At present, there are some common phenomena in primary school mathematics classroom teaching:

(1) The contradiction between teaching and learning is more prominent. On the one hand, mathematics is very useful, on the other hand, it is not necessary to learn mathematics.

(2) Teachers ignore the ability differences between students and ask two students to be equal to ordinary students by leveling, which leads to students with good grades "not eating enough" and students with poor academic performance "not eating enough", which makes them tired of learning;

(3) Students' learning is passive, overburdened, their subjective consciousness and participation ability are not strong, and they lack innovative spirit and responsible attitude. Therefore, many students feel that mathematics is not easy to learn, and it is difficult for creative outstanding students to stand out.

Our teaching philosophy is "everyone learns valuable mathematics, everyone gets the necessary mathematics, and different people get different development in mathematics." At the same time, China's "New Curriculum Standard for Primary School Mathematics" points out: "Mathematics teaching should start from students' life experience and existing knowledge background, provide them with sufficient opportunities to engage in mathematics activities and exchanges, help them truly understand and master basic mathematics knowledge and skills, mathematics ideas and methods in the process of independent exploration, and gain rich experience in mathematics activities. "However, in the previous primary school mathematics teaching, teachers attached great importance to the design of new mathematics courses and paid insufficient attention to classroom exercises. However, students have generally mastered the basic knowledge of the new curriculum in the usual classroom, so it is impossible to predict whether they can use the basic knowledge flexibly to solve problems. It is particularly important to study exercises for this problem.

Second, the process design

In order to promote the scientific research in our school, our school participated in the sub-project of Baiyun District "Study on the Effectiveness of Hierarchical Guidance in Primary Mathematics Classroom Teaching". After the school project was started, we set up a project team according to the junior, middle and senior grades, carefully studied the overall project plan of the district school, and finally established the sub-project of "Primary School Mathematics Classroom Practice Research" after comprehensive classroom teaching analysis and repeated thinking. In order to carry out the research smoothly and effectively, a strict management system has been formulated and a specific division of labor has been carried out. Qi Xin, a member of the research group, worked together to actively collect information and seek theoretical basis. President Dong drafted the draft and made the project plan. After discussion by the members of the research group, the opening report was completed. In the past year, our group of teachers studied in various forms. Studied the outline of curriculum reform, the new curriculum standards of mathematics and related books and articles; Learn excellent lesson examples closely related to the current curriculum reform and improve your theoretical understanding. I watched the videos of "Average in Statistics" by Professor Wu Zhengxian, a special teacher, and learned advanced experience for my use. Make a plan, time, place and content. Let the members of the research group deeply understand the main contents and significance of the research project in the topic of "Research on the Effectiveness of the Design of Exercise Groups in Primary Mathematics Classroom", so as to further enhance the scientific research ability and establish scientific research confidence. Scientific research activities are carried out regularly in the group. In order to ensure the quality of topic discussion, we stipulate that every teaching and research activity should achieve "four essentials": first, prepare lessons collectively, second, attend classes for all, third, reflect on lectures, and fourth, attach importance to class evaluation. Every seminar adopts the way of preparing lessons from personal conception-exchange and discussion-reaching * * * knowledge-forming lesson plans. Fully tap resources, deeply study texts, creatively use teaching materials, and pay attention to the combination of learning content to make classroom teaching more effective. Through after-class reflection, this paper summarizes the gains and losses of a class in order to improve the classroom teaching design in the future. Strive for a good demonstration class, strive to improve the effectiveness of the classroom, and explore a classroom practice teaching model that adapts to the individual differences of students and promotes the development of students at different levels.

Third, research results.

Over the past year, through the theoretical study and practice of the group members, the understanding has been further improved through the research of the topic.

(1) theoretical achievements:

1, the design is based on the outline first, and the spirit of the outline is deeply understood. Secondly, study the textbook carefully, grasp the knowledge structure of the textbook, and tap the intellectual factors of the textbook. This is the premise of implementing quality education. We ask teachers who participate in classroom practice design to grasp the scale of the outline and study and design the practice content from the height of quality education. It is stipulated that the content of exercise design should be closely related to teaching requirements, with clear purpose and pertinence. Proper exercise can meet the needs of different students. The design of exercises should be graded, combined with difficulty, with a certain number of basic exercises and slightly changed exercises, as well as some comprehensive and thoughtful exercises, but not too complicated. Try to design exercises that are in line with quality education and have practical value, so that students can develop morally, intellectually and physically.

2. Classroom teaching is the main channel for students to acquire knowledge. The research of classroom practice design is to make students engage in classroom learning better and promote students to master new knowledge through different exercises. We need to dig open materials from students' real life and carefully design classroom exercises to make them rich, vivid, open, lively and interesting. Teachers should combine teaching design with life, and have rich thinking and flexible practice.

3. Practice is a mathematical activity, which should embody "doing" mathematics. The design of exercises should be conducive to the development of students. Don't train "machines" to do problems. The basic idea of the new curriculum standard points out: "Mathematics education should be oriented to all students, everyone should learn valuable mathematics, everyone should get the necessary mathematics, and different people should get different development in mathematics." Exercise design should meet the level of different students, reflecting that everyone learns valuable mathematics.

4. The change of teachers' teaching concept and educational behavior.

(1) Establish modern mathematics teaching concept.

(2) changed the traditional way of practice.

(3) Change the traditional view of students.

5. Improve teachers' teaching level and scientific research level.

(1) Starting from the problem of "effectiveness of practice" in teaching, we adopt the method of action research to find ways to improve the effectiveness of practice, practice, reflect and communicate constantly in teaching practice activities, and constantly improve teaching behavior. Improve teachers' teaching awareness and teaching level.

(2) Since the research of this topic was carried out, the research quality of the teachers in the research group has been improved to varying degrees, and their insight and thinking ability have been developed to a certain extent. Project members wrote reflections and papers.

2. Experimental results

Classroom teaching exercises are mainly studied from the following aspects:

(1) Life-oriented and interesting practice.

In order to activate the students in the classroom, so that they can successfully apply mathematics knowledge to their lives and turn life problems into mathematics problems, the premise is to carefully design classroom exercises. In order to dig open materials from students' real life, the design of exercises should be open, interesting and directly reflect students' daily life.

Teachers design vivid and flexible exercises according to the characteristics of students' novelty, curiosity and competitiveness. Teachers pay attention to practical results, and at the same time, scientifically arrange the levels and methods of exercises, which will enable students to gain successful experience and develop their interest in mathematics. When designing exercises, children's psychological characteristics should be taken into account, starting from new practice forms, new questions and new requirements, avoiding old, boring and monotonous practice patterns and keeping the practice forms novel, vivid and interesting. Let the students do exercises, design and correct the wrong questions; Let students be doctors and design judgment questions; Let students be judges, design operation experiment questions, and mobilize students' senses to participate in practice. We can also design vivid, interesting and intuitive math exercises according to students' age and psychological characteristics, combined with students' life experience, such as guessing riddles, telling stories, picking wise stars, playing games, intuitive demonstrations, simulated performances and various small competitions. This kind of entertaining, interesting and competitive practice can not only stimulate students' curiosity and cultivate their interest in doing problems, but also achieve satisfactory results, so that students can complete the practice in a relaxed and pleasant atmosphere and understand and know mathematics knowledge in vivid and concrete situations. Why not?

For example, in the second grade, the practice design of "knowing decimeter and centimeter" is in the form of diary. This morning, I got out of a 2-meter-long bed and went to the bathroom. After brushing my teeth with a 1 mm toothbrush, I washed my face in a hurry and had breakfast. The school is not far from my home, about 90 cm. On my way to school, I saw a 2 cm tall tree broken by the wind, so I quickly found a rope 1 cm long to tie the small tree. I ran to school and saw the teacher teaching in the classroom all the time. I quickly pulled out a pen with a length of 1mm and a notebook with a thickness of 4m from my schoolbag and took notes carefully. Let the students think independently with knowledge first, and the questions in the diary make them laugh their heads off. Then communicate the problems found and correct them.

2. Diversification of exercises

For example, we oppose excessive practice in calculation, but practice makes perfect, and the cultivation of calculation ability can not be separated from moderate practice, and any knowledge needs to be gradually accepted and internalized in the process of use. We can work hard on the diversity and interest of practice forms, improve the operability of practice and realize the integration of teaching and learning; Strive to diversify exercises, enhance the playfulness, challenge and interest of exercises, and make learning full of fun. Let diversified exercises attract students' active participation, change the previous "asking me to practice" into "I like to practice" now, and turn the practice process into a small competition that challenges students and themselves; Turning practice into skill exploration, I found that I summed it up and I succeeded; Turn exercise into a small game. I play, I am happy and I like it. In this way, by giving full play to students' academic autonomy and consolidating their computing skills, students' computing ability will be improved unconsciously.

The diversity of exercises can be designed from three aspects.

(1) Design exercises according to the learning process.

1. warm-up.

In order to shorten the distance between old and new knowledge and promote the transfer of knowledge, before learning new knowledge, preview exercises should be designed according to the necessary foundation of new knowledge and students' cognitive characteristics. In order to eliminate the interference of students in judging whether a number is divisible by 2 or 5 according to the characteristics of the unit, the following exercises were designed before learning. Which of the following numbers are divisible by 3 and which numbers are not divisible by 3? 13,36,16,93,42,29,24,39 shows students that numbers with 3,6,9 are not necessarily divisible by 3, and numbers without 3,6,9 are not necessarily divisible by 3, thus preparing students for establishing a new cognitive structure. Full preparation before learning will lead students into the best cognitive state, and then a little encouragement and induction will follow.

2. Form exercises.

In order to promote new knowledge and students' understanding of existing concepts in the structure, non-artificial and substantive connections are established. When learning new knowledge, we should design exercises to learn new knowledge according to the logical structure of knowledge and students' cognitive rules. For example, when learning the calculation of rectangular area, we should help students understand the area, area unit and rectangular area according to the logical structure of knowledge; According to students' cognitive laws, we use concrete perception, generalized representation and abstract laws.

The following exercise design can show how students' knowledge is formed in the operation and practice of meaningful learning materials.

(1) Specific perception (hands-on operation by students).

① Measure the area of a rectangle with a length of 3 cm and a width of 2 cm with a square of 1 cm 2.

(2) Use 12 (or 8) sheets of 1 cm2 paper to form a rectangle. What is its length, width and area?

(2) summarize the appearance.

① Answer: The length of the rectangle is exactly 5 1 cm2, and the width is exactly 3 1 cm2. What is the length, width and area of this rectangle?

(2) Now, the plane graphics require students to tell what the area of the picture below is? (Each square represents 1 cm2)

(3) The rules are abstract.

On the basis of the above, let the students say the areas of two rectangles by measuring. And tell the measurement method, thus abstractly summarizing the calculation formula of rectangular area.

3. Consolidate the exercises.

In order to consolidate new knowledge in time and effectively, we should design targeted individual exercises according to the key points, difficulties and keys of knowledge.

For example, when learning fractional multiplication, you can design the following questions for its difficulties.

(1) How many decimal places are there in the following formula?

4×0.3()6.5×0.03()43.3×4. 1()

(2) Click the decimal point in the product of the following formula.

12.6×2.3=2898 1.26×2.3=2898 1.26×0.23=2898

(3)l . 2 1×26 =()0. 12 1×2.6 =() 12. 1×2.6 =()

On the basis of local special exercises or independent imitation exercises, some variant exercises and comparative exercises are carried out according to the characteristics of new knowledge.

(B) Design exercises according to the learning content.

Different types of learning content have different requirements for exercise design. The practice of concept learning should pay attention to clarifying the connotation and extension of concepts and mastering the essential attributes of concepts; The practice of legal study should focus on the process of understanding the law and mastering the operation; The practice of application problems should focus on cultivating students' thinking methods and thinking quality. For example, on the one hand, application problems should help students master correct problem-solving methods and cultivate the correctness of students' thinking. For example, the toy factory under study plans to produce 1000 toys, which has been produced for four days and produces 2 10 toys every day. How many toys will be produced to complete the plan? " In this application problem, in addition to imitation exercises, we can also design such a topic: the bicycle factory has been assembling 600 bicycles for 9 days, with an average of 72 bicycles per day. How did the bicycle factory complete the assembly? Let students know that judging the assembly situation requires comparing the actual assembly output with the planned assembly output. Actual output-planned output = excess output, planned output-actual output = quantity to be produced. Make students master the correct thinking method of solving problems.

On the other hand, it is necessary to prevent the problem-solving methods from being stereotyped and stereotyped. For example, in order to correct students' tendency of "seeing more and adding more" and "seeing less and reducing less" when solving application problems. You can design this exercise: Xiaohua has 9 stamps, 3 more than Xiao Qiang. How many stamps are there in Xiao Qiang? Xiaohua has nine stamps, three fewer than Xiao Qiang. How many stamps are there in Xiao Qiang? So that students can understand the importance of examining questions and change their bad habit of mechanical imitation.

(c) Design exercises based on learning feedback.

The new teaching should design targeted exercises according to various problems that students may have in the learning process, so as to effectively control and improve learning efficiency.

Length comparison exercise

For seemingly similar content, students are easily confused when studying, such as adding and subtracting fractions and multiplying fractions; The application problems of finding a multiple and finding several multiples should be compared and practiced to cultivate the ability of discrimination.

2. Judgment exercises

Students can have a correct understanding of the mistakes caused by psychological factors in the cognitive process through the practice of identifying and correcting mistakes. For example, after learning the average question, design such multiple-choice questions: a worker 1 month and February produces 350 parts, March produces 2 10 parts and April produces 220 parts. How many parts are produced on average every month?

( 1)(350-2 10+220)÷3

(2)(350×2+2 10+220)÷4

(3)(350+2 10+220)÷4

From identifying and correcting mistakes, students can understand the key to average. Above, according to the learning process, learning content and learning feedback, we briefly describe some practices in the design of new teaching plans, which should be studied and considered as a whole in actual design to achieve the best results.

3. Grading practice

Hierarchical practice can guide and help students overcome thinking obstacles, promote the gradual and in-depth development of thinking at multiple levels, and constantly sublimate knowledge and ability. According to the complexity of knowledge structure and the difficulty of understanding, teachers can peel off the complex and hidden connotations contained in knowledge and laws layer by layer, carry out multi-level development, promote and stimulate them layer by layer, which not only reveals the essence and internal laws of the whole knowledge from the surface to the inside, but also cultivates students' extensive and profound thinking.

4. Interest in practice

Interest is a non-intellectual factor that has an important influence on intellectual activities. Interest in mathematics learning is an effective way to cultivate children's good learning quality, a prerequisite to realize effective mathematics learning activities, and a manifestation of educational humanistic spirit. As a conscious motivation, interest is an important condition for holding a creative attitude towards activities. Interest tends to pursue exploration, and good interest in learning is the conscious motivation of learning activities. Once students are interested in mathematics, they will actively practice it, which is very important for the cultivation of their ability.

Four. Problems and thinking

1, when designing classroom exercises, the difficulty is not well mastered, especially the difficulty of drawing high questions. Sometimes it is difficult to design, and sometimes students find it easy.

2. We should also strengthen the study of strong theory and guide practice with theory.

3. Pay attention to the effectiveness of practice, let students become the masters of practice, and change passivity into initiative.

4. People-oriented educational concept puts forward higher requirements for the design of teachers' exercises, but due to the constraints of exam-oriented education, it is difficult to break through the content and form of exercises, and they are always used to practicing according to the types of questions.