First, activate the existing cognition and awaken the activity experience
Mathematics Curriculum Standard for Compulsory Education (20 1 1 Edition) points out: "We should attach importance to students' existing experience and let students experience the process of abstracting mathematical problems from the actual background, establishing mathematical models, seeking results and solving problems", "Effective mathematical activities must be based on students' cognitive development level and existing knowledge and experience", and analyze students' existing experience and innovation in mathematical activities. Psychological research shows that children's mathematics learning is a process of meaning construction based on their own experience and their own unique way of thinking. Learning that is really suitable for children should be a dynamic learning, a learning that can awaken the sleeping imagination and passion from the deep heart. Therefore, in classroom teaching, we should start from students' existing experience, help students accurately find the connection point between old and new knowledge, awaken students' activity experience, let students learn new knowledge vividly and effectively, accumulate activity experience and promote the effective transfer of knowledge. Grade four students have known simple decimals, can calculate the addition and subtraction of a decimal, and mastered the calculation method of integer addition and subtraction and the basic properties of decimals. These cognitions are the basis for further study of decimal addition and subtraction. Make full use of students' cognitive foundation in teaching, let them make bold attempts, explore independently, cooperate and communicate, and guide students to transfer their old knowledge of integer addition and subtraction to decimal addition and subtraction. When the teaching calculation is "2.26- 1. 18", (1) is adopted for discussion. How to arrange vertically? How to calculate? (2) Give it a try. Vertical calculation of test column; (3) say it. what do you think? How is integer addition and subtraction calculated vertically? (4) think about it. Rewrite 2.26m, 1. 18m to 2.26 226 cm.
How to calculate the unit? (5) Comparison: Compare-1.18-118 to find out the connection and difference. this
1.08 108
It can activate students' existing cognition, provide them with opportunities to engage in mathematical activities and exchanges, highlight the principle of aligning the same number and the process of abdication, successfully solve the problem of fractional subtraction, let students feel the calculation method of fractional subtraction in exploration, and change "I want to learn" into "I want to learn".
Second, experience the process of life and understand the direct experience.
Constructivism theory holds that students' mathematics learning is a process of active construction. Mathematics comes from life and serves life; Students' life experience is very rich, which is an important resource for mathematics learning. Teachers should be good at capturing mathematics in life, starting from students' familiar life experience, creating vivid and interesting life situations, guiding students to "effectively connect" life experience with mathematics experience, so that students can feel the connection between mathematics and life, experience the life process, actively construct knowledge, and then comprehend direct experience, thus surging passion and experiencing the happiness of learning success. In teaching, teachers start with life, design examples of supermarket shopping, and explain mathematical problems through the experience of using RMB. If Zhao Liang is a child who likes sports, he bought a pair of sports shoes 20. 18 yuan and a box of table tennis 9.6 yuan. How much should he pay? Mom, is 30 yuan in the bag enough to pay? How much should I get back? Students quickly solved these problems through their own experience in purchasing goods, namely
20. 18 yuan =20 yuan 1.8 points 9.6 yuan =9 yuan 6 points.
20 yuan 1 Corner 8 -9 yuan 6 Corner =29 yuan 7 Corner 8.
30 yuan -29 yuan 7 Angle 8 points =2 Angle 2 points.
This process is the process of transforming life experience into mathematical knowledge and experience of mathematical activities, and students realize direct experience in calculation. In this way, the students realize that decimal addition and subtraction are closely related to our daily life, and not learning decimal operation will affect our daily life, thus generating an urgent desire to learn decimal addition and subtraction.
Third, carry out inquiry activities to enrich indirect experience.
Mathematician Hua said: "Learning mathematics should not only get knowledge conclusions, but also go through the process of getting conclusions, because only through this exploration process can we clearly understand the accumulation and condensation process of mathematical thinking methods." Students' learning activities are not only based on watching, listening and speaking mathematics, but more importantly, it provides students with opportunities to explore and practice in person, so that students can do mathematics in indirect activities and accumulate rich experience.
Learning mathematics in connection with students' life experience does not mean that mathematics is limited to letting students borrow life experience to solve mathematical problems. If we neglect to upgrade life experience to mathematics experience, students will still hesitate in thinking despite their enthusiasm and enthusiasm for learning and lack of in-depth thinking about mathematics, which cannot reflect that mathematics teaching is the essence of mathematics teaching. Therefore, teachers must straighten out the relationship between life perception and mathematical thinking, promote students' mathematical thinking with life experience as a catalyst, guide students to upgrade direct life experience to indirect mathematical experience, and construct mathematics in mathematical thinking activities. For example, when buying sports shoes and table tennis in Zhao Liang, if students only stay in the experience of buying things in RMB, it is direct experience. In teaching, we should focus on guiding vertical calculation: (1) How to add and subtract two decimal places when calculating 20. 18+0.96? Ask the students to make it clear that the alignment of decimal points ensures the consistency of numbers, and only the consistency of numbers can ensure the addition and subtraction of numbers in the same counting unit. (2) How to add or subtract decimals from integers when calculating 30-29.78? Make students understand that according to the basic properties of decimals, integers can be written in the form of decimals, and zero is added at the end of decimals, and the size of decimals remains unchanged; After adding 30 to zero, the two decimal places are the same, which can be calculated more quickly and accurately. This provides students with opportunities to engage in mathematical activities and exchanges, helps them truly understand and master basic mathematical knowledge and skills in the process of independent exploration, enables students to experience exploration and strategies in activities, and gradually enriches students' indirect experience. Another example is 53.42-49.8, 53.4+58.6. Teachers boldly let students try and give students space and time for independent exploration and cooperation. Students exchange views on problems with each other, gradually understand the principle of "decimal point alignment" and simplification of results in the process of using mathematical language, experience the beauty of concise mathematics in activities, and experience the calculation method of decimal addition and subtraction in exploration. In this way, students personally experienced the whole process of decimal addition and subtraction in vertical calculation, and gained the experience and understanding of decimal addition and subtraction by hand; In mathematics activities, students actively explore and construct, enjoy the formation process of knowledge and enrich the experience of mathematics activities.
Fourth, strengthen inductive application and refine thinking experience.
The accumulation of students' experience in mathematical activities is a gradual process. In this gradual process, the latter is based on the former. Only when students participate in diversified mathematical activities, after repeated calls and processing, can they gradually internalize into more general experience, thus achieving rational understanding and more effectively promoting the solution of similar problems. The experience gained by students in activities is often vague and scattered at first, so it is not easy for students to feel it directly. Therefore, teachers need to help students make these vague and scattered experiences clear, organized and systematic in the learning process, and therefore stay in their minds. In teaching, we should analyze, summarize and deepen the application of students' experiences and representations, and form a unified understanding of abstract meaning. With the help of students' experience in writing decimal addition and subtraction, the initial understanding has risen to a new height through the communication between teachers and students. * * * Together with summarizing the general method of decimal addition and subtraction calculation, we can further understand the principle of decimal point alignment when columns are vertical, and urge students to think and improve their understanding of the process of decimal addition and subtraction, so that they can exercise and improve their thinking level in the activities of summing up mathematical knowledge.
Professor Zhu Dequan believes: "The emergence of application consciousness is a sign of the formation of knowledge and experience." To accumulate basic activity experience, we should pay attention to the application of students' basic activity experience, which means paying attention to the intervention of thinking. Activities without thinking can only be sketched as basic activity experiences without mathematical significance. Teachers should often let students use what they have learned to solve practical problems in modern production and life and other disciplines, so that students can further consolidate their knowledge in the process of applying mathematics, and on the other hand, they can deeply understand the position and role of mathematics in social life and appreciate its application value. After the students sum up the addition and subtraction of decimals, let the students practice: (1) Fill in: The Bird's Nest can accommodate about 9 1.2 million people, the Water Cube can accommodate about 1.68 million people, and the two places can accommodate about 1 10,000 people. Highlight the writing of decimal points, consolidate the calculation method of decimal addition and subtraction, and infiltrate the beauty of simplicity in mathematics. (2) Fast calculation. 8.88-2, 8.88-0.2, 8.88-0.02, 8.88-0.002, further emphasize the alignment of decimal points, and cultivate students' thinking ability through comparison. (3) correct the wrong question. Let students fully find out the reasons for the mistakes, make them more correct, and make the knowledge structure of experience more perfect. (4) Open questions. 20 12 London Olympic diving competition, women's 10 meter platform doubles final results are as follows:
Let students collect and process information and ask math questions. This is a process of thinking and learning. Because the questions raised by students are various, so are the methods to solve the column. In solving problems, students understand a variety of problem-solving ideas, feel the flexibility of problem-solving strategies, and improve their mathematical thinking ability. Through these exercises, students' experience rose from one level to another, which consolidated their activity experience and realized the reorganization of experience.
Fifth, guide reflection and evaluation, and develop compound experience.
Professor Friedenthal believes: "Reflection is an important mathematical activity, and it is the core and motivation of mathematical activities." Teachers should give students enough time and space to reflect, so that every student can think positively and really cultivate their mathematical ability. When students' experience in mathematics activities has accumulated to a certain extent, teachers should guide students to reflect deeply on the basis of review, so that on the one hand, they can play the positive role of empirical factors in mathematics learning, on the other hand, they can consciously avoid the negative role of empirical factors and make the accumulated experience in mathematics activities better used by students. In classroom teaching, teachers should pay attention to guiding students to evaluate and reflect after induction and reinforcement. Refine, summarize and popularize the experience of mathematical activities to make it empirical and popular. In this process, we should improve the learning method of mathematics, form the habit of reflecting on experience and develop compound experience. For example, after exploring decimal addition and subtraction, organize students to discuss and give timely evaluation and reinforcement, help students externalize the experience of decimal vertical addition and subtraction, and guide students to reflect when completing 8.88-2, 8.88-0.2, 8.88-0.02 and 8.88-0.002. What are the characteristics of these topics? So that students can accumulate the experience that the minuend is the same, the number of minuend is the same, but the position of decimal point is different and the difference is different; For another example, after students have calculated11.60-99.00 =12.6, let students reflect on how to check whether they have done it right and guide them to do it, which not only plays the main role of students, but also helps to cultivate their migration ability; When students make mistakes in calculation, they should be good at capturing the failed experience from students, adjusting teaching strategies, inspiring students to reflect, making students realize their mistakes and actively correct them, so that students can really learn the mathematics they need and make the knowledge structure of experience more perfect. At the end of the course, students can be guided to reflect: How did we get the calculation method of decimal addition and subtraction? On the basis of students' answers, the courseware is used to gradually show the activity process of students arranging decimal digits, and at the same time, the students are evaluated in time; The final reflection can be the content of knowledge and skills, as well as the content of thinking methods and activity experience.
In short, the acquisition of experience in mathematical activities is a process of accumulation and promotion. Teachers should fully activate students' original cognitive level, let students experience the life process to understand the experience, enrich the experience in inquiry activities, enhance the experience in reflective evaluation, develop the experience in inductive application, and effectively unify the acquisition of mathematical knowledge, mathematical skills and mathematical thinking methods in the process of experience accumulation in mathematical activities, so as to continuously improve students' mathematical literacy.