1 How to expand junior high school mathematics teaching
First of all, the expression of "knowledge and skill goal" is not comprehensive, and there are omissions, especially emotional points, which are the ultimate teaching points of mathematics and are often omitted in design. This is related to the fact that teacher education has been seriously influenced by exam-oriented teaching thinking for a long time, attaching importance to knowledge teaching and neglecting mathematics education. It is also related to the fact that teachers have long regarded "teaching materials" as the whole of mathematics teaching and neglected the understanding and grasp of curriculum standards. It is also because of ignoring the systematic teaching of mathematics knowledge, especially the objective existence of countless teaching resources outside mathematics, turning a blind eye to the teaching materials and mathematics life outside the classroom, and drawing a three-dimensional picture to become a unified whole. Restrain yourself and students.
Secondly, the design of "process and method objectives" is too general to form cognitive guidance for students. In the design process, the characteristics of unit knowledge are not considered, and the cognitive needs of students for this unit learning are ignored. According to the requirements of curriculum standards, "process and method goal" should prompt or clarify what kind of thinking process students need to go through when learning the knowledge points in "knowledge and skill goal" and what methods should be used to realize the learning of these knowledge, thus forming valuable learning guidance. This is a kind of guidance for students' learning behavior. A little carelessness will affect students' cognitive direction, and then directly affect the cognitive level and effect.
Third, the expression of "the goal of emotional attitude and values" is either general, superficial or biased. Let "students receive good mathematics education" is the responsibility given to mathematics by the new curriculum standards, because it is of great significance to students' all-round, sustainable and harmonious development. Mathematics teaching should start with cultivating interest, stimulating positive learning emotions, exercising the will to overcome difficulties and establishing self-confidence. Without mathematics education, it is impossible to achieve these goals. Or it is shallow, utilitarian and even irresponsible to pay attention to the teaching of "knowledge and skills". Therefore, on the basis of teachers' profound understanding and grasp of curriculum standards and teaching materials, mathematics teaching should find "emotional points" and find channels to guide students' value identification, so as to cultivate and form positive values step by step.
2 innovative mathematics teaching methods
Cultivate students' spirit of cooperation
Applying group cooperative learning in project teaching is an effective way to cultivate students' innovative consciousness. Group cooperative learning creates a lively learning atmosphere for students. In a relaxed environment, students can speak freely, express their opinions, dare to express their independent opinions, or correct others' ideas, or combine several ideas into a better idea, so as to make friends with students' collective innovation ability in the learning process, promote students' initiative, try to explore and form their psychological desire to explore and innovate. In teaching, students discuss according to the systematic materials and problems provided by teachers, which is not only conducive to multi-directional communication between students, but also conducive to stimulating the formation of students' self-innovation spirit and giving play to their own innovative talents.
For example, in the teaching of "parallelogram area", (1) first show students a parallelogram ground and a rectangle ground, so that students can compare the sizes and cause cognitive conflicts; (2) Based on a rectangular piece of paper and a parallelogram piece of paper, it is preliminarily perceived that the parallelogram area is related to the rectangular area; (3) Inspire students to imagine: how to turn parallelogram paper into rectangular paper, work in groups, draw, cut and spell, and students with poor ability also stimulate innovative thinking under the guidance of other students, while students with good ability develop their thinking through group cooperation. (4) Comparing the transformed graph with the original graph, what do you find? The area formula of a rectangle is length times width. How to calculate the area of parallelogram? (5) Students draw conclusions through practical operation and discussion. Students gain knowledge, broaden their horizons and reflect innovative thinking in the practice of group cooperation, which is more conducive to the formation of students' innovative spirit.
Create activity scenes and promote innovative thinking
Everyone has the spirit of innovation and creation, but how to develop it. As an exploratory voice, hands-on operation provides a broad space for cultivating students' innovative ability, and students' innovative sparks are often ignited in unconscious practical research. Friedenthal, a Dutch mathematics educator, believes that "mathematics comes from reality and must be rooted in reality and applied to reality." Combining the mathematical knowledge in the textbook with practical activities not only conforms to the teaching principle of integrating theory with practice, but also conforms to the age characteristics of students; It not only stimulates students' interest in learning mathematics, but also enables students to master learning skills. In practice, letting students do, think and do is helpful to cultivate students' creative thinking. For example, when the teacher teaches "abdication subtraction within 100", let the students explore independently with sticks and operate by hand to explore different algorithms. In this process, teachers give students a broad stage to fully display their thinking, and students can brainstorm, stick to one pattern and fully tap their own potential. It can be seen that in teaching, as long as children are trusted and given enough space and time to operate and explore independently, their innovative thinking ability in mathematics can be improved.
For example, in the teaching of "Preliminary Understanding of Corner", when the size of the corner has anything to do with the length of both sides, I ask the students to take out the active angle and do the calculation: (1) If the active angle is larger, will the sides be longer? (2) make the moving angle smaller and the edge shorter; (3) Cut both sides of the corner short with scissors. What happened to the angle? Students do it by themselves, cut the sides of the active corner, and draw the conclusion that the length of both sides has nothing to do with the size of the corner. Students explore laws, break through difficulties, master knowledge and learn independently in the process of observation, comparison and hands-on operation, and cultivate students' innovative ability.
3 innovative thinking in mathematics teaching
Take students as the main body and encourage students to participate more.
This teaching method fully attaches importance to and embodies the students' dominant position, and teachers play a guiding role appropriately, so that students can learn and improve with understanding and respect. So how does the teacher realize this teaching method? In class, teachers should put forward open questions according to their knowledge and students' reality, guide students to explore independently and encourage students to tell their own answers. Then, the teacher asked the students to put forward various conjectures according to their answers, and verified whether their conjectures were correct by making models and practicing. Through observation and communication, students explore the problems in the classroom and improve their comprehensive ability.
At the same time, teachers should also pay attention to whether the questions raised can further stimulate students' creative thinking and improve students' ability to study problems independently. Today's math problems are different from those in the past, and they are more flexible and changeable. There are often many different solutions to a problem, which requires teachers to gradually improve students' divergent thinking ability in asking questions, so that students can solve a problem in many ways, draw inferences from one another, come up with many different solutions to a problem, and answer the same type of questions quickly. Through the guidance of teachers, this teaching method broadens students' thinking and expands their ability, which is unique and innovative.
Pay attention to life application and use multimedia.
Nowadays, no matter which subject is taught, the combination of life and practice is advocated, so that students can widely apply what they have learned in class to their daily lives. The same is true of mathematics teaching. For example, when students encounter discounts from merchants, teachers should encourage students to use the knowledge of calculation and statistics to figure out whether the merchants are losing money and how much they can earn. For example, a building is under construction. After strengthening the cultivation of life application, students should be able to use the geometry knowledge they have learned to simulate the model of the building in their minds, estimate the angles of its corners, and ask questions and answer them themselves. Being able to apply what you have learned to life is the key to learning.
Using multimedia teaching can not only increase students' interest in learning, but also improve students' practical application ability of multimedia content such as pictures, videos and models. Most schools have introduced multimedia technology and applied multimedia teaching, and its advantages are becoming more and more obvious. The application of multimedia technology makes the original abstract mathematical problems intuitive and three-dimensional, especially in geometry course learning. With book knowledge as the knowledge base and various colorful multimedia materials as the auxiliary, the monotonous classroom adds a lot of interest. Students learn more solidly, teachers teach more easily, students explore and think under the guidance of multimedia courseware, and their ability to solve problems is greatly improved. With the application of multimedia technology, the teaching content is closely combined with real life, which reduces the boredom in mathematics learning and increases the fun of mathematics learning.
4 mathematics autonomous teaching mode
Grasp the principle of infiltrating mathematical thinking methods. The main contents of applied mathematical thinking method include macro mathematical thinking method, such as related mathematical philosophy and modeling thought, number system expansion thinking method; At the same time, there are a large number of applications of general scientific methods, such as induction and deduction, association classification and so on. When primary school students master these ideas and methods in this series of mathematical activities, their intelligence can naturally be improved, and the corresponding picture of mutual aid teaching in primary school mathematics will further become clear and beautiful.
Master the mathematical principle in learning. Objectively speaking, mathematics, as a practical and intellectual activity of human beings, has the characteristics of mathematization, and the process of learning mathematics is the process of promoting mathematization. Students are learning mathematics rather than mathematics. The study of mathematics is to learn to look at reality from a mathematical point of view, and then use mathematical methods to solve problems [2]. Therefore, if this principle is applied to the actual classroom teaching, it is essentially to transform the actual problem into describing or constructing mathematics with mathematical language.
Grasp the principle of problem-driven. Asking questions to students or helping each other is the inner soul of mathematics, and the teaching of mathematics types must be driven by questions. Problems in primary schools constitute clues, which can be used to drive corresponding teaching. Mathematics teaching in primary schools can provide suitable mathematics learning space for primary school students through constantly changing mathematical problems, help primary school students understand the essence of mathematical concepts from multiple angles, and establish essential mathematical relations.
Grasp the principle of moderate formalization. The formalization of mathematics contributes to the further simplification, strictness and systematization of mathematical theoretical system. Constructing a good structure of existing mathematical knowledge forms can conveniently provide a visual model based on conjecture and analogy for exploring and determining unknown mathematical formal structures. The formalization of mathematics generally includes three levels, namely symbolization, logicalization and axiomatization. Mathematics is actually a symbolic formal language. Proper use of a set of ideographic mathematical symbols can promote the expression of the structure and laws of mathematical objects, thus transforming the study of specific mathematical objects into the study of symbols and producing a reasonable deductive system. This process is the formal process of mathematics. The principle of moderation should be grasped in the process of formalization of primary school mathematics.
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