(1) On the overall goal, the standard proposes that students should "experience the process of using mathematical symbols and graphics to describe the real world, establish the consciousness of numbers and symbols, and develop abstract thinking."
It can be seen that understanding the meaning of numbers and symbols is very important for students to establish the meaning of numbers and symbols in the process of mathematics learning and is the basis for entering mathematics learning. In the compulsory education stage, students should learn concepts such as integer, decimal, fraction, rational number and real number. These concepts are abstract in themselves, but through the study of mathematics, students can relate the concepts of these numbers with the practical meanings they represent, such as how big a million is, how many soybeans there are in a handful, and so on. In the curriculum standards, we should attach importance to the understanding of logarithmic meaning, cultivate students' sense of numbers and symbols, dilute the requirements of excessive "formalization" and memory, and let students exercise independently in the process of learning mathematics, which not only improves their own mathematical literacy, but also helps them understand and explain practical problems with their mathematical minds.
Mathematics is closely related to real life. As early as the early 1980s, UNESCO put forward that "solving mathematical problems should be the center of school mathematics education". Therefore, valuable mathematics is more reflected in students' observation and understanding of daily life phenomena with mathematical vision and thinking, to solve problems in life, and to acquire or improve their ability to adapt to life. In the past, teachers always attached great importance to the accuracy and proficiency of students' written calculations, and students lacked estimation consciousness and estimation methods. But in daily life, it is estimation that is more widely used than written calculation. We often need to estimate the time needed to go to school and work, and the time needed to complete a task (cooking, buying food, doing homework, etc.). ), the amount of paper needed to write an article, the size of the place needed to put the refrigerator, and the cost of a trip. Therefore, it is of great value to strengthen estimation, cultivate students' estimation consciousness and develop students' estimation ability. The new curriculum standard also repeatedly emphasizes the need to strengthen estimation and downplay written calculation. Observation refers to a psychological phenomenon in which people make a comprehensive and in-depth investigation of things or phenomena around them and study and determine their nature and relationship according to their true colors. Observation in mathematics teaching activities is to consciously perceive the quantity and shape characteristics of things, that is, to investigate the structural characteristics of mathematical relations, propositions and geometric figures expressed by symbols, letters, numbers or words.
In mathematics teaching, we must attach importance to the cultivation of students' observation ability for obvious reasons:
First of all, cultivating students' observation ability is the need to achieve the goal of mathematics teaching. The "Guidance Outline of Compulsory Education Full-time Junior High School Mathematics" points out that junior high school mathematics teaching must "enable students to master the basic knowledge and skills of quantitative relations and geometric figures, and have certain computing ability, data processing ability, preliminary spatial imagination and logical thinking ability." Psychology tells us that perception and perception are the primary forms of human cognition, while observation is the advanced state of perception, which is a purposeful, planned, step-by-step and organized lasting perceptual activity. Observation is also an active perceptual activity. It is not only a direct reflection process of things in people's consciousness, but also includes positive thinking activities. In fact, in the process of observation, the observer must analyze, compare, abstract and summarize at any time according to the observed phenomena or characteristics, otherwise it will be impossible to study and determine the nature and relationship of things or phenomena through observation. It can be seen that observation is the basis of understanding and the touch of thought. Without the cultivation of observation ability, students can't have complete mathematical ability and mathematical literacy, and the goal of mathematics teaching can't be realized directly.
Secondly, cultivating students' observation ability is the need to comprehensively improve students' mathematics quality. Quality education requires that subject teaching should aim at cultivating students' innovative spirit and practical ability, and innovative ability must be based on students' comprehensive quality. Junior high school mathematics is a course that takes the basic mathematical knowledge and skills necessary for modern citizens as the basic teaching content, and learns the simple knowledge of mathematical operation and graphic relationship and its preliminary application skills. Mathematics teaching should focus on cultivating and developing students' computing ability, data processing ability, logical thinking ability, spatial imagination ability and mathematical information expression and communication ability according to the characteristics of mathematics itself. Observation ability plays a direct or indirect role in promoting the cultivation of various abilities in mathematics learning. Whether it is the recognition of figures, the grasp of the relationship between data, the discovery of basic laws and the improvement of comprehensive analysis ability, it is inseparable from careful observation. At the same time, observation in mathematical activities does not mean intuitive inspection in a narrow sense. It requires both eyes and brains, and not all observed objects have intuitive images. Therefore, observation ability is undoubtedly an important part of students' comprehensive mathematics ability.
Thirdly, cultivating students' observation ability is the need to improve students' mathematics learning quality and classroom teaching efficiency. Undeniably, there are some disadvantages in junior high school mathematics teaching, such as low learning quality of students and low classroom teaching efficiency. There are many reasons, of course, but students' observation ability is lagging behind, and the lack of observation habits and basic ability is one of the important reasons. Imagine, a student who has no observation habit and ability, how to find the internal relationship between graphics and data? Only in this way, it is not surprising that students' mathematics learning quality is low and mathematics teaching efficiency is low. It can be seen that cultivating and improving students' observation ability is one of the important breakthrough points and breakthroughs in reforming mathematics classroom teaching. In all aspects of teaching, teachers should implement observation means, fully display this teaching concept and pay attention to the cultivation of students' observation ability.
So, how to cultivate students' observation ability in mathematics teaching? The author believes that we can focus on the following aspects:
First, stimulate a strong interest in observation.
Learning is caused by internal psychological factors. Internal motivation is more active, lasting and positive than external driving force, and interest is the concentrated expression of internal learning motivation. In order to stimulate students' strong interest in observation, teachers can adopt many methods:
Attract interest with beauty. Students have an almost natural yearning for beauty. Mathematics has its own charm, and the beauty of mathematics focuses on its simplicity, unity, symmetry and strangeness. The external formal beauty of mathematical graphics, the simple and unified internal beauty of mathematical abstraction, the symmetrical beauty of quantitative relationship and spatial form, and the principle of singular beauty of mathematical thought, making full use of the characteristics and unique beauty of mathematics and guiding students to discover and explore the beauty in mathematics through observation, can stimulate students' strong interest in observation and stimulate their strong thirst for knowledge.
Used to increase interest. Guide students to observe and solve practical mathematical problems, so that students can truly understand the important role of observation in solving mathematical problems and cultivate students' lasting interest in observation. For example, in the teaching of univariate quadratic equations and coefficients, the following observation materials are put forward: it is known that X 1 and X2 are the two roots of equation X2+(k+2) X- 1 = 0, and x13-11x/kl. For this problem, the teacher draws the following conclusions by inspiring students: X 1+X2 =-(k+2) ①, x 1x2 =- 12, x13-11x. Can X2 be expressed by the reciprocal of X 1? 3. Whether it can be expressed as the sum of two and the product of two by ② ③ two deformation equations. Simple and clear deformation is found in observation, and solutions to difficult problems are implemented.
Make it interesting. Successful experience can make students feel happy and excited and enhance their confidence in learning. In mathematics teaching, students observe figures, quantitative relations and logical processes. Teachers should encourage students to take the initiative to observe as much as possible in the teaching process to create opportunities and conditions for students to succeed. Combined with the content of the textbook, students are consciously introduced to the examples of discovering mathematical theorems and solving mathematical problems through observation, and some interesting exercises are designed, so that students can summarize mathematical concepts through their own observation and analysis, discover the proofs of formulas and theorems, master the problem-solving skills of those special problems, taste the joy of success, and mobilize the enthusiasm of students for active observation.
Second, cultivate correct observation methods.
At the level of mastering knowledge and experience, junior high school students lack the basic quality of observing things psychologically, the ability of observation and the characteristics of mathematics teaching. Therefore, only by attaching importance to the guidance and cultivation of students' observation methods can we ensure the correctness of observation.
First of all, we should guide students to grasp a reasonable order when observing, and cultivate students' observation habits from whole to part and from part to whole. If unreasonable observation methods are found, they should be pointed out and corrected in time through argumentation and analysis. For example, in the initial teaching of geometry, for the observation data, it is known that figures A, B, C, D, E and F are six points on a straight line, so how many line segments are there in the figure * *? Teacher A B C D E F can ask questions after guiding students to observe and drawing observation conclusions: 1. How many line segments are there with A as the endpoint? 2. How many line segments are there with B, C, D and E as endpoints? 3. What's the difference between your observation order and the correct observation order? In order to guide students to understand the rationality and importance of orderly observing things. Secondly, we should guide students to understand gradual observation and form the habit of repeated observation and careful observation. In order to really reveal the internal laws, we need to make extensive observation from different mathematical angles: we should not only observe the apparent and obvious characteristics of things, but also observe the internal and hidden characteristics; We should not only observe the known materials, but also observe the relationship between the unknown and the implied. For example, in the teaching of isosceles triangle, for the observation data: A is as shown in the figure, in △ABC, AB=AC, P is any point on BC, PE⊥AB is in E, D PF⊥AC is in F, and CD⊥AB is in D, verifying that CD=PE+PF. E F B C P teachers should inspire students to observe the judgment theorem of big triangle and congruent triangles from the perspective of the quantitative relationship between the sum of areas and areas, so as to get multiple solutions to one problem.
Thirdly, we should guide students to understand the common observation methods (such as classified observation, from general to special observation, from special to general observation, comparative observation, etc.). ) and master the general steps of observation: make clear the purpose and task of observation; Make a careful observation plan and make full preparations for relevant knowledge; Make observation records during the observation; After observation, the obtained materials are sorted, analyzed, summarized and summarized. After a certain period of training, students can observe independently and operate skillfully.
Third, cultivate good observation quality.
Observation is not a passive gaze, not a passive perception, but a kind of "perception of thinking", which is the basis of intellectual development. Therefore, when cultivating students' observation ability, we must attach great importance to the cultivation of good observation qualities such as purpose, comprehensiveness, accuracy and profundity.
1, the purpose of training observation
Junior high school students lack the comprehensive perception ability of observation materials, and always take a few things as the perceptual objects selectively. In the teaching process, teachers should accurately describe the language of the observed object, make clear the objectives when proposing the observation task, and closely focus on the determined observation purpose when analyzing. For example, when using the matching method to solve a quadratic equation, for the materials to be observed:
Solve the following quadratic equation: ① (x- 1) 2 = 2, 2x2-2x+ 1 = 2, 3x2-2x- 1 = 0. The following observation requirements can be put forward: 1, what are the characteristics of the left and right algebraic expressions of ①? 2. Can the left side of [ms office1] ② be converted into a completely flat mode? 3. Can the left side of the formula be transformed into a completely flat pattern? By asking questions, let students observe purposefully and hierarchically, and actively perceive the observed object to achieve the purpose of observation.
2. Cultivate the comprehensiveness of observation
The comprehensiveness of observation requires reflecting the whole picture, components and their interrelationships of things through observation; Reflect a certain attribute of things in complex graphics; Point out all kinds of possibilities that may occur when perceiving an object in a certain situation. In observation, students lack a comprehensive understanding of the internal relations between things, which leads to the perception of objects can not reflect all possible phenomena from time to time. In the teaching process, teachers should help students master the basic attributes of things, analyze the inherent regularity of the observed objects on the basis of preliminary observation, and encourage students to make in-depth observation according to certain procedures. At the same time, teachers should put forward their own views on the observation results in time, discuss with students, analyze the reasons for the omissions in students' observation, and make remedies to make the observation conclusions comprehensive and complete. 3. Cultivate the accuracy of observation
Observation can not only be satisfied with understanding the whole picture of things, but also accurately grasp the characteristics of things, so as to find their similarities and distinguish their nuances for different things. Teachers should make full use of list comparison, comparative observation and other teaching methods, and use modern teaching methods to inspire students to discover the characteristics of the observed object and reveal the essence of the observed object through intuitive and dynamic pictures and pictures.
4. The depth of cultivation observation
One of the purposes of observation is to improve students' thinking ability. Therefore, observation must always be closely combined with thinking training, especially to explore the hidden conditions of the observed object. Through the cultivation of observation ability, students' mathematical thinking consciousness is abstracted and summarized, the thinking object is formalized, the thinking process is logicalized, and the thinking results are gradually applied.
In a word, mathematics teaching must attach great importance to the cultivation of students' observation ability: to stimulate students' observation interest by various means; Through training, students can master the basic methods of observation, have good observation quality, and gradually develop the habit of active observation and good observation, so that mathematics teaching can better meet the needs of quality education.
Attach reference materials.
1. Zhejiang Provincial Education Commission: Instruction Outline of Mathematics Teaching for Full-time Junior High Schools in Compulsory Education, Zhejiang Education Press,19971.9 Second Edition).
2. Wang Zixing: "Research on Psychology of Mathematics Education in Middle Schools", Hunan Normal University Press, 65438+1May 9, 999, first edition)
3. Zhu Zhixian: Psychology of Thinking Development, Beijing Normal University Press, 1986.
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