First, the combination of purpose and pertinence.
The teaching content serves the teaching objectives, and the design of the teaching objectives should closely focus on the provisions and requirements of the new curriculum standards and be implemented in the classroom teaching of each class, that is, the ultimate goal of practice is to achieve the teaching objectives. Therefore, we should design exercises according to the teaching objectives. That kind of blind, mechanical and repetitive practice is often useless. At the same time, in our practical design, purpose and pertinence are often combined, which should be both purposeful and targeted. All exercises should fully embody the principles of teaching students in accordance with their aptitude, teaching students in accordance with their aptitude and teaching at different levels, and design exercises in a targeted manner according to the teaching materials and students' reality, the requirements of teaching content and the psychological characteristics of students. First of all, we should grasp the difficulties in teaching and design special exercises; Secondly, we should design special exercises for the weak points in students' study. According to the weak links in homework, special exercises are designed to enable students to master the weak knowledge points well. For example, in the "average application problem", the emphasis is on "finding the total number and the total number of copies". You can design exercises to find the total number and the total number of copies, so that students can clarify their concepts in comparison and practice. For another example, after learning "prime factor", "decomposition prime factor" and "coprime number", students are easily confused with the previous "prime number", and special exercises can be designed to enable students to deepen the comparison between these two concepts and master knowledge accurately.
Second, the combination of hierarchy and integrity.
The quality of practical design is directly reflected in the level of practice. According to the students' learning process and the principle of step by step, the practice level is carefully designed. We often say that exercises should have a certain "depth", which is the embodiment of the hierarchical design of exercises. Therefore, our practice content should be from shallow to deep, from easy to difficult, closely linked and gradually improved. We should not only design a certain number of basic exercises, but also design some varied exercises to facilitate the exchange of old and new knowledge and expand students' thinking, and also design some comprehensive thinking exercises to help students strengthen practice and promote the transformation of knowledge into skills and intelligence. At the same time, it is necessary to design exercises at different levels according to the characteristics of students at different levels, so as to teach students in accordance with their aptitude, which is fully reflected in the practice of implementing the new curriculum standards, so that all students can participate in mathematics activities, so that different people can get different development and improvement in mathematics, so that every student can experience the happiness of learning success. As Wallace, an American psychologist, pointed out, significant individual differences between students and the quality of teachers' guidance will inevitably lead to significant differences in students' creative ability and creative personality in teaching.
The hierarchy of practice should be combined with the integrity of practice. Starting from the overall task of subject teaching, we should also pay attention to the integrity of exercises when designing exercises. The mathematical knowledge structure itself is logical and coherent. We should also carefully analyze the position and role of topics in the knowledge structure of this unit and this book, grasp their internal relations, the key and difficult points of knowledge points, design exercises in a targeted manner, and pay attention to the integrity and coherence of the knowledge system.
Third, the combination of interest and openness.
Educational psychology believes that interest is people's cognitive tendency towards something or hobby, and interest can guide, maintain and strengthen students' learning. Once students have a strong interest in what they have learned, they can actively, easily and persistently go deep into classroom practice, which will help students improve their knowledge and ability. Therefore, our practice design should stimulate students' interest in learning and reflect their interest in knowledge, so that students can complete their learning tasks in a pleasant environment. As Bruner said: "The best motivation for learning is that students have an innate interest in the materials they learn." For example, in "The Basic Nature of Fractions", in order to arouse students' interest in exercises, I designed this exercise: One day, Mother Monkey picked a big watermelon from Gua Tian. When he got home, he called two little monkeys and divided the watermelon into two parts. He is about to give it to two children. Suddenly, a little monkey quarreled: Mom, I want to eat two tablets. One piece is too little. Then another little monkey quarreled, and he also wanted to eat two pieces. This time, the mother monkey was embarrassed, because the two little monkeys were too young to be humble, and there was only one watermelon at home. Who can use the mathematical knowledge we have learned to help mother monkey solve this problem? Let the students be interested in this exercise.
Putting practice content into games and competitions can help them get rid of boredom, stimulate their enthusiasm for actively participating in practice, get twice the result with half the effort, experience the joy of success from it, and rekindle students' interest in pursuing success. Completely in line with the new curriculum concept: "create an educational environment that can guide students to actively participate" and stimulate students' enthusiasm for learning.
Exercises should be more ideological, operational, flexible and confusing, so as to make every student move, make students' thinking fly and make our classroom come alive, which is fully reflected in the openness of teaching, classroom and students' thinking in modern classroom teaching activities. The design of open questions is the key to open teaching.