First, the reasons for the learning difficulties of freshmen in senior high school
(A) the reasons for studying law
From the analysis of the results of the conversation with students, one of the reasons for the learning difficulties of senior one students is "the reason for learning the law". The junior high school teacher spoke in detail, summed up all types and practiced well. Students are used to what you say and what I listen to. They don't like to think independently and sum up the rules, so they lack learning independence. Mathematics learning in senior high school requires diligent thinking, good at summing up laws and mastering mathematical thinking methods, so as to draw inferences from others. If you continue to follow the method of junior high school, you will have difficulties in learning. Although the new textbook reduces the difficulty, it is still of no help to some students. Every time you do a problem, you will encounter difficulties, and even a problem will have many mistakes. Some freshmen also have subtle psychological changes, resulting in atresia. They don't like to raise their hands in class, and the discussion atmosphere in class is not warm enough. Some freshmen have the shortcomings of "only watching without thinking, only thinking without practice, only practicing without thinking, only thinking without understanding", lack of good mentality and are prone to impetuousness.
(B) Textbook reasons
Through the study of "new curriculum standard", we find that the second reason for freshmen's learning difficulties is "textbooks". The content of junior high school textbooks has been greatly adjusted, and the content of mathematics learning consists of three parts: basic content, expanded content and special research and practice. However, some junior high schools weaken and delete these contents that can be taught and not tested, so there is a gap in the knowledge connection between junior high school and senior high school. The content of junior high school textbooks is popular and concrete, and there are descriptive definitions for many concepts. The slope of the textbook is slow and intuitive, and the questions are few and simple, mostly constant, emphasizing the foundation and popularization of knowledge. However, the content of high school pays attention to logic and abstraction, the textbook is rigorous and standardized, the knowledge is difficult and there are many types of exercises, the problem-solving skills are flexible and changeable, the calculation is complicated and complicated, and there are many research variables and letters. Compared with junior high school mathematics, it is more difficult. Although the textbooks in junior high school and senior high school have reduced the difficulty, the reduction in junior high school is even greater. However, in senior high school, due to the restriction of the college entrance examination, teachers dare not reduce the difficulty, resulting in the reality that the actual difficulty of senior high school mathematics has not been reduced. Therefore, in a sense, the adjusted textbooks not only did not narrow the difficulty gap in the content of junior and senior high school textbooks, but increased the difficulty gap. In this way, it is inevitable that students will not adapt to mathematics learning in senior one.
(C) the reasons for teaching methods
Through interviews with students of different levels, we think that the third reason for freshmen's learning difficulties is "the reason of teaching methods". Junior high school mathematics has less content, simple questions and sufficient class hours, so the classroom capacity is small and the progress is slow, so there is enough time to repeatedly emphasize the important and difficult contents. Teachers have enough time to give examples and demonstrate the solutions of various exercises, and students have enough time to digest them. Since entering senior high school, the teaching materials are rich in connotation, with high teaching requirements, fast teaching progress and increasingly difficult topics. It is impossible to explain the key points and difficulties of knowledge repeatedly like junior high school, but high school teaching is often guided, explored, discovered and solved by students themselves, paying more attention to the process of knowledge generation, the infiltration of students' thinking methods and the cultivation of their thinking quality, which makes it difficult for students who have just entered high school to adapt to this teaching method. In teaching, high school teachers should not only carefully explain the concepts, formulas, theorems and laws in textbooks, but also pay attention to the cultivation of students' various abilities. In teaching, we should not only pay attention to the contents of books, but also supplement extracurricular knowledge. This is obviously unacceptable for freshmen who are used to "drawing gourds according to patterns" and lack the ability to "draw inferences from others". Junior high school teachers are more accustomed to teaching students by hand and paying close attention to the inspection and supervision of homework and exercises; And high school teachers have high expectations and requirements for students' initiative and consciousness in learning, which often makes some students with low consciousness lack pressure and relax their requirements.
Second, junior high school mathematics teaching convergence measures
(A) the convergence of learning methods
In view of the problems existing in freshmen's learning methods, we adopt the learning method of "two books and three studies". "Two copies" refers to notebooks and wrong books, and the specific methods are as follows:
1. Teach students to take class notes and reading notes. When listening to the class, you should pay attention, understand and listen to the key parts of the teacher. When listening, you should also pay attention to thinking and analyzing problems. Listening but not remembering, or just remembering and not listening, is bound to lose sight of one thing and lose sight of another, and the classroom efficiency is low. We should take notes appropriately and purposefully so as to understand the main spirit and intention of the teacher in class.
2. Guide students to learn to reflect, consciously collect some typical mistakes in a wrong topic set, and make appropriate comments. "Three Habits" refers to preview, practice and review. The specific methods are as follows:
1. Strengthen preview habits and arrange certain links in classroom teaching to check students' preview.
2. Instruct students to do some extra-curricular exercises after finishing the homework assigned by the teacher. When doing homework, we should not only do it neatly, but also be organized, which is an effective way to cultivate logical ability. Homework should be done independently, which can cultivate the ability of independent thinking and the sense of responsibility to solve problems correctly. When doing homework, we should advocate efficiency, and the homework that should be completed in 20 minutes should not be put off for an hour. The habit of procrastination in doing homework is easy to make people think carelessly and lose concentration, which is harmful to the cultivation of mathematical ability.
3. Emphasize summarizing and reviewing in time to enhance understanding. When summing up and reviewing, we should learn to sum up and sort out, and truly achieve "from thin to thick" and "from thick to thin". Try to write a knowledge block diagram, establish a knowledge structure, make a good summary and grasp the law, so as to clarify the concept and make it systematic, so as to better remember and master the application. At the same time, we should classify and summarize the thinking methods and problem-solving methods we have learned, and find out their respective personalities, differences and connections.
(B) the cohesion of teaching materials
As for the connection between junior high school and senior high school textbooks, I think we should correctly handle the relationship between them in teaching, make good use of the knowledge points of junior high school and make a good transition from shallow to deep knowledge of senior high school. Knowledge is interrelated. The content of high school mathematics is mostly developed on the basis of junior high school knowledge, but it is not a simple repetition, but an extension and promotion of junior high school mathematics knowledge.
1. At the beginning of the semester, we will spend a week cramming the relevant junior high school knowledge, thus connecting the junior high school knowledge with the teaching content of senior high school. We should put forward some requirements for some contents of junior high school to effectively improve students' quality. The main contents of the review are: (1) score, radical and its operation. (2) multiplication formula. (3) Factorization. (4) Functions and equations.
2. Adopting the guiding ideology of "low starting point, small steps" in the teaching process of senior one, helping students to review the past and learn new things, properly pave the way and reduce the slope.
(1) When explaining the solution of the unary quadratic inequality, you can first review the relevant contents of the quadratic function in detail, and then combine the quadratic function, quadratic inequality and quadratic equation to solve it. When the function takes a certain value, finding the value of the independent variable is to solve the equation; When the function value changes in a certain range, the range of finding the value of the independent variable is to solve the inequality. (2) When talking about the definition of function, we can start with the definition (connection point) of junior high school function, review the specific functions learned in junior high school, and then reveal the "correspondence" in the language of set, giving the function a new explanation. On this basis, we can redefine the function, so that the new definition is natural and easy to understand, so that students can deepen their understanding and cultivate the rigor of thinking. Junior high school gives the empirical definition described by "variables", while senior high school gives the theoretical definition from the height of "correspondence". But the latter did not abandon the former, but regarded the former as the object of comparison and further understanding. This difference leads to the fact that junior middle school only needs the range of function expressions and independent variables, while senior high school has a wider range of research: various forms of function expressions, definition fields, value fields, corresponding rules and abstract functions.
(3) When it comes to monotonicity of functions, we can first mention the statement in junior high school textbooks: images are on the rise, that is, the function value Y increases with the increase of X; The image shows a downward trend, that is, the function value y decreases with the increase of x, and then students are guided to express it in mathematical symbol language with the help of graphics, completing the transition from dynamic description to static description.
(C) the convergence of teaching methods
In order to make freshmen adapt to high school teaching as soon as possible and realize the goal of "smooth transition", we should adopt the teaching method of "low starting point, small gradient, multi-inspiration and hierarchical", focusing on students' basic mathematics teaching.
1. You can slow down the progress at the beginning of senior one, so that students can have a gradual adaptation process. Don't be eager to make progress or attend classes at the beginning for the sake of exams, otherwise it will only be counterproductive. Step by step, try to slow down the rhythm and slope, lay a solid foundation for senior high school mathematics, let students adapt to the rhythm of senior high school mathematics teaching as soon as possible, and create good conditions for later study. The language in the classroom is important, slow, dense and urgent; When it comes to the key points, difficulties or emphases in the textbook, the language should be slowed down and the tone should be appropriately aggravated; When it comes to doubts, the tone can be improved and the ending can be extended appropriately.
2. In the introduction of knowledge, we should carefully conceive, create novel and interesting problem situations with moderate difficulty, give full play to the role of intuitive representation, help students separate research objects from complex backgrounds, highlight the essential characteristics of knowledge, explain the ins and outs of knowledge, and reveal the process of putting forward new knowledge. For example, before talking about function knowledge, I gave students a task to record the temperature from 8 am to 8 pm, so some students made the data into a table, and some students described the data as a line chart. Through this practical activity, students have increased their perceptual knowledge of abstract concepts such as the representation of functions, the characteristics of function images and the monotonicity of functions, which laid the foundation for further rational thinking.
3. In the teaching process, we should carefully design, induce students to participate in the whole process of knowledge formation and development through observation, thinking and discussion, increase students' participation opportunities as much as possible, and let students observe, think and discuss as much as possible. In the implementation of knowledge, the "dead" textbook should be implemented first, and then the flexible textbook should be popularized. In the explanation of difficult knowledge, starting from the students' reality, the teaching materials are processed at necessary levels and knowledge is laid, and the main points of understanding and application of knowledge are summarized and illustrated with examples.