1, number sense mainly refers to the perception of logarithm and quantity, the relationship between quantity and quantity, the estimation of operation results and so on. The second layer is the number sense function. Abstract is the core of mathematics, and the abstract understanding of logarithm is the most basic. The learning of number sense is actually related to the abstraction and application of numbers. For example, primary school's estimation of length unit, area unit and unit of volume, and junior high school's estimation of irrational numbers are all related to number sense. The formation of number sense is a long process.
2. Symbol consciousness mainly refers to the ability to understand and use symbols to express numbers, quantitative relationships and changing laws. It is to use symbols to express, express what, express numbers, quantitative relations and changing laws, which is a layer of meaning. There is another meaning, that is, knowing that symbols can be used for operation and reasoning, and also drawing a conclusion, which is general. In the teaching of univariate quadratic equation, the formula for finding the root of univariate quadratic equation is an operable general conclusion. The application of mathematical symbolic language is very important in mathematics teaching. There is also the vertex coordinate formula of quadratic function, which is also training and using symbol consciousness.
3. The concept of space mainly refers to abstracting geometric figures according to the characteristics of objects, imagining the described objects according to the geometric figures, imagining the positions of the objects and their mutual positional relations, describing the movements and changes of the figures, and drawing the figures according to the description of languages. This is the portrayal of the concept of space. The concept of space has several latitudes. The first is the relationship between graphics and objects, which is a very important latitude. The second is the sense of direction described in the standard. Three, the front view, top view and left view of an object must have the concept of space.
4. Geometrical intuition mainly refers to describing and analyzing problems with graphics. With the help of geometric intuition, complex mathematical problems can be made concise and vivid, which is helpful to explore the ideas of geometric problems. To cultivate geometric intuition, students should develop good drawing habits, attach importance to the transformation of graphics, and keep the graphics in mind. Therefore, strengthening the understanding of basic graphics in normal teaching is helpful to improve students' geometric intuition. For example, when judging the nature of the vertical line and the angular bisector in a line segment, strengthening the understanding of the graph will help students understand and master the theorem.
5. The concept of data analysis means: to understand that there are many problems in real life, we must first do research, collect data and make judgments through analysis. To understand the information contained in the data and understand that there are many analysis methods for the same data, it is necessary to choose the appropriate method according to the background of the problem and experience randomness through data analysis. On the one hand, for the same thing, the data received each time may be different. On the other hand, as long as there is enough data, we can find patterns from it, and data analysis is the core of statistics. In mathematics teaching, studying the frequency distribution of data directly cultivates students' data analysis ability. With the concept of data analysis, we can study and study this part more thoroughly.
6. Computational ability, as long as it refers to the ability to perform correct operations according to laws and operations. Cultivating students' computing ability is helpful to understand computing and seek reasonable and concise computing methods to solve problems. In junior high school mathematics teaching, students' computing ability is cultivated in simplification and evaluation, equation solving and real number operation. Computational ability is particularly critical, and it is a foundation of number and algebra.
7. Reasoning ability. First of all, reasoning is the basic way of thinking in mathematics. Reasoning generally includes perceptual reasoning and deductive reasoning. The extension of perceptual reasoning includes two aspects, one is perceptual reasoning and the other is deductive reasoning. Deductive reasoning is based on known facts and certain rules, and then carries out logical reasoning, proof and calculation. In other words, from the perspective of thinking form, it is a process from general to special. In the proof of geometry, it is actually such a form of reasoning. Rational reasoning is a way of thinking that starts from the existing facts, comments on some experiences and intuition, and draws some possible conclusions through induction and analogy. Different from deductive reasoning, it is a kind of reasoning from special to general, so the conclusion drawn by reasonable reasoning is not necessarily correct, and it may usually be called conjecture and speculation, which is a possible conclusion. The geometric proof questions in junior high school mathematics are all about cultivating students' reasoning ability. Rational reasoning is very important in the whole development of mathematics. Many concepts and theorems in mathematics have undergone reasonable reasoning, such as the concepts of equations and functions, and the whole is treated as a sample in statistics.
8. The establishment of model ideas enables students to experience and understand the basic ways of the relationship between mathematics and the outside world. The process of establishing and solving models includes abstracting mathematical problems from real life or specific situations, establishing quantitative relations and changing laws of mathematical models such as equations, inequalities and functions with mathematical symbols, and then finding out the results and discussing the significance of the results. The idea of modeling practical problems, whether it is solving equations, inequalities, functions or right triangles, has a wide range of applications.
9. Applied consciousness is to emphasize the connection between mathematics and reality, the connection between mathematics and other disciplines, and how to use the mathematics learned to solve some problems in reality and other disciplines, including, of course, using mathematical knowledge to solve another mathematical problem. Equation application problems, function application problems, solving right triangle application problems and so on are all aimed at cultivating students' mathematical application ability. Standard theory; Students find and ask questions is the foundation of innovation, and independent thinking and learning to think are the core of innovation. Therefore, it is very important to encourage students to ask questions boldly, to constantly ask questions and find problems, and to give students enough time and space for independent thinking, communication and verification, so as to provide students with opportunities for innovation.
10. Innovation consciousness
Innovation consciousness may be more important. Mathematics is abstract and rigorous, but at the same time, mathematics is widely used, which should reflect innovation and creative application. In teaching, I let students learn first, find problems and solve them; Teachers lead behind, students exchange and compare with each other, and get different methods and ideas to solve problems, which cultivate students' changeable thinking and improve their innovative ability. With the help of teachers, students do math by themselves, collect materials through observation, imitation, experiment and guess, gain experience, make analogy, analysis and induction, and gradually form their own mathematical knowledge. At the same time, I also ask students to dare to question and doubt books and teachers in math class, not to be satisfied with ready-made answers or results, to be innovative and to explore solutions to math problems from different angles with divergent thinking. In practical teaching, I also ask students to listen carefully and think with their own heads when studying mathematics. Let students start with "mathematical observation" and let students understand mathematical knowledge through exploration. Students do it themselves and get first-hand information. Under the guidance of teachers, students observe, operate, discuss and sort out in a cooperative way, and finally draw similar results and conclusions, which is conducive to cultivating students' cooperative attitude and good interpersonal relationships.