"Mathematics Wide Angle" is a new teaching content module added with the new curriculum reform in the new curriculum standard experimental textbook of People's Education Press. It is a bright spot in the textbook of People's Education Press and a new attempt. It systematically and gradually infiltrates students with mathematical thinking methods, trying to present important mathematical thinking methods through simple forms that students can understand and vivid and interesting examples.
Consciously infiltrating some basic mathematical thinking methods into students in the primary school mathematics teaching stage can deepen their understanding of mathematical concepts, formulas and laws, is an important means to improve students' mathematical ability and thinking quality, is an important way to realize the transformation of mathematics education from imparting knowledge to cultivating students' ability to analyze and solve problems, and is also the real connotation of the new curriculum reform of primary school mathematics. "Mathematics Curriculum Standards" clearly states: "Students can acquire important mathematical knowledge and basic mathematical thinking methods necessary to adapt to future social life and further development through learning." In order to effectively implement this overall goal, the textbook arrangement of People's Education Edition not only makes great efforts to infiltrate mathematical thinking into every knowledge block such as number and algebra, quantity and measurement, but also takes the newly added unit "Mathematical Wide Angle" as the presentation form to further concentrate on infiltrating mathematical thinking methods into students.
Second, the content system of "mathematical wide angle"
Mathematical modeling thought
"Mathematics Curriculum Standards" points out: "Important mathematical concepts and ideas should be gradually progressive and spiral." The textbook pays attention to this requirement in the arrangement of "wide angle of mathematics" content, and systematically and step by step penetrates mathematical thinking methods.
For example, when the mathematical thinking method of permutation and combination is infiltrated into the experimental textbook, students are first arranged to have a little contact with the permutation and combination knowledge in the first volume of the second grade textbook, so that students can find out the permutation and combination number of the simplest things through observation, guess and experiment. For example, two digital cards are used to form a two-digit arrangement, and three children shake hands in pairs. And continue to learn the arrangement and combination content in the first textbook of grade three. But the goal is to continue to let students find out the number of things arranged and combined through observation, speculation, experiments and other activities on the basis of students' existing knowledge and experience. For example, how many different combinations are installed under two roofs and three roofs. Compared with the textbook of the first volume of the second grade, the content of the textbook of the third grade is more systematic and comprehensive, and the arrangement and combination are introduced respectively.
Looking at the "wide angle of mathematics" in the whole 12 textbooks, from simple classification thought to more abstract operation thought, to game theory and more complex pigeon coop principle in the last book, all show that the thinking level is from low to high, from concrete to abstract, step by step, spiraling up, and these mathematical thinking methods gradually penetrate into students to conform to the laws of mathematical cognition.
There is a certain connection between their contents, and accurately grasping the connection point of each textbook is helpful to the interpretation of the textbook. For example, the logistics problem in book 7, the problem of finding defective products in book 10, and the pigeon hole principle in book 12 all need to consider the "at least" problem when solving problems, and all need to use reasoning ability and infiltration optimization thought to find the best strategy in various solutions. When learning "digital coding", I naturally grafted the knowledge point of "finding the law"; When solving the problem of planting trees in closed squares, we need to use the "overlapping problem" to interpret it; Both the problem of planting trees and the problem of keeping chickens and rabbits in the same cage attach great importance to the construction of mathematical models, and generally go through the learning process of "problem modeling-model building-explanation and application model" ...
In the first learning period, simple permutation and combination, simple reasoning, collective thinking, equivalent substitution and so on appeared in the wide angle of mathematics. Through observation, operation, experiment, speculation, reasoning and communication, students can initially feel the wonder and function of mathematical thinking methods, be trained in mathematical thinking, and gradually form an orderly and comprehensive thinking consciousness, and at the same time cultivate their interest and desire to explore mathematical problems, discover and appreciate the consciousness of mathematical beauty, so as to achieve.
In the second phase, mathematical thinking methods such as optimization thought, game theory, solving problems caused by tree planting, digital coding, hypothesis method and pigeon hole principle were infiltrated. On the one hand, students constantly understand the mathematical thinking method, feel the charm of mathematics, cultivate the ability of analysis and reasoning, and gradually form the interest and desire to explore mathematical problems. On the other hand, they strengthen the teaching of comprehensive application of knowledge to solve problems and diversified problem-solving strategies, so that students can gradually improve their mathematical thinking ability and problem-solving ability.
Judging from the grasp of teaching objectives, the wide-angle teaching of mathematics should first be oriented to let students feel the mathematical thinking method through mathematical activities, learn to use mathematical thinking methods to try to solve problems and experience the strategies and methods to solve problems.
Because the wide angle of mathematics is for all students to infiltrate mathematical thinking methods, the original intention is to let every student be trained in mathematical thinking, gradually form an interest and desire to explore mathematical problems, and discover and appreciate the beauty of mathematics. Therefore, in order to prevent the education of "talents" from treating wide-angle mathematics as an Olympic training course, it is necessary to create more practical activities in a planned way, so that all students can observe, study and try, and pay attention to the perception of thinking methods in the activities.