Therefore, "discovering the law" should not only guide students to discover the law, but also guide them to discover the mathematical thinking method contained in it, and urge them to learn to analyze, study and solve problems, so as to enhance their independent inquiry ability in the process of discovering the law. In the teaching of "discovering laws", teachers should help students discover the inherent needs, methods and deep experiences in the process of exploring laws. In short, only by helping students learn to explore laws, accumulate experience in mathematical activities and understand mathematical thinking methods in the process of discovering laws can the educational value of discovering laws be fully demonstrated.
First, the necessity of infiltrating mathematical thinking methods in primary school mathematics teaching
1, the basic mathematical thinking method is of great significance to the development of students.
There are two clues in the primary school mathematics textbook system: one is mathematical knowledge, which is the bright line in the textbook, and the other is mathematical thinking method, which is the dark line contained in the textbook. Third-rate teachers teach textbooks, second-rate teachers teach knowledge and first-rate teachers teach methods. To be an excellent teacher, we should be good at in-depth research and excavation of teaching materials, and master the mathematical thinking methods contained in the teaching materials, so as to recreate the teaching materials.
Mi Shan Kunsan, a famous Japanese mathematics educator, pointed out: "Mathematics, as knowledge, may be forgotten less than two years after leaving school, but its spirit, thoughts, research methods and key points are deeply remembered in the mind, and it plays a role anytime and anywhere, benefiting students for life."
Mathematical thinking method is the soul and essence of mathematics. Mastering the scientific mathematical thinking method is of great significance to improve students' thinking quality, the follow-up study of mathematics, the study of other disciplines and even the lifelong development of students. It is the key to strengthen students' mathematical concepts and form good thinking quality to consciously infiltrate some basic mathematical thinking methods in primary school mathematics teaching. Not only can students understand the true meaning and value of mathematics, learn to think and solve problems with mathematics, but also can organically unify the learning of knowledge with the cultivation of ability and the development of intelligence.
2. Infiltrating the basic mathematical thinking method is the requirement of implementing the spirit of the new curriculum standard.
The revised mathematics curriculum standard takes "four basics": basic knowledge, basic skills, basic ideas and basic activity experience as the target system. The basic idea is one of the goals of mathematics learning, and its importance is self-evident. The new textbook presents some important mathematical thinking methods through the simplest examples in students' daily life, and solves these problems through intuitive means such as operation, experiment and guess. So as to deepen students' understanding of mathematical concepts, formulas, theorems and laws and improve students' mathematical ability and thinking quality. This is an important way to realize mathematics education from imparting knowledge to cultivating students' ability to analyze and solve problems, and it is also the real connotation of the new curriculum reform of primary mathematics. The idea of "realistic mathematics education" put forward by Friedenthal, a world-famous mathematician and mathematics educator, has been widely recognized by the international mathematics education community and accepted by the majority of mathematics teachers. This idea shows that a school's mathematics has a realistic nature, and mathematics comes from real life and then is applied to real life. Second, students should seek truth from facts when learning mathematics, that is, students gradually discover and draw mathematical conclusions through familiar real life. This means that the application and practicality of mathematics curriculum has become a basic trend of international mathematics curriculum reform.
For example, one of the basic characteristics of 1989 mathematics curriculum standard and American mathematics teachers association 2000 standard is to emphasize the application of mathematics; The Netherlands began the reform process of realistic mathematics education in the 1960s. By the early 1990s, almost all primary and middle school students in the Netherlands were already using mathematics textbooks based on realistic mathematics education ideas, focusing on cultivating students' mathematics application consciousness and practical ability. The mathematics curriculum in Japan has set up comprehensive subject learning, which also reflects the concern about the comprehensive application of mathematics knowledge. This series actually emphasizes a mathematical modeling idea.
The so-called mathematical model is the mathematical structure of a specific research object in the real world, which is expressed in mathematical language after some necessary simplification and assumptions for a certain purpose. The idea of mathematical modeling is a mathematical idea and method to find, put forward and understand the unsolved or unsolved problems in the real world from the mathematical point of view, and simplify them into a kind of solved or easy-to-solve problems through the transformation process, and comprehensively apply the learned mathematical knowledge and skills to solve them.
Various basic concepts in mathematics are based on their own realistic models. For example, natural number set is a model used to describe discrete quantities; Various geometric figures are also mathematical models abstracted from reality. Those basic mathematical models enable us to make inferences about practical problems related to them.
For example, in the review of the chapter on plane graphic area, I designed such a comprehensive learning topic: using the graphics I have learned independently to make a simple mosaic design for my room.
The key for students to solve problems smoothly is to clarify the knowledge relationship between various plane graphics. In teaching, the plane quadrature model S = AB can be established, and the quadrature formulas of square, parallelogram, triangle, trapezoid and circle can be derived from the right-angle quadrature formula, which communicates the internal relations of all plane graphics. At the same time, with the change of the relevant side length, it shows that these plane figures can be transformed into each other. Students have learned to model and have an epiphany.
On this basis, by exploring the mosaic of plane graphics, students can know that triangles, quadrangles or regular hexagons can mosaic planes, and then design their own room mosaic scheme. In this whole process, the basic process of "problem situation-modeling-classified solution-explanation and application" is emphasized, which guides students to actively participate, practice, think independently and explore cooperatively, realizes the change of learning style, changes the passive learning style of single memory, acceptance and imitation, and develops students' ability of collecting and processing information and communication and cooperation.
Of course, in mathematics education, strengthening the infiltration of mathematical thinking methods is not just a single thinking activity, it itself contains the influence of emotional literacy. This point is often ignored in traditional mathematics education. While emphasizing the process and methods of learning knowledge and skills, we should pay more attention to the positive emotional experience and correct values that accompany this process. The standard regards "emotion and attitude" as one of the four target areas, and compares it with knowledge and skills, mathematical thinking and problem solving, which fully reflects that the new round of mathematics curriculum standard reform attaches great importance to cultivating students' good emotion and attitude. It should include being able to actively participate in mathematics learning activities and being curious and curious about mathematics. Get successful experience in mathematics learning activities, exercise the will to overcome difficulties and build self-confidence. Understand the close relationship between mathematics and human life and its role in the development of human history, experience mathematical activities full of exploration and creation, feel the rigor of mathematics and the certainty of mathematical conclusions, and form a realistic attitude and the habit of independent thinking. On the other hand, guide students to learn cooperative learning, cultivate the spirit of exploration and creativity in the process of learning knowledge, and form a correct personality consciousness.
The connotation of modern mathematical thinking method is extremely rich, such as set thought, limit thought, optimization thought, statistical thought, conjecture and proof. These are all related to mathematics teaching in primary schools. Our primary school math teachers should be conscientious in teaching, consciously infiltrate and guide, pay attention to the infiltration of the history of mathematics, and pay attention to the summary of classroom teaching, so as to present the teaching content in a popular and life-oriented way that adapts to the age characteristics of primary school students, so that students can learn to ask, analyze and solve problems with mathematical thinking methods through practical activities, so that students' mathematical thinking ability can be effectively developed and the mathematical cultural literacy of the whole nation can be improved.