First, understand and use the current situation of the textbook exercise function
Exercise is an important part of mathematics teaching in primary schools, an indispensable link in students' learning process, the main means for students to master knowledge, form skills and develop intelligence, an effective method to improve students' ability to solve simple practical problems with knowledge, and the main way for teachers to understand students' knowledge. High-quality classroom teaching must be based on high practical quality. Specifically, on the one hand, exercises help students to deepen their understanding of mathematical knowledge, form a good sense of numbers, a scientific way of thinking and a reasonable habit of thinking, understand some important mathematical relations, laws and ways of thinking, and cultivate their initial sense of application and innovative ability; On the other hand, it also helps students acquire the necessary skills, thus laying the foundation and providing support for subsequent study and problem solving. At the same time, appropriate exercises can also help students build up their confidence in learning, feel the rigor and certainty of mathematics, improve their ability of expression and communication in mathematical language, and then form correct mathematical concepts.
The exercises in the textbook are generally discussed by experts, carefully scrutinized and carefully selected after years of teaching practice, so they are scientific, typical, exemplary and functional. However, many teachers pay more attention to the reform and innovation of classroom teaching, but disdain to do detailed research on exercises in textbooks, so that the functions of exercises are weakened and some valuable factors hidden in exercises are not fully developed and utilized. When using textbooks to practice, there are mainly the following situations:
(A) routines, practice for the sake of practice
The new lesson is over, and it is time for students to consolidate new knowledge and use it to solve problems. Teachers usually look at the exercises in this class, estimate that students can probably do a few questions, and then arrange for students to do them. They can do several questions according to the amount of time left, and seldom think about the specific function of each question, which will greatly promote and improve the learning of this class.
(2) Pay attention to the correct rate and ignore the cause of the error.
Some teachers only pay attention to the correct rate when using exercises, but ignore the reasons why students make mistakes. It is a common phenomenon that students finish their problems in class. No matter which feedback method is adopted, teachers pay more attention to who is right and who is wrong, and there are few links to analyze the causes of errors and students' thinking process, let alone understand the intention of editing and designing this topic.
(3) Pay more attention to skills than practice.
Most teachers attach great importance to the training of students' skills and neglect the cultivation of students' practical ability. The exercises in the new textbook are more exploratory and operational. Some teachers often ignore the importance of inquiry and operation when dealing with exercises. Some exercises require students to investigate and practice outside school, and students and parents need to cooperate in their studies. This is a good opportunity to apply what you have learned, but the teacher passed it by, which greatly weakened the role of operation practice.
Second, to interpret the characteristics of textbook exercises design
(A clear level of practical design
Curriculum standards point out that the presentation of curriculum content should pay attention to hierarchy. When arranging "independent exercises", our textbooks are based on basic knowledge and set up three different levels of exercises, so that students can develop their abilities in consolidating their applications. First, imitate the basic questions of examples, whose role is to strengthen students' mastery of basic knowledge and the formation of basic abilities; Then through a series of comparative analysis questions and variant exercises, students' ability to distinguish knowledge is improved; Finally, students' thinking ability and application consciousness are improved through expanding exercises.
Take the information window 3 of Unit 1 "Pay attention to pollution-fractional addition and subtraction (II)" in grade five as an example. The content of this information window is to learn the addition and subtraction of different denominator fractions and the mixed operation of addition and subtraction. There are three levels of exercises for "independent exercises" in the textbook.
Level 1:
Among them, the 1 question is the basic exercise of the mixed operation of addition and subtraction of different denominator fractions, so that students can further understand the order of the mixed operation of different denominator fractions through practice and form certain calculation skills. Question 2: With the help of the relationship between the three sides and the perimeter of a triangle, practice the addition and subtraction of fractions with different denominators to consolidate the knowledge of the perimeter of the triangle.
The second level:
The fifth problem is the expansion of the mixed operation of fractional addition and subtraction, which extends the operation law of integer addition to fractions. In this problem, students should first complete the formula according to their own ideas, and then through calculation and verification, let students realize that the law of integer addition and subtraction is also applicable to fractional addition. The design focus of this exercise is to let students discover the rules in the process of consolidating the algorithm and cultivate the ability of observation and generalization.
The third level:
Among them, questions 7, 8 and 10 are all practical questions, which are rich in content and instructive. This level of practice aims to guide students to solve practical problems in life with what they have learned, thus enhancing their awareness of mathematics application.
Through the above three levels of practice, students gradually master knowledge and realize the synchronous development of knowledge and ability.
(b) Wide selection of materials
On the premise of fully considering students' cognitive level and activity experience, the material of "independent practice" includes not only students' real feelings, but also related contents from nature and social life, as well as fairy tales that students like to see and hear. Let teaching materials become students' little helpers to know the world.
1, rich and colorful realistic materials, make teaching materials a "small encyclopedia" for students to understand the objective world.
When presenting information, the independent practice of teaching materials not only pays attention to let students solve problems in real situations, but also pays attention to the fact that the selected materials can broaden students' horizons, let students know some natural and scientific knowledge while practicing mathematics, and let students know the objective world in the process of solving problems.
For example, the second question of Unit 2 in the fifth grade, "Shandong Holiday Tour-Percentage", allows students to understand some personal income tax knowledge in the process of solving problems.
In the first volume of grade five, Unit 2 "Packing Box-Cuboid and Cube" information window 4, question 7, from which students can learn about the Three Gorges spillway dam.
The second topic of Unit 5 "Small piggy bank-understanding of RMB" in the second volume of Senior One presents the torch relay process of the 27th Olympic Games, which stimulates students' interest in learning.
The design of the above topics, on the one hand, the editor carefully selected the mathematical materials that students are interested in as practice materials, so that students can broaden their horizons and know the world while consolidating their knowledge.
2. Fairy tales in line with students' psychological characteristics, to stimulate the emotion of loving mathematics.
The selection of mathematics textbooks should be close to students' reality. Because of the age characteristics of junior students, stories are an integral part of their lives and have special appeal to them. According to this psychological characteristic of students, some interesting stories are designed in practice, which are loved by students.
For example, the fifth question of Information Window 4 in Unit 5 "Stories in the Forest-Preliminary Understanding of Division" in the first volume of the second day of junior high school presents a story of a pig and a pig splitting peaches in the form of a comic book. In the process of reading pictures and telling stories, students not only practice division, but also improve their ability to process information and their awareness of observing things with mathematical eyes.
Another example: the second question of the independent exercise of Unit 2 "It's raining-knowing clocks and watches" in the second volume of the first grade presents the learning life of a primary school student in the form of comic books. In the process of telling stories, students can make use of the time provided by textbooks, which can not only consolidate their knowledge about time, but also let students talk about how they arrange their day, cultivate students' initial concept of time and educate students to develop good habits of regular work and rest.
Show exercises with math stories. The choice of the hero of the story fully considers the interests of primary school students, mostly cartoon characters or animals that children are very familiar with. The abstract mathematical knowledge is integrated into the fairy tales that students like to hear, so that the mathematical knowledge is easy to understand and interesting. Because the material of mathematical stories is relatively rich, the exercises presented in the stories are generally comprehensive, which is convenient for cultivating students' ability to solve problems by using knowledge comprehensively.
(C) the diversity of exercises.
According to the requirements of curriculum standards, "the presentation of learning content should adopt different expressions". The practice arrangement of our textbook "Independent Practice" fully considers the psychological characteristics of children. Starting from stimulating students' practice interest and improving practice efficiency, we should innovate boldly on the basis of inheritance, design colorful practice forms, and give full play to the role of practice in students' mathematics learning.
1. Inherit the effective exercise forms that students are interested in.
For the traditional and effective practice forms that students love, the teaching materials have been passed down. Such as filling in the blanks, calculating, judging, connecting lines, walking a maze, looking for rules and other forms of practice. Colorful practice forms reduce the boredom of students' simple skill training and improve the interest and efficiency of practice.
2. Innovating on the basis of inheritance.
In addition to inheriting the traditional practice forms, the textbook also designs some new practice forms, which are loved by students.
(1) Box
The textbook sets up a novel and unique practice form of "magic box", which aims to let students explore the hidden law in the topic through observation and analysis, and use this law to solve problems.
(2) Smart house
In order to carry out the concept of "let different students develop well in mathematics" put forward by the curriculum standard, the textbook has set up the column of "smart house" in their independent exercises. The exercises arranged in the "smart house" are difficult, but most children can explore the answers to the questions by intuitive operation and positive thinking. Practice has proved that students are very interested in "smart house". In the process of solving problems, students not only experienced the hardships of exploration, but also tasted the joy of success, and at the same time improved their logical thinking ability. It provides a rich exploration garden for students, a broad space for students who have spare capacity to study, and promotes the development of students' thinking.
Third, make good use of textbook exercises to improve students' thinking level in practice.
(A) make good use of examples
Examples in textbooks are a bridge for students to learn knowledge. The exploration of learning methods and the demonstration of problem-solving methods can play a role in infiltrating knowledge, inducing methods, mastering skills, cultivating abilities and developing thinking.
1. An example of "red dot"
The design of many examples in the textbook not only pays attention to the reasonable arrangement of contents according to the knowledge system, but also pays attention to guiding students through the mathematical process with the help of these contents, infiltrating the basic learning process of "realistic problems-mathematical problems-association, speculation, experiment-induction-expansion and application", so that students can master this problem-solving strategy imperceptibly while learning knowledge and improve their mathematical literacy. Therefore, the example of the red dot cannot be taken lightly. We should make good use of its value and play its role.
For example, when designing the circumference of a circle in the textbook (Unit 1 "Gestalt-Circle" information window 2 in the second volume of the fifth grade), first put forward a realistic question: "What is the circumference of the upper altar?" Then guide the students to turn this practical problem into a mathematical problem: "Finding its perimeter is finding the perimeter of a circle". To solve this problem, we should first make students clear about the meaning of the circle, and then guide students to guess what the circle is related to from a mathematical point of view. For different conjectures, students should be organized to find ways to verify them. In order to make the conclusion more scientific, students can measure circles of different sizes. When measuring the circumference of a circle, students can be encouraged to choose different ways, such as winding a round plate with metal wire and measuring the length of the metal wire. You can also draw a point on the circular cardboard, align it with the 0 scale of the ruler, and roll it on the ruler for one week to directly measure the circumference of the circle. After the students measure the circumference of these circles, the teacher can further ask such a question: "If there is a big circle, how can we measure its circumference?" ? For example, stay in the circular playground for a week. "In order to stimulate students' desire to explore more general methods. In the process of measuring just now, students found that the circumference of different sizes of circles is different, and the size of a circle is determined by its diameter (or radius). Therefore, there must be some relationship between the circumference and diameter (or radius) of a circle. However, if it is difficult for students to explore this relationship by themselves, they need the guidance of teachers to guide students to calculate the ratio of the circumference and diameter of different circles, and then observe and compare the calculation results, and guide students to draw the conclusion that the circumference of a circle is more than three times the diameter. On this basis, the teacher further pointed out that due to some errors in our measurement, the ratio of the circumference to the diameter of the calculated circle may not be exactly the same, but in fact this ratio is a fixed number, called pi, which is expressed by the Greek letter π. Then guide the students to get the circumference of a circle = π× diameter. Through this conjecture-experiment-verification process, the formula for calculating the circumference is obtained, which is actually a mathematical process and also a process of establishing a mathematical model. Finally, the formula for calculating the circumference of a circle is applied to solve the practical problems raised at first. Students go through the process of deducing the formula for calculating the circumference, which is actually a process of "realistic problem-mathematical problem-association, conjecture, experiment-induction and summary-expansion and application", and this process embodies an important basic process of solving problems. In this way, in this process, students not only get the calculation method of pi, but also get the problem-solving strategy and cultivate their problem-solving ability.
2. Examples of "green dots"
The green dot example has two functions: one is designed simply to consolidate the knowledge of the red dot, and the other is developed on the basis of the knowledge of the red dot.
The first type: the green dot example designed simply to consolidate the knowledge of red dots. The main purpose of this example is to consolidate the knowledge of red dots. Then when dealing with it, the teacher should fully let go, let the students finish it independently, experience the happiness of success, and achieve the effect of consolidating knowledge. For example, the red dot in information window 2 in Unit 4, Book 2, Senior One, "Green Action-Addition and subtraction of numbers within100 (i)" is a verbal method to solve the problem of adding one digit (carry) to two digits. In the process of solving, students have experienced the exploration process of posing, thinking and speaking, and learned the method of oral calculation. So how many cans have they picked up for the green dot problem? Teachers don't have to let students go through the exploration process of posing, thinking and speaking, but let students do it themselves, consolidate their knowledge and test the learning effect.
The second type: the green dot example based on the knowledge of red dots. The purpose of this example is not only to consolidate the knowledge of red dots, but also to expand and extend the knowledge of red dots. When dealing with this kind of green dot example, the teacher can neither exert himself like the red dot example, nor let go completely. For example, the first red dot in the information window 1 of Unit 4 "Strange Cloned Cattle-Decimal Addition and Subtraction" in the first volume of Grade Four is the addition and subtraction of decimals with the same learning digits, and the green dot is the addition and subtraction of decimals with the same learning digits. When dealing with the green dot example, you can refer to the steps to solve the red dot problem. Students can easily transfer the calculation of decimal addition to the calculation of decimal subtraction, and get twice the result with half the effort. Finally, teachers can guide students to review and reflect on the calculation methods of decimal addition and subtraction.
(2) Grasp the basic questions.
The basic questions are the basic exercises after the new class, and the questions are mostly the reappearance of the new class examples, with the intention of trying to imitate them. This kind of exercises has a single knowledge and strong pertinence, which can arouse students to re-understand the connotation and components of knowledge and assimilate new knowledge. It is a single and partial feedback exercise on related content at the end of new teaching, which is less difficult and easier to complete. In addition to the role of consolidation, it is more important to upgrade these problem-solving methods to mathematical ideas, laying a good foundation for solving comprehensive exercises in the future. It is not only helpful for students to further understand the basic concepts, laws, formulas and properties of mathematics, but also to master basic skills such as calculation, problem solving and measurement. But also conducive to students' follow-up knowledge learning and thinking ability training.
(3) Practice thinking skillfully (* questions)
An important goal of mathematics learning is to train students' thinking and promote the development of their thinking ability. The characteristics of primary school students' thinking development are: from concrete image thinking to image association, and then from image association, they gradually form abstract logical thinking ability for simple things. In order to speed up the transition from concrete thinking in images to abstract thinking and develop students' thinking ability at an early stage, it is a practical and effective method to train students with thinking problems in textbooks.