The cultivation of students' mathematical thinking ability and logical ability is not a one-off event. We need to start teaching slowly and consciously guide and guide them. We should pay attention to certain methods and draw inferences from others. For example, for a problem, we should also pay attention to mathematical theory and mathematical analysis. Don't do it just for the sake of doing this problem. After reading the questions, don't rush to calculate the questions you ask. According to the known conditions, we should think about what information can be calculated through the known conditions and what information we don't know. After this process, maybe we can guess the original intention of the questioner, the knowledge points he wants to test and all the questions he will ask. This process is actually training our thinking ability, but it is not over. We can change the known conditions in the topic. Maybe the result of doing this problem will become the known condition we meet next time, but now the known condition in the topic will become the required answer for the next question. How should we change our thinking to get the answer easily? When we follow these steps to complete a topic, it is really finished. This is what we call drawing inferences from others. It seems that only one problem is done, but in fact, it is a kind of problem, which not only cultivates students' thinking, reduces their burden, but also cultivates students' fun in the process. But for students with relatively high ability, they can challenge the high difficulty, because some topics don't have only one solution, and there may be two or more solutions, and we usually use the most basic method. This requires students who are good at thinking to think in a different way, which will simplify the steps of doing the problem. If students can think and discover consciously and often, they will develop this kind of thinking over time, so that the efficiency and accuracy can be greatly improved during the examination, thus freeing up more time for other finale questions, which is why there will be students with full marks or even close to full marks in the senior high school entrance examination and even the college entrance examination, which requires teachers to start training from the upper grades of primary schools. Because junior high school courses are more difficult and are based on certain thinking ability, senior high school courses are more difficult and have heavier tasks, so there is no time and energy to cultivate students' mathematical thinking ability and logical ability.
Otawa, a math problem in primary school, is closely related to our lives. Don't blindly guess or imagine the situation when doing problems, but turn life problems into mathematical problems and use mathematical thinking to understand and imagine. For example, two students play games on the turntable together. A student turns 15 times and B student turns 20 times, but the probability that A student turns to the red zone is one in five, while the probability that B student turns to the red zone is one in ten. So who turns to the red zone more often? This simple math problem is closely related to our childhood. You can't just guess, but judge by your own mathematical thinking ability. We can calculate the number of times A and B turn into the red area by multiplication, which is our mathematical thinking ability. Now that we know the probability of turning into the red area from the topic, it is easy for us to know the probability of turning into other areas. @ is our logical ability. We can infer a lot of information from the known conditions and collect many conditions implied in the topic. It seems that the ability of logical thinking does not play a big role in this small topic, but this kind of training is very important. When we were in middle school, this kind of logical ability can help students find a lot of hidden information, which is very useful to help students solve those comprehensive problems, problems with too many known conditions and long descriptions, so that students will not be vague and unable to start.
Of course, reflection and evaluation after solving the problem is also a very important link. We should start with the problems that students often make mistakes and are prone to make mistakes in exams, find out the root causes of students' mistakes, start with the root causes, cultivate students' ability to find, analyze, solve and summarize problems, and guide students step by step, instead of talking about topics for the sake of topics, let students talk more about all the knowledge points they can think of. Finally, integrate all the students' thinking points, so that students can know which knowledge points they didn't think of and why other students thought of them but didn't. It is easy for students to find their own shortcomings in comparison and pay more attention to them in future study. This progress is also obvious.
In a word, it is very important to cultivate the mathematical thinking ability and logical ability of senior primary school students, and it is also a gradual process. The cultivation of this kind of thinking will make students more relaxed and happy in mathematics learning, and will not make mathematics seem so boring, which will ultimately benefit students for life.