Confucius, an ancient educator and thinker, put forward that educating people should be "deep, shallow, beneficial and respectful", that is, he advocated "teaching students in accordance with their aptitude, which varies from person to person" Mathematics Curriculum Standard also points out that "different people have different development in mathematics", which requires that our mathematics teaching must pay attention to each individual with differences, adapt to the different development needs of each student, give full play to each student's wisdom potential, and let top students, middle students and students with learning difficulties "eat well" to promote the development of each student on the original basis. However, in the actual classroom teaching process, it is often a "one size fits all" phenomenon, which puts the same requirements on students and adopts the same means, which leads to students' weariness of learning, thus leading to polarization of teaching effect, and the unsatisfactory phenomenon of poor students "carsick" and top students "accompanying students". For students of different levels, I designed exercises suitable for all levels. In the preliminary exploration of layered practice, I will elaborate my method of layered practice in primary school mathematics design from the aspects of multi-level practice, open practice and exploratory practice.
First, practice design should be hierarchical.
In order to make every student develop, we can use the method of designing exercises in different levels to create different opportunities for students at different levels and let all students develop. In teaching, we can divide the whole class into three grades: A, B and C according to the students' specific conditions. Layer A is students with relatively low intelligence and non-intelligence factors, poor acceptance and difficult homework; Grade B is a student with high intelligence, but less self-motivation, not diligent in study and unstable academic performance. This kind of student has the greatest learning potential; C-level students have high intelligence factors, quick response, strong acceptance, fast problem solving and the ability to explore, analyze and solve problems independently. After students are stratified, homework can be designed according to the specific teaching content, so that students at all levels can study fully and effectively, so as to reward students for consciously, actively and actively making progress towards higher-level goals when reaching lower-level goals. How to divide the exercises into basic exercises, improving exercises and expanding exercises;
Basic exercises require every student to master. Improving exercises is comprehensive, emphasizing the connection of knowledge, and solving problems must be skillful, which requires more than 80% of students to master, and a few students can master it step by step with the help of others. Outward bound training is the highest level of training, which is more comprehensive and requires higher application ability and greater accuracy. Such exercises can encourage students to discuss freely, adopt cooperative learning methods and try to solve problems, which requires some students with higher education to master. For example, when learning to find the rules, we can design the following exercises: The first level is the basic exercise: What is the 48th number in 0. 1358 96 135896 ...? The second level is improvement exercise: What is the 48th number in 0.33 1358 96 135896 ...? The third level is the expansion exercise: 0. 1358 96 135896, what is the sum of the first 48 numbers ... By designing this hierarchical question, every student can be developed and improved, which not only follows individual differences, stimulates students' learning motivation, but also improves the teaching effect, thus achieving "student-centered, student-centered". Different students have made different progress in mathematics. This kind of cooperative learning makes students understand the importance of cooperation, and allows students to seek the cooperation of others to solve problems when they can't solve them themselves.
Second, practice design should be open.
In layered practice, designing topics with diversified problem-solving strategies can not only stimulate students' curiosity in learning, but also arouse their enthusiasm and initiative in learning, so that students can change from "let him learn" to "I want to learn". It plays a great role in improving students' innovative ability. After learning the comparison of decimal sizes, I can design such a topic: 0.7.
Through the openness of design questions, a problem can be solved in many ways, so that students can know that there is more than one way to solve the problem, let students give full play to their potential, let his thinking diverge, and thus broaden the thinking of solving problems.
Third, practice designing inquiry questions.
In mathematics exercises, well-designed exploratory questions can help students solve problems by comprehensively applying what they have learned, thus satisfying students' thirst for knowledge, stimulating students' exploration spirit and making them jump up and pick fruits. This higher-level practice can not only broaden students' thinking, but also help to improve classroom teaching efficiency. So as to cultivate students' good thinking quality. For example, after learning "addition and subtraction within 10,000", I designed a thinking question "1+2+3+4+5+ ... 99+ 100". At first, some students who have spare capacity were confused and helpless, but after careful study. Through this kind of exploration, students can feel the sense of accomplishment gained by solving a difficult problem, and the feelings after solving the problem are beyond words, and their hearts are full of joy.
Practice has proved that the implementation of hierarchical exercises in primary school mathematics design is conducive to improving the purpose, hierarchy and initiative of teaching and learning, overcoming the passivity and blindness of thousands of people, and truly embodying the new curriculum spirit of "people-oriented, teaching students in accordance with their aptitude". We also achieved the following advantages:
1 It is conducive to mobilizing everyone's learning enthusiasm and initiative and creating a good classroom teaching atmosphere.
2. Realize the basic idea that "different students get different development in mathematics, and everyone learns valuable mathematics".
3. It is conducive to cultivating students' independent thinking ability, so that students at all levels can reach the position of "jumping".
4. A successful incentive mechanism has been formed, which has stimulated students' inherent potential and ensured that every student has made progress.
5. Cultivate students' learning motivation, experience the happiness of learning success and stimulate their learning enthusiasm.
6. It improves the correct rate of students' exercises, and also plays a good role in reducing students' schoolwork burden.