Second, how can we achieve the overall goal of mathematics teaching in primary schools?
(1) Choose to learn the basic knowledge related to scientific modernization, and integrate theory with practice.
(2) Let students fully realize the importance of learning mathematics.
3. What is the purpose of mathematics teaching in primary schools?
① Let students learn basic knowledge well.
② Cultivate and develop students' ability, pay attention to cultivating students' computing ability and logical thinking ability, develop students' spatial concept, apply what they have learned and solve practical problems.
③ Enable students to receive ideological and moral education.
4. What are the principles for determining the content of primary school mathematics teaching?
(1) According to the objectives of mathematics curriculum.
② Meet the needs of students and promote their development.
③ Reflect social progress and the development of mathematics itself.
5. Why should modern teaching ideas be infiltrated into primary school mathematics textbooks? How is it infiltrated?
① Modern mathematical ideas such as set, function and statistics are permeated in the textbook, which is helpful for students to deepen their knowledge and understand some contents, and to further study mathematics and modern science and technology.
Methods: According to the characteristics of primary school students, adopt an intuitive teaching form suitable for primary school students, so that students can intuitively feel mathematics and accumulate some perceptual knowledge of modern mathematical thought.
6. What are the principles for arranging the content of mathematics teaching in primary schools?
(Same as 4)
7. What are the requirements of primary school mathematics in cultivating computing ability? How can we meet these requirements?
① Primary school mathematics should cultivate students' ability to calculate integers, decimals and fractions. It is also required to be correct and fast, and at the same time pay attention to the rationality and flexibility of calculation methods to cultivate students' good calculation habits.
(2) It is necessary to: a) let students master the basic knowledge of calculation such as the operation rules, properties and rules of integers, decimals and fractions; B) Train students to often use simple and reasonable calculation c; Let students remember some basic and commonly used mathematical operations; Improve the calculation speed d; Focus on key points and difficulties; The focus and content of teaching are directly related to the further mastery of teaching knowledge.
Eight, what is logical thinking? How to cultivate students' logical thinking?
The so-called logical thinking is an orderly, coherent, regular and well-founded cognitive activity process.
(2) Requirements: (a) Create teaching situations so that students can learn knowledge in specific situations; B) Encourage students to think independently and guide them to explore freely, cooperate and communicate; C) Strengthen students' language expression training and cultivate students' thinking ability; D) In short, in order to cultivate students' logical thinking, it is necessary to combine the teaching content and carry out training in a planned and purposeful way, so as to cultivate creative and innovative talents.
9. What is the concept of space? How can we form students' initial concept of space?
1 The so-called concept of space refers to the representation of the size, shape and mutual position of objects in the brain. Representation refers to the image left in the brain by things perceived in the past.
We must attach importance to the teaching of the basic knowledge of geometry, so that students can observe, make, measure, draw and calculate. Gradually obtain the mutual representation of the shape, size and mutual position relationship of objects.
X. how to carry out ideological and moral education for students in combination with the teaching content?
(1) arouse students' learning enthusiasm and educate students to study mathematics hard, so as to revitalize China and realize the four modernizations of the motherland.
(2) Through the training of mathematics, form the habit of treating learning strictly.
③ Pay attention to the practical activities of applying knowledge and highlight the purpose of learning. Mathematics is an indispensable basic tool for learning science and technology.
XI。 What are the four stages of the content of integer textbooks, and what is the focus of each stage?
The first stage: addition and subtraction within 20, focusing on the addition and corresponding subtraction of one digit, which is the basis of multi-digit calculation.
The second stage: multiplication and division within 100. The key point is to learn integer multiplication and corresponding punishment well, and master oral calculation and written calculation addition and subtraction initially.
The third stage: the operation of addition, subtraction, multiplication and division within 10,000, focusing on learning the multiplication and division of pen-based addition, subtraction, multiplication and division.
The fourth stage: it is a multi-digit multiplication and division method. The key point is that the multiplication and division number is two or three digits, which is a generalization and improvement of the meaning law and operation nature of the four operations of integers.
What is the status of integers in primary school teaching?
Integers are widely used in daily life and production. It is the most basic tool to solve daily practical calculation problems, and it is also the minimum basic knowledge and skills that every primary school student must master. This part of the content is the basis for primary schools to learn decimals and fractions well, and it is also the basis for further study of mathematics and other disciplines. At the same time, this part is the beginning for students to learn mathematics. Enlightenment education has the greatest relationship with students' interest in learning and the cultivation of good study habits, which directly affects their future study. It can be seen that the four operations of integers and integers play a very important role in primary school mathematics.
Thirteen, what method does the textbook use to calculate the carry addition and abdication subtraction within 20?
Use visual teaching AIDS to let students experience the image impression of carry and give way. In the composition and application of numbers, we can further deepen our understanding of advance and retreat. However, the textbook of carry addition for calculating less than 20 adopts the "ten-complement method", and the textbook of abdication subtraction adopts the inverse operation method. Subtraction is the inverse operation relationship of addition and is calculated by addition.
Fourteen. What are the two stages of fractional teaching? What is the focus of each stage?
The first stage: arranged in the sixth volume, the teaching content is a preliminary understanding of fractions, simple addition and subtraction operations, and the focus is on understanding the meaning of fractions.
The second stage: arranged in the eighth and ninth volumes, the teaching content is the concept, nature, four operations and percentage of fractions, with the emphasis on systematically mastering the concept and algorithm of fractions.
Fifteen, how is the initial understanding of algebra arranged in the textbook? What are the teaching requirements?
The preliminary understanding of (1) algebra makes use of the relationship between the characteristics and contents of numbers, and takes into account the age characteristics and cognitive rules of primary school students. It adopts the appropriate cooperation of arithmetic knowledge and gradually introduces it on the basis of arithmetic knowledge. After learning to use the relationship of known numbers, introduce unknown x and learn simple equations. On the basis of learning integer, decimal, four operations and application problems, it uses the relationship between known number and obtained number in four operations to learn.
(2) Teaching requirements: ① Make students understand the meaning and function of using letters to represent numbers, learn to use letters to represent common quantitative relations, operational properties and calculation formulas, and learn to use numerical values instead of letters to calculate in formulas. ② Make students understand the meaning of equations and learn to solve simple equations; ③ Let students learn to set equations and solve some relatively easy application problems.
Sixteen, how to arrange the application questions? What are the teaching requirements for each grade?
① The arrangement of application problems is based on the internal relationship between application problems, the coordination of attention and recognition, the concepts and rules of four operations, and considering the acceptance ability of Xiao Xu and others, the quantitative relationship is arranged from easy to difficult, and the parameters are solved from less to more.
② Addition and subtraction, one-step application problems are arranged in Grade One, slightly complicated one-step application problems and general two-step application problems are arranged in Grade Two. Middle school students' thinking has developed to a certain extent, and their abstract thinking ability has been gradually improved, which has a certain foundation for the structure, characteristics and solving methods of two-step application problems. Therefore, in the third grade, the steps and methods of solving and summarizing a slightly complicated two-step application problem and general application problem are arranged, and the equations for solving three-step application problems are listed. Grade five students have a certain foundation of mathematical knowledge and a certain development of logical thinking ability. The fifth and sixth grades can solve some complicated multi-step application problems, learn to solve basic application problems with proportional knowledge, and look at the scales on the map to further improve the ability to solve application problems with arithmetic methods and equations.
17. How is the preliminary understanding of geometry arranged? What are the teaching requirements?
1. The arrangement of primary school mathematics textbooks on the preliminary understanding of geometry follows the characteristics and internal relations of shape and number, and pays attention to the relationship between shape and number. At the same time, it also follows children's cognitive rules, from simple to complex, from easy to difficult, and gradually appears in all grades. Know the straight line and angle first, then know all kinds of plane figures, and calculate the area and perimeter of these figures. With the knowledge of lines and surfaces, we can know three-dimensional graphics and make related calculations. From the internal relationship of geometry knowledge, we should first know the line segment and angle, mainly the right angle, to prepare for knowing the rectangle. In the future, the concept of angle is introduced comprehensively, and the angle is measured with a protractor, which lays the foundation for understanding triangles.
2. The teaching requirements are: 1 Master the characteristics of common plane graphics and three-dimensional graphics, understand the connections and differences of various graphics, correctly understand and identify various graphics, and imagine the appearance of a graphic with theory when seeing or hearing a graphic. 2 master the perimeter, area, volume and size of the area unit, and have a clear concept; Understand and master the algorithms of perimeter, area and volume of some common geometric bodies, and use them correctly.
Eighteen, the textbook "Vertical Line" requires students to see, think, fold, measure and draw everything.
Let the students see that the intersection of two straight lines forms four angles. Think that one angle is a right angle and the other three angles are angles. Draw two mutually perpendicular line segments, measure whether each angle is a right angle, and draw two mutually perpendicular lines.
Function: To lay a foundation for learning the contents of rectangles, squares, cubes and cuboids in the future and apply them to real life.
Nineteen, "Cuboid and Cube Profile", what is the basis of teaching, and what is the significance of learning this part?
The content of 1 is taught on the basis that students master the characteristics, perimeter and area calculation of rectangles and squares.
The significance of learning this part of the textbook lies in: 1 Cuboid and cube are the most basic geometric bodies, and the volume calculation of cuboid is the basis of other geometric bodies. 2. Stereograph is an important development of plane graphics, which plays a great role in cultivating students' spatial concept through teaching.
20. What books are the contents of quantity calculation arranged in? Why is this arrangement?
I. Book 1: Understanding Hours by Integers Book 2: Understanding Monetary Units and Weights by Numbers and Calculations Book 3: Understanding Length Units of Meters, Centimeters Book 4: Understanding Kilometers and Kilograms Book 5: Understanding Kilometers and Tons, Hours, Minutes and Seconds Book 6: Calculating Area Units by Rectangles and Squares Book 7: Understanding Year, Month and Day Book 8: Measuring Angle and Measuring Land to Find Area
Second, the reason is that in the knowledge of quantity measurement, there are many units of calculation, and each unit of measurement has several units of different sizes. The propulsion speed and conversion units among various units of measurement are not exactly the same, and there is little perceptual knowledge in this respect, so it is difficult to establish the concept of various units of measurement, so this arrangement has been made.
2 1. What is a statistical chart? What are the steps to make a statistical chart?
1. Statistical chart shows interrelated statistical data in tabular form. 、
2. The steps of making statistical chart are as follows: design 1 to define the purpose of making statistical chart; Design charts according to the purpose and data, mainly designing vertical and horizontal titles, which should be simple and clear for people to see clearly; 3. Fill in the data in the appropriate columns and check them carefully; 4. The title is simple and clear, reflecting the main contents of the statistical chart; 5. Please pay attention to the unit name, data source and date of investigation and tabulation of the data in the table.
22. Examples of conceptual analysis of teaching materials.
Mathematical concept is the reflection of the quantitative relationship and the essential attribute of spatial form in objective reality in the human brain. The research object of mathematics is the quantitative relationship and spatial form of objective things. In mathematics, the color, material, smell and other attributes of objective things are regarded as non-essential attributes and discarded, and only the same attributes in shape, size, position and quantity are retained. In mathematical science, the meaning of mathematical concepts should be precisely defined, so mathematical concepts are more accurate than general concepts.
There are many concepts in primary school mathematics, including the concepts of number, operation, quantity and measurement, geometric shape, ratio and proportion, equation and related concepts of preliminary statistical knowledge. These concepts are important contents of elementary school mathematics basic knowledge, and they are interrelated. Only by grasping the concept of number clearly and firmly can we understand the concept of operation, and mastering the concept of operation can promote the formation of the concept of divisibility of numbers.
Concepts in primary school mathematics textbooks have different forms of expression according to the acceptance of primary school students, among which descriptive expression and defined expression are the most important two.
1. Define formula
Definition is a method to reveal the connotation or extension of a concept in concise and complete language. The specific method is to explain the new concept to be defined with the original concept. These defined concepts grasp the essential characteristics of a class of things and reveal the essential attributes of a class of things. Such a concept, in the analysis, synthesis, comparison and classification of a large number of inquiry materials, has changed from intuition to representation and then to rational understanding. For example, "a triangle with two equal sides is called an isosceles triangle"; "An equation with unknowns is called an equation" and so on. The concepts, conditions and conclusions defined in this way are very obvious, which is convenient for students to grasp the essence of mathematical concepts at once.
? 2. Descriptive expression
Describing concepts in some vivid and concrete language is called descriptive. This method is different from definition. Descriptive concepts are generally established by students' perception of representations and choosing representative special cases as reference objects. For example: "When we count objects, 1, 2, 3, 4, 5 ... are called natural numbers"; "Things like 1.25, 0.726 and 0.005 are decimals" and so on. This concept will improve with the increase of children's knowledge and understanding, and it is generally used in the following two situations in primary school mathematics textbooks.
One is to describe the original concepts such as point, line, body and set in mathematics. For example, the concept of "straight line" in textbooks is described as follows: take a straight line and tighten it, and it becomes a straight line. Plane is explained by class desktop, blackboard surface and lake surface.
The other is that for some difficult-to-understand concepts, if it is difficult for primary school students to understand with simple and general definitions, they will use descriptive expressions instead. For example, the understanding of a straight cylinder and a straight cone can't be defined by a rotating body like middle school students, because primary school students still lack the viewpoint of movement, and they can only describe their characteristics vividly through physical objects, but can't reveal their essential attributes in the form of definitions. In the process of observation and spelling, students realize that the characteristics of a cylinder are that the upper and lower bottom surfaces are equal circles and the side surfaces are rectangular.
; Generally speaking, in mathematics textbooks, the concept of lower grades in primary schools is more descriptive. With the gradual development of primary school students' thinking ability, definitions are gradually adopted in middle school, but some definitions are only preliminary and need to be developed. In the whole primary school stage, because of the contradiction between the abstraction of mathematical concepts and the visualization of students' thinking, most concepts are not strictly defined; Instead, starting from the actual examples that students know or the existing knowledge and experience, we should try our best to help students understand the essential attributes of concepts through intuitive and concrete images. For the concepts that are not easy to understand, we will not give a definition for the time being or adopt the method of gradual infiltration in stages to solve them. Therefore, the concept of mathematics in primary schools presents two characteristics: one is the intuition of mathematical concepts; The second is the stage of mathematical concept. When teaching mathematical concepts, we must pay attention to full understanding.
For example, when learning the meaning of multiplication, we can introduce it from the meaning of addition. For another example, when learning the concept of "divisibility", it can be introduced from "division". For another example, learning "prime factor" can be introduced from the concepts of "factor" and "prime number". For another example, when learning the concepts of prime numbers and composite numbers, the concept of divisor can be introduced: "Please write down all divisors of the numbers 1, 2, 6, 7, 8, 12,1,15. How many divisors do they have? Can you give a classification standard to classify these figures? Can you find a variety of classification methods? Of all the classification methods you have found, which one is it?
For example, when studying Average, teachers can first present students with a life situation of "kindergarten children fighting for candy", so that students can think about why some children are happy and others are unhappy. What should I do to make everyone happy? What should we do next? What are the teachers in this kindergarten likely to do?
For example, when teaching the concept of "isosceles triangle", teachers should not only use common graphics (Figure 6- 1( 1)), but also use variant graphics (Figure 6- 1(2), (3) and (4)) to strengthen this concept, because it is used.
(1) What is the circumference of a rectangle? What is the area of a rectangle?
(2) What are the commonly used units of measurement for perimeter and area?
(3) In Figure 6-3, are the perimeters of two figures A and B equal? Are the areas equal?
(4) Each small square in Figure 6-4 represents one square centimeter. What is the area of this figure? The circumference is, cut a knife and put it together into a square. What is the circumference of this square? What is the area?
Twenty-three, the calculation and analysis in the textbook as an example.
There are three examples in the textbook to teach the vertical calculation of division, and the examples on 1 page focus on solving the problems of vertical structure and calculation steps. The material used in the example is to distribute 46 pencils to two girls on average, so that students can get 2 bundles, then 3 pencils and 23 pencils each, and sort out their ideas. First, 40÷2=20, then 6÷2=3, and then 20 and 3 are combined into 23. The textbook regards these perceptual knowledge as the necessary basis for accepting vertical division meaningfully. In vertical division, two color blocks are used to show the division process in two steps, and students are guided to upgrade their operating experience to calculation methods. The vertical meaning and writing position of each quotient are very important. The question asked in the textbook is "Why is it written in ten digits?" Let students think and understand the position of quotient in pencil division.
The example on page 7 focuses on solving the problem that the remainder on the divided ten digits should be combined with the number on the unit to continue the division. The material of the example is that badminton with five tubes and two (52) is divided into two classes on average, and students are willing to operate it. In the operation, they can first assign two shuttlecocks to each class, and then combine the remaining 1 shuttlecocks with the other two, and continue to score on average. On the basis of activating the direct experience of continuing to divide the remaining 12 badminton, let the students complete the vertical calculation independently, and further understand that the remaining ten digits divided in the vertical form are 1 "ten", which can be divided by 12 in combination with two digits.
The example on page 9 focuses on solving the problem that the unit of quotient is 0. The materials of the examples can still arouse the enthusiasm of students, and the quotient is 20, not 2. Then through vertical calculation, we can further understand why we should write 0 in the unit of quotient. The textbook encourages students to have their own ideas, such as 2 divided by 3 is not enough to quotient 1, so quotient 0. If you don't write zero in the number, the quotient is not 20 ... as long as the idea is correct.
24. Examples of teaching material analysis's algorithm.
Origami (addition and subtraction of fractions with different denominators)
four
Sunday arrangement (mixed operation of fractional addition and subtraction)
Fractions and decimals 2
Third, the characteristics of compiling unit textbooks and teaching suggestions
1. Explore how to calculate the addition and subtraction of different denominator fractions through practical operation.
In order to let students intuitively understand the addition and subtraction of different denominator scores, in the lesson of "origami", the textbook arranged the students' origami activities, and raised the question of how much two children used through origami. Subsequently, the textbook arranged a group of activities to make a puzzle of the two parts, so that students can clearly see how the two parts are combined. Then, the process of digital symbol operation is expounded by comparison. Because students have an intuitive image structure, it is easy to understand the principle of division before operation when they enter the digital symbol operation. Similarly, for the subtraction of fractions with different denominators, although the textbook directly presents the calculation method of digital symbols, it is arranged according to the students' cognitive rules. Of course, different teaching designs can also be adopted for students in different regions. If students' cognitive ability is weak, they can still use the origami method mentioned above to help students understand the significance and calculation method of subtraction.
2. Guide students to discover the method of conversion between fractions and decimals through independent exploration.
It is an important feature of this set of teaching materials that students explore ways to solve problems independently. Similarly, in the study of this unit, the learning contents of the four situations all have such characteristics. Especially in the lesson of "watching extracurricular time", the textbook does not use a hard rule to explain how to convert fractions and decimals, but focuses on how to compare two different numbers. First of all, the textbook suggests how to compare two numbers that express time in different forms. This is the first time that students have encountered similar problems and need to use what they have learned to find solutions. Secondly, the textbook arranges four specific exploration methods to illustrate the methods that students may appear in their exploration. These four exploration methods all use more detailed space to show how fractions are converted into decimals and how decimals are converted into fractions. In the teaching process, when students have such a method, they only need the proper guidance of teachers.