First, an overview of the basic ideas of mathematics
Mathematical thinking is the result of the relationship between spatial form and quantity in the real world reflected in people's consciousness through thinking activities. It is brewed in the process of the formation, development and application of mathematical knowledge.
The so-called basic ideas of mathematics mainly refer to the ideas that depend on in the process of mathematics production and development, and the thinking ability after mathematics learning. It is not a case, but must exist as a universal thought and is the main line of mathematics teaching. Mr. Shi Ningzhong, the former president of Northeast Normal University and the leader of the revision of compulsory education mathematics curriculum standards, pointed out that the basic idea of mathematics should meet two conditions: first, the idea that must be relied on in the process of mathematics production and development; Second, these thoughts should conform to the thinking characteristics of mathematics learners and be reflected in daily life.
The basic ideas of mathematics are embodied in abstraction, reasoning and model thinking. In primary school mathematics teaching, teachers should pay attention to the rational infiltration of some basic ideas, strengthen the improvement of primary school students' learning ability, thinking ability, problem-solving ability, exploration ability, induction and summary ability, association ability and practical ability, effectively cultivate students' innovative consciousness and increase students' interest in learning and exploration.
Second, infiltrate the basic ideas of mathematics in the teaching process and guide students to think constantly.
Primary school is in the primary stage of students' mathematics learning. Teachers should guide students to fully experience and understand the occurrence and development of mathematics, pay attention to the inspiration of students' mathematical thinking, and apply scientific teaching methods to promote students' understanding of basic mathematical ideas.
(A) the infiltration of the basic ideas of mathematical abstraction
Abstract, as the most basic thinking method in mathematical activities, is embodied in the formation of mathematical concepts and principles in primary school and the process of solving problems. The infiltration of the basic idea of mathematical abstraction is beneficial to effectively cultivate students' mathematical vision and consciousness, gradually deepen the level of abstraction, and improve their ability to analyze and solve problems.
For example, the understanding of natural numbers is generally understood by gradually abstract concepts, which is also a process of gradually understanding abstract thinking. From the perspective of directly abstracting real things, we can know relatively small natural numbers such as 1, 2, 3, 4, 5, but for relatively large natural numbers such as 5000000, 10000000, most of them are beyond the range of experience that primary school students can understand, so the understanding of this relatively large natural number needs some basis. Abstracting from the concept of a decimal, the characteristics of "order" are formed, so that students can understand a natural number and add 1 to get the next natural number larger than it 1.
(B) the infiltration of the basic ideas of mathematical reasoning
Human thinking forms are mainly divided into image thinking, dialectical thinking and logical thinking. Logical reasoning is the main embodiment of logical thinking and the foundation of the internal development of mathematics. The basic idea of mathematical reasoning is to form a deep understanding of the logical relationship between mathematical research objects through reasoning, promote the cultivation and improvement of reasoning ability, and then solve practical problems.
Reasoning is the thinking form and process from one or several propositions to another, which is mainly divided into two ways: induction and deduction. Deductive reasoning is the most commonly used reasoning method in mathematics, which is the process of deducing individual or special conclusions according to general conclusions or general premises; Inductive reasoning is a reasoning method that generalizes the general principle process from a series of concrete facts. In the process of primary school mathematics teaching, teachers can guide students to feel and comprehend reasoning thoughts, and at the same time, combine specific reasoning activities to promote the formation of mathematical thinking.
Take the simple mixed operation of 1 channel as an example: 4×2 1+59×4=? When calculating the result of this problem in a simple way, teachers can guide students to do decomposition: first, according to the multiplication exchange law, the problem is transformed into: 2 1×4+59×4, and then according to the multiplication distribution law, it is transformed into: (2 1+59).
×4, and then calculate the result step by step through the operation sequence. Deductive reasoning is manifested everywhere in the operation process of this problem. After such reasoning operation training, students are fully trained in the thoroughness and order of thinking, which promotes the germination and development of their mathematical ideals and ideas.
(C) the infiltration of the basic ideas of mathematical models
The idea of mathematical model mainly refers to the idea of using mathematical model to deal with and solve practical problems from a concrete prototype. It builds a bridge between the real world and mathematics, transforms problems into mathematical models, and then answers them. This basic mathematical idea of modeling was gradually developed with the continuous development and progress of computer technology in the second half of the 20th century. It is also a basic mathematical idea to solve practical problems in modern mathematics teaching.
There are two basic models of mathematics teaching in primary schools: "number of copies × number of copies = total" and "number of parts+number of parts = total". The first model includes unit price, total price, quantity, distance, time and speed in our life. For example, two buildings, one is 43 meters high and the other is twice as high as its 22 meters high. So, how many meters is the second building? The key to solve this problem is to guide students to apply equations to find the equal relationship between two buildings, and then put the known and unknown quantities in the same position before answering questions, which is conducive to the flexibility and smoothness of students' thinking process. The equation contained in this kind of problem and the general form of this kind of equation "AX B = C" are mathematical models that can effectively answer this kind of practical problems.
In a word, although primary school mathematics is relatively simple, it also contains many profound mathematical ideas. The new mathematics curriculum standard also takes "letting students get the basic ideas of mathematics" as one of its general goals, gradually guiding students to "understand" the ways and requirements of getting the basic ideas of mathematics, further promoting the process of primary school mathematics curriculum reform, and enriching and developing students' mathematics literacy. Primary school mathematics teachers should continue to study and think about mathematics theory, carry out teaching practice and exploration scientifically, and strive to achieve the goal of the new curriculum, thus having a far-reaching positive impact and great guiding role for students to acquire basic mathematics ideas.