First, the reasons for cultivating students' logical thinking ability in senior high school mathematics teaching
(A) logical thinking ability itself is very important.
Logical thinking ability is the ability to use scientific methods to make correct and in-depth thinking through complex processes such as observation, comparison, analysis, in-depth thinking and expansion, and finally get rational answers; It is necessary for us to observe the cognitive world correctly and form a correct world outlook and values; At the same time, it is also an indispensable ability to find out the essence through phenomena in many complex things. Without logical thinking ability, the cognition of things will stay at a superficial level, and it is difficult to guide and promote practice with correct thinking, which is unfavorable to the development of individuals, a company, a country and a nation. Therefore, as a high school student who is in the critical period of cultivating various abilities, paying attention to the cultivation of his logical thinking ability is the only way to implement quality education, and it is also the proper meaning to cultivate socialist successors with all-round development in morality, intelligence, physique, beauty and labor.
(B) the characteristics of high school mathematics.
As mentioned above, high school mathematics is a subject that focuses on abstract thinking, rational thinking and logical thinking, which is different from Chinese and English that focus on perceptual thinking. Although there are perceptual thinking factors in high school mathematics, such as guessing a proposition (whether correct or not), logical thinking should be the more core and essential way of thinking in mathematics. It is precisely because of this characteristic of mathematics that when learning high school mathematics, we should grasp the main contradiction of "logical thinking", suit the remedy to the case, consciously improve the ability of logical thinking, and lay a good foundation for learning high school mathematics well.
Second, the strategy of cultivating students' logical thinking ability in senior high school mathematics teaching
The cultivation of students' thinking ability is a long process, which cannot be achieved overnight. Generally, articles about logical thinking ability start with the way of logical thinking and the basic methods of reasoning. We discuss how to cultivate students' logical thinking ability in high school mathematics teaching. We might as well start from the whole teaching process and conduct investigation and exploration in stages and tasks. Usually we divide the teaching process into several stages: preview before class, classroom teaching and review after class.
Preview before class: learn to think and sort out the basic context.
If interest is the father of learning, then thinking is the mother of learning. To cultivate students' logical thinking ability, students should be urged to finish the preview before class seriously and actively. The basic task of pre-class preparation is to clarify the basic concepts and have a basic understanding of the mathematical problems involved in the textbook. However, the cultivation of high school students' logical thinking ability can't stop there. As the name implies, a key word of logical thinking ability itself is "thinking". Only when students examine books with questions and think about related propositions can they concentrate and get rid of the interference of rough reading, and then feel the charm of mathematical thinking in layer-by-layer reasoning and stimulate their interest in learning mathematics. Teachers urge students to finish the preview before class and let them think with relevant questions, which is actually an important step to cultivate students' independent exploration ability and reasoning ability. For example, when studying the chapter "Function", teachers can first arrange several questions to think about: what is a function, what indispensable elements are included in the definition of a function (judging whether it is a function is also a basic feature of a function), and what kinds of functions are there. Let students read books with these basic questions, seek answers, and mark the places they don't understand, so that they can listen to lectures in a targeted way. Pre-class preparation seems to have no direct connection with the cultivation of students' logical thinking in senior high school mathematics teaching, but it is not. Pre-class preparation is an important prerequisite for students' autonomous learning time and the smooth progress of the classroom, which can lay a good foundation for students to master knowledge and cultivate logical thinking ability.
(B) classroom teaching: dredge the logic of knowledge and deepen the understanding of the knowledge chain.
Senior high school math teachers should consciously cultivate students' logical thinking ability in class. One of the basic tasks of classroom teaching is to guide students to dredge knowledge and clarify the main context of knowledge, but this is only the most basic requirement of senior high school mathematics teaching. Teachers should also let students learn to think correctly and deeply understand the relationship between the core of knowledge points and knowledge, so as to establish an effective knowledge network. For example, when explaining the chapter "series", the summation formula of arithmetic and proportional series are two basic ideas to solve the series problem. Teachers should focus on letting students master the process of verification and summarize under what circumstances this way of thinking can be applied. In the study of high school mathematics, we must get rid of the traditional teaching method of rote learning. Some people will question that it is essential to memorize some concepts and formulas in order to solve high school math problems. We don't doubt that rote learning helps us to answer related math questions quickly, but it can't be the dependence of students' answers. Just as students will forget the summation formula when they meet arithmetic progression, if we grasp the context of the summation formula with logical thinking and deduce it again, the summation formula will come out. This is why many students who are good at logical thinking usually don't spend a lot of time memorizing formulas and concepts, but they can also get relatively high scores. In addition, teachers should guide students to answer questions from different angles and in different ways to deepen their understanding.
(c) After-class review: check for missing parts and broaden the logical horizon.
After-class review is an important stage to consolidate knowledge, check and fill gaps, and broaden logical horizons. At this stage, teachers can arrange appropriate exercises for students to consolidate their knowledge, and can also test students' understanding through exams. These forms seem to be just consolidating knowledge points, but they are actually another opportunity for logical thinking training. In addition, we often say that "learning mathematics and physics well is not afraid to travel all over the world". One of the inspirations of this sentence is that the study of high school mathematics is closely related to life practice. In fact, many mathematical problems can be found in real life, and many practical problems can be accurately answered by establishing mathematical models. Therefore, high school math teachers should encourage students to observe life and try to apply what they have learned, which is not only the requirement of applying what they have learned, but also the key link in the cultivation and practice of high school students' logical thinking ability. The learning of logical thinking ability should go through the process from learning to life, and then reflect on learning from life.
In a word, the cultivation of logical thinking ability in senior high school mathematics teaching is of far-reaching significance. Teachers should make good use of every teaching process to effectively improve students' logical thinking ability. At the same time, it advocates applying what you have learned and returning knowledge to life application itself, which is another leap to improve logical thinking ability.