In the teaching of research-based learning in mathematics, a new relationship of equality, democracy and mutual learning can be established between teachers and students, creating a good learning atmosphere for students to explore, debate and learn from each other. Research-based learning of mathematics pays attention to problem solving, but pays more attention to students' inquiry learning process.
The materials used in research-based learning of mathematics are generally in the form of topics, and each topic discusses a special topic. The subject of mathematics inquiry learning is not only the synthesis and practical application of the mathematics knowledge that students have learned, but also has good training value for students to explore and solve problems. For senior high school students, a better topic should be the mathematical problems that students have experienced in their life practice, or the mathematical problems that are closely related to the local social and economic development. Therefore, when determining research topics, teachers should not only provide, but also encourage students to abstract mathematical problems through observation, investigation and thinking of social life, thus forming research topics. Let's talk about the choice of research topics in mathematics research-based learning from two aspects: the principles and sources of subject determination.
First, determine the principles of research topics
1. Adaptive principle
Students are the researchers and solvers of research topics and the protagonists of research-based learning. Therefore, the choice of research topics should be adapted to the existing knowledge level of students, and the difficulty of the topics should be in the hands of students. Questions that are too difficult or too easy are not suitable for students to learn. When choosing a topic, we should make full use of what we have learned, so that students can deepen their mastery and application of what they have learned and understand the process and basic methods of scientific research through in-depth research on a problem.
2. Question principle
When choosing a topic, it is not to provide a textbook that students have not learned for students to learn, understand and remember, but to present students with a mathematical problem that needs to be studied and explored. This kind of problem is often some background materials, and students can use what they have learned to solve it through mathematical modeling.
3. Open principle
Mathematics inquiry learning is the most open in time and space, which requires students to go out of the classroom and books, collect information through various channels such as media, network and investigation, choose reasonable research methods and draw their own conclusions. In addition, due to the differences in hobbies, life experience and learning ability, the understanding of the subject, the positioning of research objectives, the design of research process and methods, the use of means and the expression of research results can be different. Therefore, the topic selection should enable students to apply the existing mathematical knowledge and solve it from different angles and levels. At the same time, in the process of project solving, the arrangement of learning time, the determination of project starting point, the choice of research methods and the expression of results should be quite flexible, so as to provide enough space for learners and instructors to give full play to their individuality and talents, rather than emphasizing the uniqueness and standardization of conclusions.
4. Social Principles When determining the research topic, we should emphasize the connection between mathematics and social life. The main goal of the mathematics inquiry learning course is to cultivate students' ability and consciousness to find and solve problems by using the mathematics knowledge they have learned. Therefore, we should pay special attention to the mathematical problems closely related to social development and people's lives when selecting topics, so that students can learn the methods of finding problems, cultivate innovative consciousness and ability, and further understand the universality of mathematical application through research and study of research topics.
5. Practical principles
Practicality is a feature of inquiry learning. In the process of solving research topics, research-based learning of mathematics should enable students to get their own experience of participating in research and exploration and experience the whole process of scientific research through a series of practical activities such as social investigation, information collection and processing, conclusion expression and analysis and verification, so as to gradually form a positive attitude of being good at questioning, being willing to explore and trying to learn, and stimulate students' desire for exploration and innovation.
Second, the source of mathematical research topics
1. Study the textbook deeply and get the topic from it.
Mathematics textbooks are an important source of research topics, and the newly compiled high school mathematics textbooks (exercises) provide us with a large number of research-based learning topics. If we pay attention to the teaching materials, we can find many topics suitable for students to explore.
The characteristics of these topics are that students can use the mathematical knowledge they have learned in recent years to solve them quickly through exploration and cooperation, and teachers give them appropriate guidance, which has the characteristics of "short, flat and fast".
2. Combining life and social reality, the topic is widely used. Students should be encouraged to refine practical problems into mathematical research topics from real life and production, and be guided to "observe carefully and learn mathematics everywhere". Teachers can also choose and write some research topics closely related to society, production and daily life for students to choose and solve. These topics should have certain practical value and interest to attract students to conduct research and exploration. For example, the following topics:
(1) When you go to the bank to deposit money, the annual interest rate for five years is different from that for one year. Ask the students to investigate the interest rate of bank deposits, and then solve the following problems: A and B each go to the bank to deposit 65,438+0,000 yuan on the same day. A keeps it for five years, and B keeps it for one year. After receiving the principal and interest at the end of each year, they will be deposited together for one year, and the interest tax will be paid at 20% each time. Q: After five years, which income will be greater, and what is the difference between the total principal and interest?
(2) There are five machines working on a production line, and the distance between them is equal. We need to set up an inspection table on the production line, and the parts can not enter the next process until they pass the inspection. If the working efficiency of five machines is the same, where should the inspection table be placed to minimize the sum of the distances traveled by moving parts? What if it is n machines? What if the efficiency of these machines is different?
(3) Investigate the newspaper sales of newsstands (purchase price, selling price, how much each newspaper will lose if it can't be sold), count the sales situation for one month, make decisions for newsstand owners, and maximize the benefits.
(4) Investigate the insurance companies' endowment insurance types and dividend distribution methods. Some people will take out insurance at the age of 40, or deposit the insured amount in the bank year by year. Suppose this person's life expectancy is 75 years old, please compare these two investment methods to determine whether this person has a large income from insurance or bank deposits.
(5) It is called "golden number" and the aspect ratio of the rectangle is called "golden rectangle". This rectangle looks beautiful, so some people think that the length-width ratio of a newspaper layout is the golden section ratio. Please go to the school reading room to measure the aspect ratio of 10 newspapers and magazines, find out what their ratio is, and why do you use this number?
(6) At present, many people have installed solar water heaters. Please use your knowledge of mathematics, physics and geography to explain the tilt angle of the water heater in different seasons, so that the sun can shine directly on the water heater at noon, thus achieving the maximum thermal efficiency. According to your research, what suggestions can you make to water heater manufacturers?
3. Students ask their own questions to make sure that senior high school students have a certain degree of observation and imagination. Once their enthusiasm for studying problems is mobilized, their ability to observe things, ask questions and solve problems is often beyond the imagination of teachers. The following questions are put forward by students through observing life and summarizing and refining:
(1) When I go to the supermarket with my parents on holidays, I often have a long queue when I pay at the cashier. How to arrange the cash register reasonably to make customers queue for the shortest time?
Shops often put up discount signs to attract customers. What is a "discount" The Secret Behind? What is the purchase price and the original price? Investigate the purchase price and the original price, and calculate the actual profit after the discount?
(3) What is the distance between two buildings in a residential area, so that the ground floor of each house can get sunshine from 10 to 2 pm every day in winter?
(4) Rainwater is collected in different containers in rainy days, and the rainfall is calculated respectively, and compared with the forecast of meteorological station.
(5) When a football player shoots, he faces the opposing goalkeeper. What is the relationship between the shooting angle of the goalkeeper and the ball speed and moving speed in order to shoot the ball into the goal? Teachers need to analyze and guide students to ask questions from the aspects of feasibility and practical value to prevent unrealistic. However, we should give priority to encouragement and let students put forward ideas to solve problems that the current knowledge structure can't solve temporarily, and we can't easily deny them and dampen students' enthusiasm. Some topics can be appropriately added to make it more practical.
In the implementation of inquiry learning in mathematics, students can be assigned topics in class or after class, so that students can conduct inquiry learning after class, collect information and materials for research, study together by one or several people, and then communicate in class. Teachers are mainly listeners, but they can also express their views, opinions or questions. They should not pursue the perfection of the conclusion, but should pay attention to the students' participation process.