I. teaching material analysis
1. The position and function of teaching materials
As far as the application value of knowledge is concerned, probability is a basic model reflecting the laws of nature. Probability has become a common word, which provides a basis for people to make decisions.
As far as the humanistic value of the content is concerned, the research probability involves the dialectical relationship between necessity and chance, which is a good carrier for cultivating students' application consciousness and thinking ability.
2. Key points: ① Understand the uncertainty and frequency stability of random events;
② Correctly understand the meaning of probability.
Difficulties: ① Understanding the relationship between frequency and probability;
② Correctly understand the meaning of probability.
Second, the analysis of learning situation
1. Psychological characteristics of students
Although high school students have certain abstract thinking ability, the definition of probability is too abstract.
It is difficult for students to understand.
2. Students' existing cognitive structure
(1) Junior high school learned the concepts of random events, impossible events and inevitable events.
(2) Students may have some vague understanding of probability in their daily life.
(3) Students have flexible thinking, strong hands-on ability and good experimental foundation.
3. Motivation and interest
Probability is closely related to life, and this knowledge can arouse students' interest.
Three. Teaching objectives:
According to the above teaching material analysis, considering the psychological characteristics of students' existing cognitive structure, I set the following teaching objectives:
1, knowledge and skills:
(1) Understand the concepts of inevitable events, random events and impossible events from the events in daily life.
(2) Through the coin toss experiment, correctly understand the concepts of frequency and probability, and the relationship between them.
(3) Use probability knowledge to correctly understand the practical problems in life.
2. Process and methods: Students further cultivate their awareness and ability of cooperation and communication through experiments, statistics and other activities in class.
3. Emotions, attitudes and values:
(1) Through experiments, students' observation ability, practical ability, summing-up ability, and communication and cooperation ability among students are cultivated.
(2) Through teaching, cultivate students' ability to combine practical problems with mathematical theory, and improve students' inquiry ability.
(3) Through the infiltration of mathematical history, strengthen dialectical thinking and cultivate students' diligent and rigorous scientific spirit.
Fourth, teaching strategies.
In order to highlight the key points and break through the difficulties, so as to achieve the teaching objectives. In the teaching process, the following operations are planned:
1. Teaching methods
(1) Carefully design the teaching structure so that students can experience the inquiry process of questioning, solving and applying.
(2) Create situational cases to attract students' attention and stimulate their interest.
(3) Reasonably design mathematical experiments, cultivate students' spirit of "doing" mathematics through hands-on operation, and enjoy the joy of success brought by "doing" mathematics.
(4) Make full use of software-assisted teaching to facilitate classroom operation and knowledge organization, make teaching more vivid, and ensure that students' attention is always focused on the classroom.
2. Teaching methods
This course carries out the teaching idea of "teacher-oriented, student-centered and thinking-centered", adopts the heuristic teaching method guided by constructivism theory, pays attention to students' experiments and explorations, and combines students' group discussion and induction.
5. Teaching tools: computers, coins, and student birthday questionnaires.
Six, seven links of teaching procedure and design
1. situational introduction: lead out the theme of this chapter and let students experience the necessity and importance of learning probability.
Introduce the topic with "Is the class the same as Amanome?"
There are two reasons for designing this introduction: (1) Students attach great importance to birthdays and are very interested in this issue; (2) Students generally have a wrong understanding that "there are people with the same birthday in the class" is a small probability event.
When I realized that "the probability that two out of 50 people are in the same Amanome can be as high as 96.5%, and basically all classes will have the same person from Amanome", there was a big gap with my original understanding, and I fully felt the magic of probability;
Reasonable table design in advance, field investigation of class birthdays, finding people with the same birthdays, fully mobilizing the class atmosphere, thus greatly stimulating students' interest in learning probability. (In case there is no classmate from Amanome, even if the probability is as high as 96.5%, it is still possible that it will not happen. ) Let the students cite examples of life and study, and combine the chapters and charts to make them feel that probability is everywhere, that it is useful, that mathematics is also useful, and that learning probability is very important.
2. Clear the topic: Let the students make it clear that the focus of this lesson is the probability of random events.
By distinguishing the differences of four events, this paper introduces the classification of events, summarizes the concepts of impossible events, inevitable events and random events, and makes it clear that the focus of this lesson is the probability of random events.
The design intention of example 1 is to deepen the understanding of event classification and concept, and emphasize that the result is relative to the condition by changing the condition of "event b";
The design intention of exercise 1 is to introduce the allusion of "waiting for the rabbit", so that students can analyze this allusion with the knowledge of mathematical probability, which permeates the educational significance of mathematics and embodies that mathematics comes from life. At the same time, students feel that knowing the probability of random events will help us make correct decisions.
3. Concept construction: Find the method of obtaining the probability of random events, get the concept of probability, and compare the discrimination frequency and probability.
Step 1: Guide students to estimate the probability of an event with the frequency obtained from the experiment.
Creating a scene on the spot: The most direct way to guide students to perceive and solve problems is to experiment.
Step 2: Through the coin toss test, the definition of probability is deduced to break through the difficulty.
(1) Organize students to toss coins. According to the past practice, in order to pursue better experimental results, the guided throwing method ensures the randomness of the experiment and embodies a teaching concept of teacher-led and student-centered. Understanding the concept will also have positive significance. The specific operation steps are as follows:
In strict accordance with the requirements in the book, let each student do 10 coin toss experiment and fill in the experimental results in the book form. Take four students as a group, count the experimental results of the students in this group and fill in the form. Make full use of the powerful function of excel software to assist teaching, calculate the frequency of each group and draw a line chart. Students personally experience the uncertainty of random events. When the number of experiments is relatively small, the frequency is unstable. Ask the students to observe the table in the data summary part, and intuitively perceive the frequency instability.
(2) Through computer simulation experiments, a large number of coin toss experiments are repeated, so that students can dynamically feel that the frequency of each experiment is uncertain, but it is stable near a certain constant.
(3) Combining with a large number of independent repeated experiments made by mathematicians in history, compare the line charts of two frequencies, draw a conclusion and form a statistical definition of probability.
This paragraph is the difficulty of this section, and it is necessary to transform the intuitive impression of data and charts into abstract probability definitions. Through experimental operation, chart observation, group discussion and induction, this difficulty is well broken through, and the concept and relationship of frequency and probability are correctly understood through coin toss experiment. The teaching goal is to cultivate students' ability of observation, practice and summary, as well as the team spirit among students.
4. Deepen the concept: further clarify the difference and connection between frequency and probability.
I arranged two exercises.
Example 2 Real-time training, the design intention is to implement the key points to let students master the method of estimating probability with frequency, emphasizing the stability of frequency and the certainty of probability;
Exercise 2 aims to show that the results of each experiment are random and further strengthen the theme of this lesson;
Through tables and images, students can vividly and intuitively feel:
Difference: the frequency is random and cannot be determined before the test; Probability is a fixed value, which exists objectively and has nothing to do with experiments.
Connection: With the increase of test times, the frequency will stabilize around a constant, and the estimated value of probability will be obtained.
Practice feedback
(1) Design intention of Exercise 3: This exercise synthesizes the key points of this lesson, which can give good feedback on the implementation and consolidate the knowledge gained through training.
6. Summary
The function of summary is to guide students to remember and deepen the problem, so that knowledge becomes a system. Let students try to summarize the knowledge content and research methods, so as to improve their awareness of reflection and summary and their language expression ability. At the same time, I will make supplements to help students fully understand and master new knowledge. Especially in the process of summing up, the mathematical ideas of this lesson will be put forward: experiment, observation, induction and summary.
Exploration after class
Book exercise 1
The design intention of this inquiry is to consolidate the content of this class and build a bridge for the next class.
Seven: blackboard writing
Design intention: Reasonable and neat blackboard writing can help students better grasp the content structure of this lesson.