(A) the formation of a' statistical concept'
1. Difficult
Concept, different from simple skills such as calculation and drawing, is a feeling that needs to be cultivated in the process of personal experience. Some people call the statistical concept "data sense" or "information concept". No matter what word is used, it reflects the train of thought triggered by a set of data, infers all possible results, and consciously associates it with solving related problems by statistical methods. Specifically, the concept of statistics can be embodied in the following aspects: recognizing the role of statistics in decision-making and thinking about data-related issues from the perspective of statistics; Able to make reasonable decisions through the process of collecting data, describing data and analyzing data; Can reasonably question the source of data, the methods of collecting and describing data, and the conclusions drawn from the data.
The core goal of learning statistics is to cultivate students' statistical concepts. In the survey of students' impression of statistics, the information obtained is as follows: (1) Statistics is classification; (2) Statistics is calculation; (3) Statistics is addition; (4) statistics is to fill in statistical tables; (5) Statistics is to draw a statistical chart or answer questions according to the statistical chart. ...
Explain what? Explain that there are deviations in the teaching of statistical knowledge. Our teaching attaches importance to imparting knowledge points, and the assessment of statistical knowledge is limited to the assessment of knowledge points. Therefore, in the teaching process, the focus is on the calculation of relevant data, and students have not experienced the statistical process, so it is difficult to form a correct statistical concept. 2. Solution strategy
There is a potential statistical significance in students' life experiences. For example, before buying the annual get-together, the Life Committee will definitely investigate students' preferences, and then make purchases in combination with most students' preferences. The focus of our teaching is to help students tap this subconscious, and pay attention to cultivating students to consciously think about related issues from the perspective of statistics, that is, when encountering related issues, they can think of collecting data and analyzing data. The following points (1) should be done well so that students can experience the whole process of statistical activities.
The establishment of ideas requires personal experience. The most effective way for students to gradually establish statistical concepts is to let them really participate in the whole process of statistical activities: asking questions, collecting data, sorting out data, analyzing data, making decisions, communicating, evaluating and improving. Learn statistical methods and infiltrate statistical ideas in participating activities. From another point of view, the development of mathematics often goes through such a process. First, we ask questions, then collect and sort out information related to this problem, and then make some judgments based on this information to explain or solve the initial problem. Asking questions is especially important. There are no purposeful problems, such as the teacher asking students to count how many flowers there are and how many people there are. What will such statistical activities leave in students' minds? Asking questions should take into account students' interests, make them willing to participate, and be conducive to teachers' subjective education. For example, we can carry out a variety of problem investigation activities, such as investigating junior high school students' favorite extracurricular activities, favorite books, favorite people, favorite subjects and so on. And we can also investigate students' ideals at this stage. In addition, the survey questions can also be found in newspapers, magazines, TV broadcasts, and the Internet, but students should be guided to pay attention to the data provided by the above channels. Is its source reliable and reasonable? By using reasonable investigation materials, students can take statistics as an important means to understand society, improve their ability to analyze and solve problems, and better understand the real society. At the same time, they can treat the data released by news media and advertisements rationally and form their own views on many things in the real world.
Einstein said: "Pure logical thinking can't tell us anything about the empirical world. All knowledge in the real world begins with experience and ends with experience. " Empirical observation accumulates data, and then makes some judgments from the data. This kind of activity helps to cultivate students' discovery ability and innovative spirit.
In short, we must pay attention to let students experience the whole process of activities. We should not only collect data, fill in statistical tables, draw statistical charts and calculate data, but also feel the role of statistical charts and draw relevant conclusions from them.
(2) Let students experience the influence of statistics on decision-making in real situations.
An important way to cultivate students' awareness of thinking from the perspective of statistics is to show the wide application of statistics in teaching with life examples, so that students can experience the role of statistics in decision-making in the process of solving practical problems.
For example, count the sales of several goods in the store within one month and put forward your suggestions on the purchase of goods in the store; The fact that water resources are scarce all over the world is well known. Ask students to make statistics on the water consumption of their homes or schools, and put forward reasonable suggestions on water saving. Let students investigate the things they are interested in, and interpret the statistical results in combination with the obtained data, make simple judgments and predictions according to the results, clearly express their views and communicate with their peers. In the process of solving problems, they can understand the role of statistics and gradually establish a statistical perspective to think about problems.
(B) the rationality of sampling
1. Difficult
Statistics is based on sample data, through sorting, describing and analyzing the data, we can find the characteristics or laws of the data, and then infer the overall characteristics. Therefore, whether the sample is representative is very important in statistics. Different samples will produce different conclusions. So how to sample more reasonably is still a lot of confusion for students. 2. Solution strategy
Through learning, students understand the difference between general survey and spot check, and make clear the necessity of spot check. However, because the data we want to get can correctly reflect the actual situation, the samples taken should be generally representative. Whether the sample is well drawn is a very important question. For example, I want to know the academic performance of students in this field. I found 100 students, but they are all students in the experimental class. I want to know about the daily study time of Beijing students, and I have found students from key schools, so this sample is not representative. Whether it is representative or not is a core issue of the sample. So, how can we be representative? It's random sampling.
Why is random sampling representative? For example, to know the eyesight of junior high school students in Beijing. If random sampling is needed, it is assumed that 3% students have a vision of 5. 2, then the probability of obtaining vision is 5. 2 is 3%. If 5. 0 accounts for 40%, so the probability of drawing 5. 0 is also 40%. This random sampling ensures that the percentage of each visual acuity value is the same as that of the whole sample. In addition, because the lottery has nothing to do with the order, if the first student is selected, the probability of vision is 5. 2 is 3%, so the probability of the second and third students' vision decline is also 3%. Random sampling can make the percentage of different vision in the sample roughly the same as that in the population. In other words, randomly selected samples can well reflect the overall situation. Why random sampling is representative. This is exactly what we said earlier. The object of probability statistics research is this randomness, that is, the phenomenon of uncertainty. Therefore, when we first came into contact with the two basic concepts of population and sample, our teacher should be aware of this randomness. In the learning process of sampling method, we should talk about the role of random sampling and randomness to ensure that this sample is representative, so as to correctly understand this concept. And the difference between it and different concepts in the past, otherwise we introduced the student union operation method, but I don't know why this method is used so much, so it can't be used flexibly in life.
So how to randomly sample? Random sampling is not easy to do, for example, throwing a one-dollar coin at random, and a certain face may face up more than half of the time. It is said to be a random shot, but because of the angle and height of the shot, the result is actually not random, so the problem of randomness seems simple, but it is still very difficult to do, which is what our teachers should pay attention to. There is no need for students to delve into such problems in junior high school if they want to understand them. But let students understand in specific situations that different samples will lead to different statistical conclusions.
For example, in order to improve the time of concentrated physical activity, a school wants to know the time of extracurricular physical exercise for junior high school students and ask students to do a survey. Firstly, the sample size is determined according to the total number of students in the school. The sample size is too small, unrepresentative and too large, which is time-consuming and laborious. Secondly, choose the location of the survey, and let all kinds of students participate as much as possible, such as libraries and sports fields. If you only study in one place, it is easy to lack representativeness. For example, if you only choose the sports ground, you will definitely come to the conclusion that students exercise too much every day. On the contrary, if you only do research in the library, you will definitely come to the conclusion that exercise time is seriously insufficient. In addition, we should also consider that different grades have different academic burdens, which leads to different after-school hours. Therefore, it is necessary to investigate by grade. It can be seen that there are many factors to be considered in the sampling process, which are also complicated. In junior high school, students should combine the purpose of the survey, determine the survey objects and methods, and make them as representative as possible.