Numbers Nursery Rhyme I say one, one, one, one piece of paper and one pen. When learning mathematics and doing exercises, you need paper and pen.

I say two, two two two, how many two are there on the body, count the left and right sides, eyes, hands, feet and ears. I say three, three three three, wearing a bright red scarf on the chest, with three corners and three sides, we all like it.

I said four, four four four. In front of me is a long table with four corners and four sides. Use it to read and write. I said five, five five five, five-pointed star, shiny. There are five stars on the national flag, and I am the little star.

I say six, six six six, June Day is so happy, singing, dancing and playing games, the flowers of the motherland are so happy. I said seven, seven seven seven, there are seven days in a week, Sunday, no school, being a good helper for mothers.

I say eight, eight eight eight, to express my condolences to the old aunt who is a soldier. You sweep the floor, I clean the windows, and the aunt smiles at me haha. I say nine, nine nine nine, September 10th is Teacher's Day. I respect teachers and be polite. Everyone praises me for being such a good baby.

I say ten, ten ten ten. There are fingers on both hands. Ten fingers are very useful. Learn from Lei Feng and do good deeds. Clap your hands and sing. You clap once and I clap once. Get up early every day to practice physical fitness.

You take two shots, I take two shots, and you have to bring a small handkerchief with you every day. You take three shots, I take three shots, and change your shirt after taking a shower.

You shoot four times, I will shoot four times to eliminate flies and mosquitoes. You shoot five, I shoot five. If you have phlegm, don’t spit it anywhere.

You shoot six, I shoot six, don’t throw away the melon rinds and shells. You shoot seven, I shoot seven, don’t worry when you eat and chew carefully.

You shoot eight, I shoot eight, cut your nails and brush your teeth frequently. You shoot nine, I shoot nine. Wash your hands before eating.

You shoot ten, I shoot ten, don’t eat dirty things. Logarithmic Children's Rhyme I say one, who is right, which one washes his face the most? You talk about it, I talk about it. Kittens love to wash their faces.

I say two, who is right? Which tail is like a fan? You say two, I say two, the peacock's tail is like a fan. I say three, who is against three, which one runs away and disappears? You say three, I am against three, the rabbit runs away and disappears, I am against four, who is against four, which one is round and full of tattoos? You say four, I say four, the hedgehog is round and full of thorns.

I say five, who is against five, which one jumps up the tree? You say five, I say five, and the monkey jumps up the tree. I say six, who is against six? Which one is swimming in the water with a flat mouth? You say six, I say six, and the duck swims in the water with its flat mouth.

I say seven, who is right? Which one makes people get up early? You say seven, I say seven, the rooster calls people to get up early. I say eight, who is right? Which one has the longer nose? You say eight, I say eight. The elephant's trunk is long and big.

I say nine, who is right? Which desert should I walk in every day? You say nine, I say nine, camels walk in the desert every day. I say ten, who is right? Which farmland has the ability? You say ten, and I say ten. Oxen are capable of plowing the land.

Use children's songs to help memory. Children's songs are simple, rhythmic, and easy to remember. They are deeply loved by children and are the most easily understood and accepted literary form by students.

When boring mathematical formulas and rules make students feel "tired of learning", the key points and difficulties in the textbooks are compiled into children's songs to make mathematical knowledge "alive". When learning numbers 1-10, writing and memorization are difficult. Therefore, children's songs are designed or used to help students remember.

1 is like a pencil, thin and long, 2 is like a duck floating on water, 3 is like ears listening to sounds, 4 is like a red flag fluttering in the wind, 5 is like a scale hook to buy vegetables, 6 is like a whistle beeping, 7 is like The sickle cuts the grass, 8 is like twisting a twist, 9 is like a spoon for serving rice, and 10 is like ham and eggs. In this way, students can speak catchy, vivid and easy to remember. It also reminds them of their kindergarten life experience and makes them happy to memorize.

When studying "Position and Direction", the students lacked spatial concepts because of their young age, so I used the students' familiar reference objects to compose nursery rhymes to help memorize them. Get up in the morning and face the sun, and think about it; the front is east, the back is west, the left is north, the right is south; stretch out your left and right hands, remember the southeast, northwest, and direction; the map directions are prescribed, up is north, and bottom is South; left is west, right is east, children must distinguish them clearly.

When learning the comparison of numbers, I got to know ">""".

7. What to learn in the first volume of primary school mathematics

(1) Numbers and Algebra 1. Unit 1 "Numbers in Life".

Based on children’s counting experience and combined with specific situations, they can understand the meaning of numbers within 10, be able to recognize, read and write numbers from 0 to 10, and use them to represent the number or number of objects. The order of things, a preliminary understanding of the meaning of cardinal numbers and ordinal numbers, a preliminary feeling of the close connection between "numbers" and life, a preliminary experience of the fun of learning mathematics, and the initial formation of good study habits. 2. Unit 2 "Comparison".

Through the mathematical activities of comparing specific quantities, obtain the understanding of ">, 3. The third unit "Addition and Subtraction <1>". Experience abstracting addition and subtraction formulas within 10 from practical problems and explain them and application process, understand the meaning of addition and subtraction, and initially feel the close connection between addition and subtraction and life; be able to correctly calculate addition and subtraction within 10 orally, and master the skills of decomposition and synthesis of numbers within 10; by sorting out addition and subtraction formulas , and explore regular activities to cultivate and develop number sense.

4. Unit 7 "Addition and Subtraction <2>" Experience the specific operations and generalizations of numbers from 11 to 20. process, initially understand the place value principle of decimal notation, be able to count, read, and write numbers within 20 days, master their order, compare their sizes, and conduct simple and organized thinking combined with problem-solving activities; experience Communicate the process of each algorithm with your peers, experience the diversity of algorithms, learn to carry and subtract within 20, gradually become proficient in addition and subtraction within 20, and be able to solve simple problems, feeling the close connection between addition and subtraction and daily life , feel the rationality of the mathematical thinking process.

5. Unit 8 (2) Space and Graphics 1. Unit 5 "Position and Sequence" to experience the before and after. , the position and order of up, down, left, and right, use front, back, up, down, left, and right to describe the relative position of objects, and establish preliminary spatial concepts.

2. Unit 6. "Understanding Objects". Through activities such as observation, operation, and classification of real objects and models, gain intuitive experience with simple geometric objects, and be able to intuitively identify whether their shapes are rectangles, squares, cylinders, or balls, and be able to intuitively identify rectangles, squares, and cylinders. Or three-dimensional figures such as balls.

(3) Statistics and Probability 1. Unit 4 "Classification". Combine the classification activities that must be carried out in daily life, feel the necessity of classification, and be able to follow the given standards. Or choose a certain standard to compare, arrange and classify objects, and experience the consistency of the activity results under the same standard and the diversity under different standards in these activities.

2. Unit 9 " Statistics. Carry out statistical activities based on simple and realistic problems, experience the whole process of data collection, organization, description and analysis, and feel the necessity of statistics; understand statistical tables and visual statistical charts with examples, and be able to fill in the corresponding icons ; Be able to ask and answer simple questions based on the data in statistical charts, and share their ideas with peers

(4) Practical activities The text and exercises in this textbook provide many suitable for first-year primary school students. Practical activities or small surveys. For example: 1. Find and talk about it.

"I am looking for 3 people who are taller than me" "I am looking for 2 people who are the same age as me". try to find. ”

2. Talk about the places where 0 is used in life. 3. Talk about the addition problems you find in life.

4. Tidy up the room where you live. , tell your companions how you organize them. 5. Go to the library or bookstore to see how the books are classified, and tell your companions

6. Investigate The Sun Has Just Risen. , about what time is it? When is the sun just setting? Investigate the number of boys and girls in each group of your class, and try to ask some math questions. 7. Investigate the school attendance of the 10 students in your class. > (1) Go to school by car or walk? (2) Walk in groups or alone? etc. Students will gain good emotional experience and gain some preliminary experience through the above-mentioned observation and investigation and other practical activities. Students have experience in mathematical practical activities, can use the knowledge and methods they have learned to solve simple problems, and feel the role of mathematics in daily life.

Teaching plan (1) Mathematics teaching must conform to students’ cognitive level. Mathematics teaching must follow students’ psychological rules for learning mathematics and conform to students’ development level and mathematics acceptance ability.

Teaching that meets students’ developmental levels should have a practical background, draw on students’ experiences, use language acceptable to students, allow students enough time to derive meaning through exploration and examination of mathematical concepts, and enable students to opportunity to discuss their ideas. (2) Gradually cultivate students' awareness and ability of cooperative learning. In order to prevent group learning from becoming a mere formality, students' communication skills must be carefully cultivated.

Communication involves both information output and information input, so talking, listening, reading, and writing are basic communication skills; in addition, for mathematics, communication should also have descriptive skills. (3) Design and arrange activities based on the purpose of mathematics activities. Mathematics teaching activities are mathematics teaching. Each teaching activity should have a clear purpose, and the activity itself is the means and process to achieve the purpose.

(4) Doing exercises and writing homework are necessary links to consolidate knowledge and acquire skills in mathematics classroom teaching. (5) Pay attention to the evaluation of students’ mathematics learning and evaluate students’ mathematical concepts in conjunction with the process of learning mathematics. knowledge understanding. Only when students understand mathematical concepts and their meanings or explanations can they understand mathematics and "do mathematics" meaningfully.

(6) Pay attention to the evaluation of students’ initial problem-finding and problem-solving abilities. When evaluating problem-solving, you should first pay attention to evaluating students’ description of the problem, that is, how to verbally describe the problem presented in the situation map. The language describes it completely. (7) Pay attention to the evaluation of students’ emotions and attitudes in learning mathematics. To evaluate the emotions and attitudes of first-year students in learning mathematics, relevant information is mainly collected through classroom observation, such as their participation in class discussions, trying to solve problems, and independent Or in group learning, their emotions and attitudes towards mathematics learning are always displayed. It can be seen whether they have confidence, whether they are interested, whether they are willing to explore, whether they have perseverance, whether they are curious, and who dares to question.