Teacher Blog How to teach lessons in primary school mathematics teaching

The so-called lecturing means that teachers use education and teaching theories and teaching materials as the basis to prepare for their peers, experts or leaders to analyze the status and function of the teaching materials and students' existing cognitive basis for a certain lesson. It is a form of teaching research and communication that explains the teaching objectives, selects appropriate teaching methods and learning guidance methods, and explains the design ideas of the teaching plan. It can be an elaboration and explanation of the teaching plan before class, or an introduction and analysis of the teaching design after class. In principle, the scope of each lecture is the content of one class teaching material, including three parts: lecture materials, teaching methods, learning methods, and lecture teaching procedures.

To teach a lesson well, I think teachers must first do the following:

1. Teachers must have a good cultural foundation and be able to use refined language to teach Express.

2. Master the content and requirements of the new curriculum standards, and accurately grasp the new curriculum standards.

3. Understand the system and arrangement characteristics of primary school mathematics textbooks, and know the status and role of each part of content in primary school mathematics learning. (That is, thoroughly understand the teaching materials)

4. Have a high level of educational and teaching theory and use it to guide the teaching process.

In the entire teaching process, having a refined level of language expression is the prerequisite, grasping the syllabus and new curriculum standards is the criterion, thoroughly understanding the teaching materials is the foundation, and using educational and teaching theories to guide the teaching process is the key. So how should primary school mathematics lectures be taught? Now I will talk about a superficial understanding based on the relevant knowledge and learning experience I have learned, as well as some insights from writing lecture notes.

1. Talking about teaching materials - teachers explain their knowledge and understanding of teaching materials

Teaching materials are the object and content of students' learning. Grasping the teaching materials is the most basic basis for teachers to impart knowledge and implement classroom teaching. Only by deeply understanding the teaching materials and understanding the purpose of the teaching materials can teachers formulate better teaching plans and provide prerequisites for improving teaching.

Talking about the teaching materials, the following points are required:

1. Introduce the status, function and significance of the teaching content to the audience.

This is the opening sentence of the lecture. First, the teacher should introduce the specific teaching content to the audience in detail, and explain clearly the position of the teaching content in this unit, this book and even the entire primary school level. Status, function, significance, etc. (that is, clarify the relationship between this content and the previous and previous knowledge. It is taught on the basis of what content has been learned or mastered. What effect does learning this content well have on what content will be learned in the future? What effect does learning this content have on students’ mastery of the content in the future? What is the significance of knowledge, forming abilities, cultivating emotions, attitudes, values, etc.)

Take the lesson "Understanding of Angles" as an example. First, the teacher must introduce the teaching content which is the Jiangsu Education Edition of primary school mathematics. The understanding of the corner of Book Seven will be introduced next, and the status and role of the teaching materials will be introduced. (Combined with lecture materials)

2. Put forward specific and clear teaching objectives.

In primary school mathematics lectures, teachers often use psychology, education and other methods such as "based on the psychological characteristics of primary school students, concrete to abstract, concepts, logical thinking, thinking quality, judgment and reasoning, deduction and induction" However, in the application, some teachers do not understand it correctly and use it incorrectly. In order to avoid this kind of mistake, teachers must first understand and master the meaning of some commonly used teaching terms so as to avoid making jokes. When formulating class teaching objectives, the following terms are generally used:

(1) Cognitive objectives: divided into three levels: understanding, understanding and mastering.

Understanding (knowing, knowing): refers to knowing the meaning of learned terms, concepts, properties, rules, formulas and other mathematical knowledge, and being able to repeat and identify it. It refers to having a perceptual and preliminary understanding of the knowledge learned, being able to say what it refers to, and being able to identify it.

Understanding: refers to knowing the origin of the above knowledge, being able to explain it in your own language, and understanding the connections and differences between related knowledge. It means having some rational understanding of the knowledge learned, being able to express its exact meaning, and knowing its uses.

Mastery: refers to the ability to apply learned knowledge to analyze, judge, reason and calculate on the basis of understanding to solve some simple problems. It can explain some truth.

(2) Skill objectives: divided into three levels: learned, relatively proficient and proficient.

Learning: refers to being able to correctly complete mathematical activities such as measurement, drawing, production and calculation according to the methods learned.

Comparatively proficient: refers to the ability to complete the above teaching activities quickly by reducing intermediate links through practice. It refers to reading, writing numbers, oral arithmetic, written arithmetic, etc., to achieve a correct and relatively rapid level through training.

Proficiency: refers to the ability to complete the above-mentioned activities flexibly and quickly independently.

(3) Ideological and emotional goals: divided into three levels: feeling, experience and preliminary.

Feeling: refers to the psychological tendency to have a certain understanding of and identify with the interests, attitudes, ideological and moral education involved in mathematics teaching.

Experience: Refers to the above-mentioned education, the ability to actively carry out corresponding psychological activities in new situations, and initially affect one's own behavioral practice.

Initial possession: refers to the gradual formation of relatively stable psychological qualities and ideological concepts through teaching and practical activities, and the ability to guide one's own behavioral practice.

(4) Cultivating mathematical abilities. Previous training views believe that primary school students’ mathematical abilities mainly include three aspects: a. calculation ability, b. logical thinking ability, and c. spatial concept. The new curriculum standards propose some new abilities, namely the ability to learn independently and conduct inquiry, collaborative learning ability, innovation ability, etc.

a. Cultivation of computing ability

There is a difference between computing ability and computing skills. Computing ability is a combination of logical thinking ability and computing skills. It can be divided into two stages: the first is the primary stage, which requires understanding arithmetic, mastering rules, and correct calculations. The second is the proficiency stage, which requires mastering the properties of operations to make calculations reasonable and flexible.

To improve the calculation ability of primary school students, we must achieve the following three aspects:

1. Thoroughly understand arithmetic, master the rules proficiently, and develop calculation skills.

① From concrete to abstract, clarify the principles and summarize methods and rules. ② Consciously apply the rules to ensure correct calculations. ③ Simplify the calculation steps and compress the thinking process. ④Completely unaware of the rules, achieving calculation "automation". ⑤ Organize the rule system to form a cognitive structure.

2. Strengthen the teaching of oral arithmetic and operation laws and properties, improve calculation efficiency, and develop students' thinking ability.

① Oral arithmetic is the basis of written arithmetic and is widely used in daily production and life. ②For the laws of operation and properties, one must understand them and the other must be able to use them.

3. Develop good calculation habits and improve calculation accuracy.

① Review the question carefully. Complete the order of operations in the first trial, the characteristics of the exercises in the second trial, and the characteristics of the data in the third trial. ② Pay attention to estimation. ③Insist on checking calculations.

b. Initial logical thinking ability.

This sentence is a sentence that mathematics teachers will definitely use in their lectures. This point is pointed out in the "Nine-Year Compulsory Education Primary School Mathematics Syllabus" and the "New Curriculum Standards", which require students to develop preliminary logical thinking abilities.

Logical thinking is the process in which people reflect reality with the help of concepts, judgments, and reasoning in the process of understanding. It is different from image thinking. It uses scientific abstract concepts and categories to reveal the essence of things and express the results of understanding reality. Logical thinking is a kind of definite rather than ambiguous; consistent rather than self-contradictory; organized and well-founded thinking. In logical thinking, thinking forms such as concepts, judgments, and reasoning and methods such as comparison, analysis, synthesis, abstraction, and generalization are used. The degree of mastering and applying these forms and methods is the ability of logical thinking.

In teaching, it is necessary to combine relevant content to train students to conduct preliminary analysis, synthesis, comparison, abstraction, and generalization, judge and reason about simple problems, and gradually learn to think about problems in an orderly and well-founded way; At the same time, pay attention to the agility and flexibility of thinking.

Although logical thinking ability is composed of many components, the high degree of abstraction of mathematics leads to their great generality. Therefore, it can be said that abstraction and generalization ability are the basis of other mathematical abilities and the basis of logical thinking ability. Core, that is, it is the core of the core of mathematical ability. Therefore, in primary school mathematics, abstraction and generalization abilities should be cultivated as the most basic and important components.

Strengthening the "double base" and paying attention to the "process" is the primary way to cultivate students' mathematical thinking ability.

A Generalization ability B Abstract ability (concrete – representation – abstract – concrete) C reasoning ability (1. Ask students to state the basis for the conclusion based on new conclusions; 2. Start from existing conclusions and guide students Introducing new conclusions) D association ability (close association, similar association, contrast association, causal association, analogy association, reverse association) E transformation ability (reversible transformation, hypothesis transformation, old and new transformation).

The basic ways to cultivate students' preliminary logical thinking ability are:

1. Demonstration - teaching combined with knowledge, giving students information on "how to think correctly" intuitively and easily.

2. Instructions - For those where old and new knowledge are closely related, you can grasp the basic ideas for solving new problems and inspire students to deduce them on the basis of existing knowledge.

3. Training – combined with the teaching of relevant content, purposefully and plannedly train students to gradually learn to think about problems in an orderly and well-founded way, and describe the thinking process more completely.

c. Cultivation of spatial concepts.

Preliminary spatial concepts are the third main ability to be cultivated in primary school mathematics teaching. The concept of space in primary school mathematics is mainly about the representation formed in students' minds by the shapes, characteristics and properties of geometric shapes. The new curriculum standards require students to gradually form representations of simple geometric shapes, sizes and mutual positional relationships, be able to identify the geometric shapes they have learned, reproduce their representations based on the names of geometric shapes, and develop preliminary spatial concepts. The process is mainly through observation, operation, abstraction, generalization, etc., combined with the teaching of preliminary knowledge of geometry to help students form correct spatial concepts and then cultivate spatial imagination. 1. Through observation, establish a clear representation, abstractly summarize the essential attributes of graphics, and form a correct spatial concept. 2. Through operations, establish clear representations, abstract the essential attributes of graphics, and form correct spatial concepts.

d. Cultivation of innovative ability

Cultivating students’ innovative ability is essentially to cultivate originality of thinking. The so-called originality of thinking refers to the creative spirit of thinking activities and the intellectual quality displayed in novel solutions. The "originality" here not only depends on the results of creation, but mainly on whether there is a creative attitude in thinking activities. Students can independently and consciously master mathematical concepts, discover proofs of theorems and laws, and discover novel solutions to examples taught by teachers in class. These are all concrete manifestations of original thinking.

3. Analyze the arrangement ideas, structural features, key points and difficulties of the teaching materials.

Accurately grasping the key points and difficulties of teaching content is a prerequisite for giving a good class. If you cannot grasp the key points and difficulties of teaching a class, it will be impossible to design a high-quality class, let alone a good one. Complete the teaching tasks well. Therefore, when analyzing teaching materials, explaining the emphasis and difficulty of teaching is an indispensable and important link. So how do we accurately grasp the key and difficult points of teaching a lesson? I think we need to do the following two things well:

First of all, we must correctly understand the meaning of the teaching focus and teaching difficulties. I think the teaching focus refers to the focus of the content being taught, that is, the focus of the teaching material, which is what students are expected to learn or master, so it depends on the teaching material. Teachers must accurately grasp the key points of teaching. They must thoroughly understand the teaching materials, understand the layout characteristics and intentions of the teaching materials, know what students are expected to learn in this part of the teaching, and know what knowledge and abilities a lesson is intended for students to master and develop. Find out what’s most important about these. In view of the age characteristics and cognitive patterns of primary school students, the teaching content of each lesson in primary school mathematics textbooks generally revolves around one key point, but there are two or more teaching points in a small number of classes, which requires teachers to be serious. Study the teaching materials carefully to grasp them accurately. Teaching difficulties refer to learning blind spots that students may encounter or knowledge points that have difficulty in understanding during the process of solving key teaching points. Therefore, the grasp of teaching difficulties must not only consider the difficulty of the teaching content, but also combine the knowledge level and ability of the students being taught, and comprehensively Various factors ultimately lead to the difficulty in teaching a lesson.

Secondly, we need to understand the connection and difference between the two. In daily lesson preparation, we often find that some teachers regard teaching key points and teaching difficulties as the same concept, thinking that the two are the same thing. This is because the connection between the two is not clear.

Teaching focus and difficulty are similar, but not exactly the same: the key to determining teaching focus is the teaching material, which refers to the focus of the teaching content and the objective existence of the teaching content. It does not change due to changes in other factors. The difficulty of teaching is determined based on many factors. Although it is also determined based on the teaching content, it is not the only condition. It must be combined with the actual situation of the students. The same teaching content, the difficulty when teaching in a class is as follows Yes, but teaching in another class may not be a difficulty for students. This is because there are certain differences in cognitive levels and knowledge structures among students. Therefore, the determination of teaching difficulties is affected by many factors and is not static.

4. Analyze the situation of students and sort out and organize the teaching content accordingly.

What we are talking about here is actually the lesson preparation we often talk about, which requires not only preparing teaching materials, but also preparing students. The so-called preparation of students means that teachers, as teachers, must be able to understand the ideological and moral character, cultural level, thinking ability and other aspects of the students they face, and organize and organize teaching based on the content of the textbook, and determine the teaching content. Law and study of law.