Today, with the deepening of education reform, teaching students to learn to learn has become a slogan with the characteristics of the times. Suhomlinski said that "to learn to learn, you must first learn to read". "Mathematics Curriculum Standard" emphasizes to cultivate students' abilities, including mathematics reading ability, application ability and inquiry ability. In recent years, reading comprehension has become a new type of mathematics in senior high school entrance examination, which has a strong choice function. Therefore, in junior high school mathematics teaching, we should attach importance to reading teaching. This paper attempts to discuss the teaching of mathematics reading in junior high school.
First, the educational function of junior high school mathematics reading teaching
Mathematical reading refers to the learning and acquisition activities that focus on mathematical problems or related materials, take mathematical thinking as the foundation and link, and use mathematical methods and concepts to know, understand, learn knowledge and feel mathematical culture. Junior high school mathematics reading has the following educational functions:
1. Math reading helps to improve math language level and enhance math communication ability. Mathematical communication refers to the dynamic process of using mathematical language and methods to carry out various mathematical activities. Mathematical communication plays an extremely important role in learning and using mathematics. The carrier of mathematical communication is mathematical language, and cultivating students' mathematical language ability is the basis of improving their mathematical communication ability. Only through mathematics reading can we standardize our own mathematics language, exercise our understanding and expression ability of mathematics language and improve our mathematics language level, thus establishing a good mathematics language system and improving our mathematics communication ability.
2. Mathematics reading helps to give full play to the role of mathematics textbooks. Mathematics textbooks are carefully compiled by experts on the basis of fully considering students' physiological and psychological characteristics, educational and teaching principles, characteristics of mathematics subjects and other factors, and have high reading value. Bell, a famous American mathematics educator, believes that we should take textbooks as the source of students' learning materials, not just the source of teachers' own lecture materials, and we must pay attention to the reading of mathematics textbooks. Teachers must pay attention to guiding students to read the text carefully.
3. Math reading is helpful for individual learning, so that every student can develop. Modern education should enable every student to get all-round development. It is impossible to achieve this goal only by collective teaching. The effective method is to combine collective teaching with individual learning, and the key to effective individual learning is to teach reading.
In order to achieve the goal of mathematics education and make mathematics no longer difficult to learn, we must attach importance to mathematics reading teaching.
4. Mathematics reading is conducive to inheriting the humanistic spirit of mathematics. As a kind of culture, mathematics is not enough to inherit mathematical culture and even human civilization. It is not enough for a math teacher to teach only by relying on the knowledge in math textbooks, and it is not enough to inherit excellent math culture and experience the humanistic spirit of mathematics through reading. Ignoring mathematics reading will lead to the weakening of mathematics humanistic spirit and the imperfection of mathematics literacy.
5. Mathematics reading conforms to the modern educational thought of "lifelong education, lifelong learning". The future society requires people not only to have solid and generous basic knowledge, but also to have strong self-study ability to engage in lifelong learning, so as to adjust themselves to the changes of social development at any time. Mathematics teaching in junior high school attaches importance to mathematics reading, cultivates students' ability to acquire mathematics knowledge independently with reading ability as the core, and enables them to acquire lifelong learning skills, which is in line with modern educational thought.
Second, the particularity of junior high school mathematics reading teaching
Mathematics reading process, like general reading process, is a complete psychological activity process, including various psychological activity factors such as the perception and recognition of language symbols (words, mathematical symbols, terms, formulas, charts, etc.). ), assimilation and adaptation of new concepts, understanding and memory of reading materials, etc. At the same time, it is also an active cognitive process of constant hypothesis, proof, imagination and reasoning. However, due to the symbolic, logical, rigorous and abstract nature of mathematical language, mathematical reading is different from general reading.
1. Mathematics reading requires strong logical thinking ability. Because mathematical language is highly abstract, in the process of reading, students must identify and read the relevant mathematical terms and symbols in perceptual reading materials, understand each term and symbol, and correctly analyze the logical relationship between them according to mathematical principles, so as to finally achieve a real understanding of the materials and form a knowledge structure, which involves a lot of logical reasoning thinking.
2. Mathematics reading needs intensive reading. The mathematical language is accurate. Every mathematical concept, symbol and term has its precise meaning, and there are no ambiguous or ambiguous words. The wrong conclusion in mathematics is clear, and there is no specious but ambiguous conclusion. When students try to read and understand a mathematical material or a concept, theorem or its proof, they must understand the exact meaning of every mathematical term and symbol, and cannot ignore or omit any words they don't understand. Therefore, browsing, fast reading and other reading methods are not suitable for mathematics reading learning.
3. Mathematics reading needs careful reading. Mathematics reading requires careful reading and analysis of every sentence, every noun term and every chart to understand its content and meaning because of the logical rigor in the compilation of mathematics textbooks and the characteristics of mathematics "evidence in words". Generally speaking, newly emerging mathematical definitions and theorems cannot be read over and over again, but should be carefully read and analyzed until the meaning is understood. This often happens in math reading. We know every word, word and sentence in a mathematical material, but we can't understand its reasoning and mathematical meaning, let alone its mathematical thinking method. This contradiction between the formal expression of mathematical language and the content of mathematics determines that mathematics reading must be hard to think and think.
4. Mathematics reading is often a combination of reading and writing. On the one hand, mathematics reading needs to remember important concepts, principles and formulas, while writing can speed up and strengthen memory. When reading mathematics, the important content is often remembered by writing or taking notes. On the other hand, in order to simplify the compilation of teaching materials, the reasons for mathematical reasoning are often omitted, and the process of operational proof is often short. When reading, if the span from the previous step to the next step is large, it is necessary to use paper-and-pencil calculus reasoning to "bridge the road" in order to read smoothly; In addition, when reading mathematics, it is often required to summarize the problem-solving format, proof ideas and knowledge structure block diagram from the text, or cite some counterexamples and variants to deepen understanding, which often requires students to take notes.
5. Math reading needs flexible thinking. The language in mathematics textbooks can be said to be the fusion of ordinary written language, mathematical symbol language and graphic language. Mathematics reading focuses on understanding and comprehension, and one of the actions to realize the purpose of comprehension is to transform the content of reading communication into an acceptable language form. So mathematics reading often needs to change the reading content flexibly. For example, turn a problem expounded in an abstract way into a problem expressed in a concrete or less abstract way; Convert the relationship expressed in symbolic form or chart into oral form, and convert the relationship expressed in oral form into symbolic form or chart form; Convert some concepts expressed orally into intuitive graphic forms; Express a normal definition or theorem in your own clearer language.
Third, the main content of junior high school mathematics reading teaching
Reading teaching in junior high school mathematics teaching mainly includes the following aspects:
1. Read the directory title. The title of the catalogue is the outline of the textbook and the essence of each chapter. Reading the title of the table of contents is equivalent to understanding the frame structure of the full text. Read the content of the textbook to make the title of the catalogue concrete. Gradually develop the habit of "title association".
2. The concept of reading rules. The description of laws and concepts in mathematics textbooks is very rigorous. To correctly understand the words, words and sentences in the concept, and to correctly translate written language, graphic language and symbolic language; Pay attention to finding positive and negative examples or objects in combination with reality; Understanding the connotation and extension of concepts means being able to distinguish similar concepts and know their scope of application.
3. Read mathematical theorems. Pay attention to the conditions and conclusions of the distinction theorem; This paper discusses the ways and methods of theorem proving, and analyzes the correctness, advantages and disadvantages of the proving methods by comparing with the teaching materials. Pay attention to similarity theorem, analyze and compare, and master application; 4. Think about whether the theorem can be reversed, generalized and extended.
4. Read mathematical formulas. Understand the ins and outs of the formula and deduce the formula; Understand the characteristics of the formula; Pay attention to the application conditions of the formula, understand the internal relations of the formula, and understand the application, reverse use, combination, variation and skillful use of the formula.
5. Read math examples. Carefully examine the questions, analyze the key points in the process of solving problems, and work hard to solve problems; Compare the advantages and disadvantages of the solution with the textbook to make the expression of the problem-solving process concise and conform to the writing format; Pay attention to summing up the law of solving problems and strive to explore new ways to solve problems.
Fourth, the teaching principles of junior high school mathematics reading teaching
Reading teaching in junior high school mathematics teaching should follow the following teaching principles:
1. Subjectivity principle. Fundamentally recognize and respect students' subjectivity, let students actively participate in the whole process of mathematics reading activities, take their own reading activities as conscious objects, and constantly monitor and adjust them; Plan the reading process and obtain the necessary information and materials by yourself; Constantly cultivate the habit of self-monitoring and self-adjustment, and gradually learn to explore mathematics reading and learning.
2. The principle of difference. Differences in students' individual development area, learning style, knowledge base and thinking quality lead to differences in students' reading ability. This also determines that teachers must pay different attention to students at different levels. In the process of reading, students' independent reading provides enough time for teachers to patrol the classroom, so that teachers can turn unified learning into individual guidance, focusing on individual poor reading ability.
3. Internalization principle. The basic condition of internalization is the perceptual level of mathematical language, which includes not only the understanding of the concepts, laws, laws and formulas of mathematics itself, but also the control and adjustment of students' metacognition level. Therefore, students should constantly practice various specific monitoring strategies and skills in the reading process, and then gradually internalize them into self-monitoring ability, so as to flexibly use these strategies and skills for self-monitoring under new conditions.
4. The principle of feedback. Personal awareness and ability of self-feedback and self-evaluation are very important. Teachers should timely, accurately and appropriately evaluate students' self-monitoring, and guide students to gradually learn to feedback and evaluate learning methods, strategies and results. At the same time, under the guidance of teachers, students adjust and improve their own reading monitoring process, strategies and results, and constantly improve the level of abstract generalization of thinking, so as to continuously develop and improve their own mathematical cognitive structure.
5. Constructive principle. Reading process is a process of mathematical construction, which is a process of constructing mathematical structure and understanding formal movement by alternately perceiving parts and whole of mathematical materials. In the process of reading, students take the initiative to explore, make full use of the unique logic of mathematical knowledge and the structural characteristics of mathematical content, constantly guess and estimate from the above in appropriate places of the text, and then correct it by comparing with the known ones, so as to obtain new knowledge.
Five, the basic strategies of junior high school mathematics reading teaching
Every chapter and section of the mathematics textbook is equivalent to a logical exposition. Mathematics teachers should become consultants and coordinators of students' reading textbooks, and choose appropriate reading methods according to the characteristics of mathematics textbooks and students' cognitive development level. This requires teachers to give scientific and clear guidance.
1. Create problem situations to stimulate reading interest. Interest is the best teacher, the internal motivation of learning and the key to developing intelligence. With interest, students can have a strong thirst for knowledge and take the initiative to learn. In junior high school mathematics teaching, teachers can create problem situations and stimulate reading interest according to the characteristics of textbooks, students' age characteristics and personality characteristics, with textbooks as the carrier and language training as the main content. Before students read, teachers can create some problem situations with appropriate difficulty to induce and maintain students' interest in reading. The problems created should be incisive, specific, targeted, appropriately difficult and enlightening. Set suspense by presenting the phenomenon that conflicts with students' original knowledge; Or provide several contradictory schemes and solutions, so that students have cognitive conflicts, stimulate students' curiosity and thirst for knowledge, and stimulate students' interest in reading.
2. Strengthen method guidance and master reading methods. With the accumulation of reading experience, students' reading comprehension ability is constantly improving, and teachers should guide students to read mathematics in different ways: at the first level, teachers should first compile an outline, so that students can read textbooks and understand the main contents of textbooks under the guidance of the outline, so as to achieve the purpose of initially understanding concepts, theorems, formulas and laws through reading; At the second level, because the concepts, properties, laws, formulas, problem-solving methods and operation steps in mathematics textbooks are very rigorous and logical, teachers should analyze the textbooks properly, skillfully select the important and difficult points and thinking methods, and let students really understand the textbooks; At the third level, the focus is on design problems or questions raised by students, and exploration and application are carried out, so that students can really use knowledge to solve practical problems. He is good at understanding new knowledge from the height of general principles, grasping new materials from the perspective of knowledge system, thinking thoroughly, and truly understanding the strict logical relationship contained in textbooks, thus improving the understanding level and enhancing the flexibility of solving problems.
3. Optimize the reading process and improve reading skills. The process of mathematics reading is a positive thinking process, and teachers should arrange reading time reasonably according to different reading tasks and nature. Let students read, let them think while reading with questions, and let reading get twice the result with half the effort. Mathematics reading can't be browsed only by eyes, but must be fully coordinated with eyes, mouth, hands and brain. Students should be guided to ask questions in reading. The process of asking questions is a process in which students gradually understand questions, and it is also a process in which thinking ability is developed and self-learning ability is improved. Asking questions makes students observe more carefully, gradually improve their ability to find problems and make their natural thinking more thorough and profound. Students should be guided to make comparisons in reading. Comparison can make students give full play to their subjective initiative, make students contact with the old and the new, realize the positive transfer of the learning process, and achieve the purpose of drawing inferences from others. The commonly used comparison methods are seeking differences in similarities and seeking common ground in differences. Let students understand that a lot of old knowledge can help us solve new problems by seeking differences through similarities; By seeking common ground while reserving differences, students can realize that although mathematical problems are ever-changing, there are many problems with the same laws and a lot of knowledge with internal relations.
4. Expand reading content and cultivate reading habits. Mathematics textbook is the carrier of basic mathematics knowledge, and it is undoubtedly the main content of mathematics reading. By reading mathematics textbooks, we can not only learn knowledge, explore laws and exercise our thinking, but also perceive the beauty of mathematics through mathematical figures and laws. In addition, extracurricular mathematics popular science books, including mathematics history, mathematics learning methods, interesting mathematics and mathematics lectures, mathematics learning guides and mathematics and natural science journals for junior high school students, are also indispensable reading materials for broadening students' mathematical horizons and developing students' mathematical thinking. Expanding reading content and cultivating good reading habits can make students improve their reading ability quickly. On the basis of understanding, practicing and training can improve students' reading speed, thus saving learning time and improving learning efficiency.