According to the curriculum standards of the new curriculum reform and the requirements of senior high school mathematics teaching, in order to effectively implement quality education, reform teaching methods and means, change teaching materials into practical teaching materials, organically carry out school-based courses, cultivate students' comprehensive practical ability and innovative ability, cultivate students' exploration spirit and consciousness of using mathematics, take reading and thinking in textbooks as basic materials, promote the process of research-based learning of senior high school mathematics, and conduct research on this issue, aiming at deepening classroom teaching content, promoting independent research and learning, so as to explore senior high school mathematics.

Second, the specific objectives of the activity

1. Knowledge objective: By studying the number of elements in a set, explore the relationship between the number of elements in a finite set and compare the number of elements in several sets.

2. Ability goal: be able to explore problems in many aspects, angles and levels, use knowledge to solve problems, and cultivate students' divergent thinking and innovative thinking ability.

3. Emotional goal: to study this topic, to stimulate students' enthusiasm and interest in learning, to enjoy the fun of exploring success, and to cultivate scientific attitude and spirit.

Third, the implementation process and methods of activities

1. Show the contents of the activity and the issues to be considered (5 minutes)

(1), the school canteen bought two kinds of goods, the first is ballpoint pen, pen, eraser, notebook, instant noodles, soda * * *, and the second is ballpoint pen, pencil, sausage and instant noodles * * *. How many kinds of goods have you bought twice? Answer twice, one * * * input 10(6+4), right? How to answer? What are the methods? So what conclusion can be drawn (the relationship between the number of elements in the set)?

(2) The school held the track and field sports meeting first, with 8 participants from a certain class, and then kicked off the class 12 participants, with 3 participants in both sports meetings. How many students in this class took part in two sports meetings? How to answer? From this, the following conclusion (the relationship between the number of elements in the set) is solved? Another example is: there are 30 students in a class, among whom 15 likes basketball, 10 likes table tennis, and 8 students don't like either. How many people like basketball but don't like table tennis? How to answer?

(3) Can we draw a similar conclusion about the union and intersection of three or more sets? How to express it? For example, the school will hold a sports meeting and be established ... If there are 5 students participating in the 1 00m run, 6 students participating in the 200m run, 7 students participating in the 400m run, 2 students participating in the100m run, 3 students participating in the100m run and 5 students participating in the 200m run,/

(4) Design a method to compare the number of elements in set and set B=.

2. Division of activities and schedule (25 minutes)

The whole class learns the above four questions in large groups (* * * four large groups). The first study (1), the second study (2), the third study (3) and the fourth study (4). Each group is required to appoint a person in charge by the students themselves, and the students organize specific activities to make it clear that the students are the spokespersons of the exchange center for the next activity. Spare groups can help you think about the problems of other groups. Teachers went down to each group to inspect, understand the situation and give necessary guidance.

3. Activity exchange (15 minutes)

Please ask the spokesmen of each group center to answer the questions assigned to them, and other students in the class will supplement them. The teacher will guide the students to summarize and draw a conclusion:

① enumeration method

The problem (1) involves a small number of set elements and is special. Can use enumeration method to write, will soon solve this problem, can be summarized from special to general way of thinking:

② Graphic method

When the number of elements in the set is small and not specific, the Wayne diagram of the set is drawn according to the meaning of the question, thus solving practical problems such as problem (2) and reaching this conclusion.

③ Number-shape combination method

Using the relationship between set and schematic diagram, according to the unknown quantity, we can set an appropriate unknown quantity and establish an equation to solve it, such as the second problem in problem (2). If the number of people who like basketball but don't like table tennis is X, there are (15-x) people who like both and [10-( 15-x)] people who like table tennis but don't like basketball. According to the meaning of the question, there are: x+( 15-x). So there are 12 people who like basketball but don't like table tennis.

④ Induce the speculation.

By solving problem (3) and combining problems (1) and (2), we can draw a conclusion and guess.

⑤ Concept derivation method

By solving problem (4), most students can easily get A, so according to proper subset's concept, the number of elements in set B is less than that in set A.. This conclusion comes from the connotation of the concept.

⑥ "correspondence" method

After research and discussion, there is a conclusion among students that "the number of elements in set A is equal to the number of elements in set B". A few students use the concept of "correspondence": this conclusion is obvious. What a great idea!

Four. Activity evaluation

Making full use of reading and thinking, a high school mathematics textbook resource, and carrying out extensive second-class activities can stimulate students' interest in learning, develop their creative potential and help them improve their ability of inquiry and innovation. Through the research of this topic, there are at least the following successes: first, the classroom knowledge has been deepened, and the knowledge learned has been further consolidated and expanded; Secondly, cultivate students' inquiry ability and change their learning methods. Thirdly, students' awareness of using knowledge to solve problems is enhanced: with the background of solving problems, students' awareness of using knowledge is significantly enhanced and their ability to solve problems is significantly improved through division of labor, cooperation and appropriate guidance; Fourth, cultivate students' thinking quality. Through the study of question (4), we have come to different conclusions, but they are all reasonable. Students are controversial and have developed critical thinking.

Verb (abbreviation of verb) matters needing attention

1, the teacher should be fully prepared for the topic. ① Carefully study the materials; (2) access to relevant information or research results; ③ Make a careful activity plan. Never go to class without preparation or insufficient preparation.

2. Avoid the discipline of "activity research class", and let students do their own activities without artificial constraints.

3. Actively guide students to do a good job in "communication-cooperation" activities, fully listen to students' opinions, and let students sum up their own practice and research results to avoid being arranged by teachers and imposed on others.

4. Insist on guiding students to write activity summaries and experience summaries, sum up research methods and achievements, and avoid ignoring classes in class and not consolidating after class.

Reference: Teaching and Research Learning Fu Hailun, Teachers' College of Shandong Normal University

On Lai Feng's Teaching Design of Inquiry Learning

Teaching Curriculum Standards People's Education Press

Teaching is a standard experimental teaching and research book for senior high school published by People's Education Press.