At present, there is a serious problem for the first-year junior middle school students to learn mathematics, that is, they are not good at reading math books and often memorize them. For example, when learning the concept of square root, students all know that "generally speaking, if the square of a number is equal to a, then this number is called the square root of a" "positive numbers have positive and negative square roots, and the two are opposite; The square root of zero is zero; Negative numbers have no square root. " But when making a judgment question, 4 is the square root of 16 (); The square root of 16 is 4 (). The first of these two judgments is always wrong, but the last one can be all right. Because they are familiar with "a positive number has two square roots", but they can't understand the concept of square root well, because they don't understand the concept of square root well, which makes freshmen's self-study ability and practical application ability not well cultivated. Therefore, attaching importance to the guidance of reading methods is very important to improve the learning ability of junior high school freshmen. In the teaching process, teachers should guide students to learn reading methods, so as to achieve eye-to-eye, mouth-to-mouth, and mind the opponent. To learn a new chapter, first read it roughly, that is, browse the branches of what you have learned in this chapter, then tick while reading, get a general understanding of the content of the textbook and its key points and difficulties, and mark the places you don't understand. Then read carefully, that is, according to the learning requirements of each chapter after the festival, read the content of the textbook carefully, understand the essence of mathematical concepts, formulas, laws and thinking methods and their causal relationship, grasp the key points and break through the difficulties. Thirdly, read as a researcher, that is, explore the context, structural relationship and arrangement intention of knowledge from a developmental perspective, and summarize the main points, so as to "understand" the book, form a knowledge network and improve the cognitive structure. When students master these three reading methods and form habits, they can essentially change their learning methods and improve their learning efficiency.

Second, guide students to listen

Freshmen in grade one often can't adapt to the increase of courses and classroom learning, so they can't see anything, lose their energy and reduce the efficiency of attending classes. Therefore, it is the key to improve learning efficiency to attach importance to listening teaching and let them learn to listen. In mathematics teaching, we should first cultivate students' concentration and ability to listen attentively, activate students' original cognitive structure, and coordinate students' information reception with teachers' information output, so as to obtain the best learning effect. Secondly, we should train students to listen, pay attention to the key points of learning emphasized by teachers in each class, pay attention to the methods and processes of introducing and deducing theorems, formulas and laws, pay attention to the tips and handling methods of key parts of examples, pay attention to the explanations of difficult problems and the final summary of a class, so that students can grasp the important and difficult points and attend classes along the process of knowledge development, which can not only improve the efficiency of listening, but also make students "listen".

Third, guide students to think.

Mathematics learning is a process in which learners form a new mathematical cognitive structure through "assimilation" or "adaptation" between old and new knowledge on the basis of the original mathematical cognitive structure. Because this kind of "assimilation" or "adaptation" work must be completed by each learner relatively independently in the end. Therefore, in the teaching process, teachers should guide students' thinking, and teachers should focus on the following points: ① Starting from the "nearest development zone" of students' thinking, heuristic teaching should be carried out to cultivate students' active thinking and make them think. (2) By creating problem situations to carry out inquiry teaching, students' thinking habits are finally cultivated, so that students can learn to think deeply; (3) To train students' abilities of observation, comparison, analysis, induction, reasoning and generalization by digging "problem chain", so that students can learn to be good at thinking; (4) Evaluate by reviewing the advantages and disadvantages of problem-solving strategies and methods, train students to analyze and make them learn to reflect. In addition, we should be good at exposing the thinking process in the teaching process, leaving some time and space for thinking, so that students can "think at the turning point of knowledge, at the difficult points of problems, at the solution of contradictions and at the exploration of truth", so that students can achieve a comprehensive understanding.

Fourth, guide students to write

Freshmen in senior high school often have problems such as disorganization and logical confusion in problem-solving writing. For example, students are prone to make the following mistakes when learning the operation sequence of mixed operation of multiplication, division and power: (–3) 2 =–32, (2× 3) 2 = 2× 32, (3 \ \ 4) 2 = 32 \ \ 4 and so on. In addition, when learning the mixed operation of rational numbers, there will be such a situation that 8-8× (3 \ \ 2) 2 = 0× 9 \ \ 4 =1,which is mainly because we don't pay much attention to guiding students' writing in teaching. In teaching, teachers should correct students' mistakes in time. For example: ① We should teach students to transform written language into mathematical symbol language, and pay attention to the preconditions of mathematical calculus in mathematical symbols; ② Students should learn to write and express while reasoning, and master common writing formats in repeated training; ③ Train students to analyze and draw according to known conditions, and correctly transform written language into intuitive graphics, so as to better combine numbers and shapes to solve problems. In this way, through multi-form and multi-level intensive training, students can form correct writing habits by analyzing writing and paying attention to rigor and logic.

Fifth, guide students to remember.

It is very beneficial for students to teach them how to overcome forgetting and memorize mathematical knowledge in a scientific way. Because junior high school freshmen are in the primary logical thinking stage, they have more mechanical memory components and less understanding memory components when memorizing knowledge, which can not meet the new requirements of junior high school students. Therefore, it is an inevitable requirement for junior high school mathematics teaching to attach importance to the guidance of students' memory methods. In teaching, we should first pay attention to the reform of teaching methods, abandon full-time irrigation and avoid students' "indigestion". Secondly, we should be good at teaching students corresponding methods in combination with mathematical practice. For example, understanding mnemonics, because what you understand can be accurately and firmly remembered, so you must "understand first and then remember". (2) Simplified mnemonics can be divided into two categories, one is to "condense" words, and the other is to express abstract memories with letter symbols. (3) Image memory method, which is vivid, intuitive and memorable, helps to remember by visualizing knowledge. (4) Contrast memory method, "only by comparison can we identify", put similar problems together, find out the differences and connections, distinguish similarities and differences, and enhance the memory effect. ⑤ Formula memorization method weaves mathematical knowledge into "jingles", which is vivid, interesting, impressive and not easy to forget. ⑥ Systematic memory method, which establishes a complete knowledge system, is convenient for mastering knowledge as a whole and can be used to help memory. In addition, students should also be clear about various memory methods.

In short, the guidance of junior high school freshmen's mathematics learning methods must be synchronized, coordinated and persistent with the teaching reform. Efforts should be made to combine changing ideas with teaching methods, in-class and out-of-class, learning methods and teaching methods, teachers' guidance with students' exploration, unified guidance with individual guidance, and establish a criss-crossing learning method guidance network to promote students to master the correct learning method. At the same time, it is necessary to integrate theory with practice, vary from person to person, teach students in accordance with their aptitude, and fully mobilize students' learning enthusiasm.