First, the way to cultivate mathematical ability in mathematics teaching
Mathematical thinking ability reflects the needs of mathematical understanding and construction, and also reflects the requirements of mathematics' own characteristics, which is the core of mathematical ability; In addition, the core of quality education is innovative education. What we call mathematical ability has many contents, but in its core content, it must be positioned to promote students' innovative ability.
(A) the cultivation of applied mathematics ability
Mathematics is a language and an indispensable way to know the world. The ability to use mathematics is one of the most basic qualities that future citizens should have. The mathematics syllabus of nine-year compulsory education clearly stipulates that "students should be trained to abstract practical problems into mathematical problems" and "form the consciousness of using mathematics".
1. Reproduce the process of knowledge formation and cultivate students' awareness of using mathematics. Mathematical concepts and laws are mostly abstracted from practical problems, so in the teaching of mathematical concepts and laws, we can't just teach these mathematical knowledge to students, but ignore the analysis and abstraction of their prototypes. Starting from actual cases or students' existing knowledge, we should gradually guide students to abstract and summarize the prototype, understand the abstract process of knowledge, and understand its use and scope of application, so that students can form an understanding of the ways that must be followed in learning and applying mathematics. This can not only deepen students' understanding and memory of knowledge, but also stimulate students' interest in learning mathematics and enhance their awareness of using mathematics.
2. Create conditions for students to use mathematics to solve practical problems. Mathematical thought is a rational understanding of the regularity of the formation of mathematical knowledge and methods, and a fundamental strategy to solve mathematical problems. Mathematical methods are the means and tools to solve problems. Mathematical thinking method is the essence of mathematics. Only by mastering the mathematical thinking method can we really master mathematics.
Therefore, mathematical thinking method should also be one of the basic qualities that students must possess. There are many basic mathematical knowledge and methods in the current teaching materials. In teaching, we should fully tap the mathematical thoughts and methods reflected by the basic knowledge of mathematics, design the teaching objectives of mathematical thoughts and methods, infiltrate, strengthen and summarize the teaching contents in time, arm students with mathematical thoughts and methods, and make them truly masters of mathematics.
(B) the cultivation of thinking ability
The quality of thinking is an important determinant of national quality. In order to promote the development of students' thinking ability, we must pay attention to students' thinking activities in the process of mathematics learning, study the development law of thinking activities, and study the related types, functions, structures, internal relations and their functions in mathematics teaching.
1. The teaching ideas that attach importance to the cultivation of mathematical thoughts include:
(1) conforms to the concept. The mathematical language is accurate and clear, which makes the mathematical operation possible.
② Drawing ideas. According to the mapping principle, we can get method of substitution, elementary transformation method and generating function method to solve the problem.
③ Turn to thoughts. The essence of transformation is to turn new problems into solved problems and complex problems into simple and easy-to-solve problems. It is a basic idea to deal with mathematical problems. Substitution, collocation, grouping and reduction to absurdity are all concrete applications of transforming ideas.
4 decompose ideas. It is characterized by breaking the whole into parts, and its essence is the dialectical thought of decomposition-combination and division-combination.
⑤ Parameter thought. Parameters are the bridge to communicate the conditions and conclusions of problems. Introduce new variables when solving problems, or treat a variable in a problem as a known number and solve problems according to known conditions. Method of substitution, ratio method, principal component method and undetermined coefficient method are all concrete applications of parameter thought.
⑥ inductive thinking. Starting from several simple, individual and special situations, the general laws and properties are summarized. That is, in a special to general way of thinking.
⑦ Analogical thinking. It is a form of reasoning that two things are known to have some similar properties, so they may be similar in other properties.
8 deductive thinking. Logical reasoning method from general to special.
Pet-name ruby model thought. Practical problems can be mathematized and solved by mathematical models. Mathematical thought plays the role of "soul" in the whole mathematical system. Only by reappearing the teaching of mathematical thought can we improve students' ability level, cultivate students' mathematical concepts and good quality, and then improve students' mathematical quality.
2. Attach importance to the teaching concept of "problem solving". As a teaching mode or process, problem solving is an effective way to cultivate students' mathematical quality. Professor Zhang Dianzhou of China Normal University pointed out, "Solving problems is against pure imitation. It is more based on problem scenarios, constructing mathematical models, providing mathematical imagination and practical operation, encouraging divergent thinking, inducing creativity, and embedding mathematics into living cognitive processes rather than dead knowledge accumulation. I think' problem solving' is a breakthrough that can affect the current mathematics education. It is not contradictory to the' enrollment rate', which is conducive to popularizing mathematics and improving the quality of mathematics in an all-round way. " Paying attention to "problem solving" is in a sense paying attention to the application value of mathematics. Now "being able to solve simple practical problems by using what we have learned" is listed as one of the purposes of mathematics teaching, which requires us to conform to social development and strengthen the teaching of mathematics application.
In teaching, we should pay special attention to cultivating students' good thinking quality, so that students' thinking has a clear purpose and direction and their own opinions; It not only has broad ideas, but also exposes the essence of the problem; Not only dare to innovate, but also analyze specific problems.
Second, pay attention to the individual differences of students' abilities and all students.
According to students' "individual differences", we can understand how students with different development levels understand and use knowledge, inject different information in time, and adjust students' learning psychology and cognitive development level. According to students' psychological differences, establish a good teacher-student relationship for all students. Help underachievers overcome psychological barriers, care for them, give them confidence to learn well, and improve their courage to overcome difficulties. At the same time, we should pay attention to catching the problems of underachievers in time, discovering their bright spots, designing some questions that underachievers can answer in a planned way, protecting their self-esteem, stimulating their thirst for knowledge and enthusiasm for learning, so as to achieve large-scale gains.
In short, strengthening quality education in mathematics teaching is to improve the quality of education and teaching in an all-round way and improve the overall quality of students. Only in this way can quality education be pushed to a new height, and our quality education will certainly achieve gratifying results.