First of all, highlight the fun of practice. Interest is the best teacher. Design scientific and interesting exercises, highlighting the hierarchy of exercises. Design different types and levels of exercises, from imitative basic exercises to suggestive variant exercises to independent thinking exercises. To apply what they have learned in mathematics to practice, teachers should not only be good at digging up mathematical materials in life, introducing mathematical knowledge into students' practice and mathematizing life problems, but also be good at applying what they have learned in classroom books to practice, so as to solve practical problems and promote students' deeper understanding of knowledge. As the saying goes, "Interest is the best teacher." It is a powerful driving force to promote students' learning, which requires teachers to create vivid and interesting scenes in design exercises to stimulate students' interest in learning. For example, when teaching calculation problems, students will lose interest and the effect will not be good if teachers use mechanical repeated exercises to consolidate new knowledge. Therefore, I often design activities such as "picking apples", "playing games" and "treating trees with woodpeckers", so that students can do problems in an atmosphere of "entertaining and entertaining", with strong interest in learning and good results. The problem is the core of mathematics. Question consciousness is a kind of exploration consciousness and the starting point of creation. If there is a problem, you can think and explore; Only exploration can bring innovation and development. Therefore, as a teacher, when designing after-class exercises, we should grasp the pulse of the topic and design the topic well. Let the monotonous exercises become interesting, and let the students' thinking and ability be fully cultivated.
For example, the teaching exercise "1000 sheets of paper are 9.2 cm thick. How many centimeters is each piece of paper? " The student's formula is: 9.2÷ 1000=0.0092 (cm) Teacher's question: Pointing at a piece of paper in the math book randomly, ask: Can you find out the thickness of this paper? This problem is further discussed with a casual question. Without such in-depth exploration of this topic, many students stay at the level of knowing how to do it, but they don't know how to solve such problems in real life. So a stone stirs up a thousand waves, and the problem arouses students' infinite interest. With the deepening of exploration, new problems are constantly emerging. First, there is not enough paper for math books; Second, it is difficult for a person to operate; Third, how to minimize the operation error. These new problems do exist in the process of students' exploration, which enlivens their thinking and stimulates their desire for exploration. What if there is not enough paper? Students think of stacking several math books to make 100 or 1000, knowing that only math books can reduce errors. How can one person operate so many books? So students naturally think of finishing this work with their classmates, and they can consciously achieve a clear division of labor and natural cooperation. How to reduce the error? The only way is to press the book tightly.
The problem is to arouse students' desire to explore, and the design of this problem has reached and surpassed this goal. In this problem, we should not only tell students to use what they have learned to solve practical problems, but also cultivate students' good sense of cooperation, cooperation ability and operation ability. In the whole process of exploration, I developed my thinking and exercised my ability.
Second, highlight the application of exercises. Educator Suhomlinski said: "Knowledge is used to make students feel that knowledge is a sublime force, which is an important source of interest." For example, the practical application of calculating the actual distance between two cities on the map according to the scale is conducive to developing students' ability to use knowledge. Students observe, collect and record "mathematical problems" and "mathematical examples" in life, and use mathematical concepts and attitudes to explain and express the quantitative relationship of things. They use their intelligence and wisdom to solve the collected problems with what they have learned, so they are no longer simply reciting and memorizing the ready-made knowledge in books, but actually "solving problems". By solving problems, students' ability to solve problems is improved, and in this process, they learn mathematical ideas and methods, and also improve their interest and confidence in learning mathematics. The design of classroom exercises should be positive. Mathematics originates from life and must also be rooted in life. Solving practical problems with what you have learned in real life is the meaning of learning mathematics. So I always adapt some realistic topics into meaningful exercises to enhance the motivation of learning. It can be seen that practice should be linked with real life, and a bridge should be built between "mathematics classroom" and "life mathematics", which not only makes students care about social life from an early age, but also reflects the reality of mathematics learning. Most of the exercises in textbooks come from life, and once these vivid contents are included in textbooks, they appear abstract and dull. If the teacher can creatively restore and recreate the exercises in the textbook and integrate the mathematics exercises into life, the original exercises can be used by me. For example, when teaching "interesting jigsaw puzzle", jigsaw puzzle is a childhood toy for students. The students have all played. Students find it interesting to combine toys with graphics. When playing, let the students go from two to three, then to four to six, and finally spell out beautiful patterns with seven. Students can taste the happiness of puzzles in their hands. How to extend the knowledge in class to outside class, so as to give full play to students' creativity? It is suggested that students cut out the paper graphics at the back of the book, put together a collage after class, paste the graphics you put together with a jigsaw puzzle on a piece of white paper, and award creative prizes in class. Judging from the works handed in by students, some are imitations of books, but more are different. This not only gives students the opportunity to show themselves, but also reflects the uniqueness of homework under the new curriculum.
Third, the design of exercises should be diversified. The design of classroom exercises should conform to the age characteristics of students and adopt flexible forms. The design of exercises should also be gradient and open, so that students can understand and master knowledge in the process of simple application, comprehensive application and innovation, and at the same time take care of the level of students at different levels in the class, so that they can all benefit, so that students really like going to school mathematics from the heart. Some wrong questions often appear in the after-class exercises of some new courses, with the aim of making students use their knowledge to analyze and consolidate the methods and concepts they have learned through analysis. Most teachers will ask students to "observe carefully, is there anything wrong, where is it wrong, why is it wrong, and how to correct it?" Students will not have high expectations when answering these questions. But for other types of questions, analysis questions generally only let students find out the mistakes and answer why they are wrong. Few teachers will consider the question of "how to correct it".
For example, when teaching triangles, the teacher should tick the line segments that can be spelled into triangles; Feedback those who can spell; Reflections on the topic 1, 2, 4 What can be spelled into a triangle? The third topic is when can't you spell a triangle? Feedback here is generally the end of the exploration of this problem. However, if the teacher changes the handling method of this analysis question and skillfully uses the wrong resources in the third question, not only can the students judge why they can't be surrounded by what they have learned, but they can also think from the opposite side, "If a 2 cm line segment is replaced by a few cm line segment, should it be replaced by a triangle?" "If you change the 6 cm line segment into a few cm long line segment?" This is to "mend after the sheep is dead" and let students know that they should "correct when they know their mistakes". Students can find problems according to what they have learned, and they should also be able to solve problems according to what they have learned. Moreover, there are many ways to solve problems, and the answer can be uncertain under the correct premise. Suddenly, in the process of students solving math learning problems, teachers will find that students will make many mistakes in a certain knowledge point because of their incomplete grasp of knowledge or mistakes in understanding. When designing exercises, teachers can start from the places where students are prone to make mistakes and often make mistakes, design some topics appropriately, and deliberately set "traps" to "lure" students astray. Then, organize students to discuss and analyze each other, find out the reasons for the mistakes and summarize the preventive measures. Let students learn in the process of constantly making mistakes and correcting them, so as to have "immunity" to mistakes. Therefore, this treatment can not only enable students to consolidate what they have learned, but also cultivate students' ability to use knowledge, and cultivate students' divergent thinking, so that students can understand that mistakes are also beautiful.
Fourth, highlight the practical level. Students exist as concrete living individuals. When designing problems, we must clearly affirm the individual particularity of students' cognitive activities and face up to their differences in existing knowledge and learning motivation, so the design problems must be hierarchical. The so-called hierarchy means that there are all kinds of small problems in the problem, some of which are shallow, medium and difficult to meet the needs of students at all levels. This has formed a series of problem chains. Shallow memory problems can be used for simple mechanical imitation, deep problems can be used for mastering and consolidating new knowledge, and high-level problems can be used to guide students' knowledge transfer and application. Topic arrangement can be from easy to difficult, forming a gradient. Although the starting point is low, the final requirement is higher, which conforms to the cognitive law of students, so that students with average grades can correctly answer most exercises, and students with excellent grades can also solve difficult exploratory exercises, so that all students can be improved to varying degrees. Teachers should design different types and levels of exercises, from basic imitation exercises to improved variant exercises, and then to expanded thinking exercises, so as to reduce the slope of exercises, and at the same time, encourage students with innovative ideas without sticking to books. Take care of students at different levels, so that students at different levels have the opportunity to experience success and keep their enthusiasm for learning. If necessary, some open questions should be designed in class exercises. It is beneficial to stimulate students' interest in learning and promote students to change passive learning into active learning. There are some problems in after-class exercises, which are usually called open questions because of uncertain conditions or unique solutions or conclusions. These open questions are conducive to stimulating students' interest in learning and prompting them to change passive learning into active learning. You can't be lazy by "forcing" students to use their brains. Mathematics open questions are not as monotonous as closed questions, but more interesting and challenging. Students have a sense of accomplishment and experience happiness in the process of solving problems. Mathematics open questions are more suitable for cultivating students' interest in learning mathematics; It is conducive to changing students' learning methods and prompting students to take the initiative to explore, exchange and cooperate with each other; It is conducive to cultivating students' good thinking quality and promoting students' profound, extensive and critical thinking; It is conducive to cultivating students' innovative spirit, innovative consciousness and innovative ability, and promoting the implementation of innovative education in mathematics open-ended teaching. Obviously, due to the opening of the topic, there will be various answers. This is exactly what we want to achieve-"the more the better". And some of those after-school exercises are not as obvious as open questions, but they can also be "the more the better" In the teaching process, if we can give students the initiative in learning from their perspective, provide them with opportunities to engage in mathematical activities and let them explore new knowledge independently, not only can we cultivate students' inquiry consciousness, but also develop students' various abilities.