Reflections on the teaching of statistics and probability 1 i. On "Classification and Statistics"
Generally speaking, classification is to make things orderly, and classification is to understand the whole more deeply. Doing statistics is to make decisions and guide actions according to quantitative results. In short, we can't classify for classification, but count for statistics.
I think the purpose of these cases in textbooks is not clear:
1, statistics "How many teeth have changed" is introduced as the theme, which is very innovative. But what is the use of statistics? Can you change it early? Come on, okay? The purpose is not clear enough;
It is useless for students to count the size of shoes they wear. This is only necessary when the class orders a pair of shoes for everyone. The boss who sells shoes may also need it;
3. Some scenes have inappropriate design goals. For example, designing the types of books borrowed by schools leads them to prefer "comics" to "literature". It is suggested that libraries sell more "comics". This is inappropriate. If you don't like literature books, I'm afraid you need to introduce them more, not necessarily buy less.
Second, the judgment of classification.
A bunch of things can be classified from different angles, that is, there are many judgments about classification. However, step by step, first one judgment, then two judgments, and gradually cultivate.
A pile of geometric figures can be classified by color, shape and size, step by step, not by three judgments at once. Ask the first-year students, "How else do you score?" This question is too broad.
Classification is not a single knowledge point. Expanding classification as a knowledge point will increase students' burden. As a mathematical thinking method, classification is contained in mathematical situational decision-making. With the deepening of knowledge content, the difficulty of classification will increase.
There are many kinds of classification, but many of them are worthless. For example, in a pile of geometric figures, I can be divided into two categories: one is "red triangle" and the other is "non-red triangle". Do we need such a classification? Another example is that there is food and clothing in a batch of things, including an ice cream Then, I classify, one is cold and the other is not. Is this classification interesting? Although the share is not bad.
Classification is not the more the better. Classification means that you get "good", that is, it is valuable and can help decision-making. Classify only when necessary, not the more the better. When you see an object, you have to classify it, and aimless division will only confuse things. It is misleading to pursue various classifications aimlessly.
Three. About data collection
Now, it is emphasized to be connected with students' daily life. The textbook requires students to do a lot of surveys and collect data. But there are also many problems. For example, counting students' sleep time, students themselves don't know the exact sleep time every day.
Fourth, the understanding of "possibility"
Nowadays, textbooks for middle and lower grades keep repeating the judgment of "necessity, possibility and impossibility", which is often standing still. After learning the "fraction", we can simply understand and calculate the classical probability. At this time, the probability can be quantitatively analyzed, which embodies the value of mathematics.
The understanding of general possibilities can be achieved without teaching. Li Jun, Department of Law and Mathematics, East China Normal University, investigated that there was no probability in the primary school curriculum in China in the 20th century, but compared with other countries with probability content, students' understanding of possibility was basically the same.
Reflection on the Teaching of Statistics and Probability 2 Statistics and Probability mainly study the data in real life and random phenomena in the objective world. By collecting, sorting, describing and analyzing data, it depicts the possibility of events and helps people make reasonable decisions. The main goals of learning statistics and probability in primary school are: to cultivate students' random view of the real world, to master the methods of data collection, collation, description and analysis, to gradually form the concept of statistics, and to help students understand people, nature and society through the study of statistics and probability; Facing a large number of data and uncertain situations, we can make more reasonable decisions, form the consciousness of mathematical analysis and improve the ability to solve problems.
It is the main goal of probability learning to understand random phenomena (uncertain phenomena) in the real world and make reasonable judgments under uncertain circumstances. Therefore, random thoughts have infiltrated into mathematics classroom since childhood, which not only brings convenience to future study, but also makes students' study closer to life. For the possibility of some simple events in life, our first thought is to collect data by statistical methods, and then analyze and judge the data, which is the concrete embodiment of ability and consciousness. For example, what is the probability of five heads up and five tails up in ten coins? We must first find out how many possible outcomes there are in ten coins, and then we can draw a conclusion that the probability of five heads up and five tails up in ten coins is 10%. In statistics teaching, students should not only go through the statistical process, but also learn some simple methods to collect, sort out and describe data. According to the cognitive level and experience of students in different classes, let students complete a task or engage in an activity as a starting point, and give their own methods to complete the task according to the results in the activities of collecting and processing relevant information.
Reflections on the Teaching of Statistics and Probability Chapter III "Statistics" and "Probability" are all about collecting, sorting, analyzing and describing data, so as to gain an understanding of some overall laws, thus helping people to make appropriate choices and judgments on a large number of complex information. When reviewing this part, I pay special attention to two points:
(1) Guide students to review and sort out the statistics and probability knowledge they have learned independently, and then I will guide and sort it out.
When teaching, let me review first: What knowledge about statistics and possibility did you learn in primary school? Students' memories are scattered, disordered and incomplete, which I sorted out when students communicated. According to the statistical process, from the classification and counting of data to statistical tables, charts, statistics, and then to the possibility, let students form a clear context of knowledge in their minds. Then review the concepts, characteristics and scope of application of statistical charts and statistics through group discussion, so that students can form a more comprehensive understanding of the characteristics of various statistical charts.
(2) Guide students to participate in the whole process of statistics.
In teaching, I asked students to discuss and design a questionnaire about students' personal situation in groups, and then exchanged supplementary survey items with each other, forming a relatively complete questionnaire for the whole class. After all the students fill out the questionnaires, they form a series of original data, and each questionnaire is a data sample.
On this basis, you can investigate the items you are interested in, such as your favorite TV programs and special dishes.
Reflections on Statistics and Probability Teaching Chapter IV Statistics and Probability runs through the whole primary school stage, and every textbook contains statistics or probability, so it is also a compulsory part of the final exam of grade six. So when reviewing, although you don't need to take out every textbook and review it again, you can consolidate several kinds of statistics through practice questions. The content of statistics is relatively simple, and students have a good grasp on the whole. It is mainly the difference and connection between the three statistical charts, and sometimes there is a judgment question or multiple-choice question in the exam. Secondly, the general exam has a big problem, drawing the main statistical chart and solving some simple practical problems according to the topic information.
However, when reviewing, the focus is on emphasizing some differences and connections, as well as some frequent mistakes and some small details that are often forgotten. For example, a bar chart can mainly see the differences in quantity and data of various quantities; The broken line statistical chart mainly shows the trend of quantity increase and decrease, and also shows the quantity of various quantities; The fan-shaped statistical chart mainly shows the relationship between the part and the whole, that is, the percentage of the part to the whole, and no specific figures can be seen, which can only be obtained through calculation.
You also need to pay special attention to some small details, such as drawing a bar chart, paying attention to the same width of each bar and marking a specific number on each bar. When drawing a statistical chart of broken lines, numbers should also be marked at the inflection point, and whether they should be connected with the origin. When drawing a fan-shaped statistical chart, it is necessary to mark the percentage that specifically represents the above and the corresponding percentage.
In short, students should explain and correct problems in time if they have problems in the process of doing the problems.
Reflections on the Teaching of Statistics and Probability 5 Today, the county teaching and research section came to our school for teaching guidance. When I was in the third grade, I took a paper class on statistics and probability. Although the content of this class is not very difficult, I feel that there are still many problems in my classroom teaching after one class. The classroom teaching effect is not ideal.
The allocation of class time is unreasonable, and the key topics are fully displayed on the blackboard. The consolidation work has not been done well. Class summary is a mere formality. Did not grasp the rhythm of classroom teaching. It is impossible to further summarize and refine knowledge and methods, and it is impossible to understand what you have learned from the height of mathematical thought.
Through the comments of Mr. Liu in the teaching and research section, Ben will make efforts in the following aspects in the future examination paper evaluation:
1, grasp the rhythm of classroom teaching and let students solve key mistakes in class.
2. Pay attention to the connection of knowledge before and after, further summarize and improve the knowledge and methods, and understand what you have learned from the height of mathematical thought.
3. Guide students to summarize the effective methods in solving problems in time, find the best learning path suitable for students, and improve their academic performance.
4. Guide students to learn how to learn through the evaluation of test papers, and cultivate students' good test habits.
Reflection on Statistics and Probability Teaching 6 Choose two examples. One is the situation of tourists in a tourist attraction during the "Eleventh" holiday in 2008, which shows the different characteristics of the same set of data with histogram statistics and broken line statistics; The second is the statistical results of a city's population from 1999 to 2007. It is required to analyze the changes of urban population and predict the urban population in five years.
There is no difficulty in the whole teaching process in this class. Students' learning state is good and teaching effect is good. On the basis of completing the teaching content in the book, I added the teaching of fan-shaped statistical charts, and compared the three statistical charts together, so that students can understand the characteristics of the three statistical charts more clearly and apply them selectively.
Teaching Reflection on Statistics and Probability 7 As a continuation of compulsory education, mathematics learning in junior middle school will consolidate and deepen students' understanding of logarithmic analysis methods and expand their experience of uncertainty and probability. Through the whole process of data processing, students can understand the role of statistical methods in decision-making
Through experiments, theoretical analysis and other methods, gradually cultivate students' habit of thinking deeply and experience the characteristics of thinking with probability. Probability statistics in the basic education stage is not only important for specific knowledge, laws and rules, but also important for the learning of processes, ideas and concepts. The purpose is to let students know the basic idea of probability statistics and its application in social life. Providing realistic problem scenarios in teaching, allowing students to really participate, facing the problems to be solved, actively designing schemes, collecting data, making decisions, finding arguments for maintaining their own views, and discussing and communicating with others will all benefit them for life.
Teaching Reflection on Statistics and Probability 8 Combining the examination questions and teaching experience over the years, students have four possible situations in the exam:
(A) easy to complete (not difficult)
This kind of questions appear in the fill-in-the-blank questions, such as finding the probability of simple events, finding the average value and finding the pattern, which can generally be completed by all candidates.
(2) I made a mistake at first sight.
This kind of problem is mainly because some concepts and definitions in probability statistics are not skilled, vague and chaotic, such as finding the median, without paying attention to rearranging the data; In the bar graph, we don't pay attention to the unit size of the bar length and width, which highlights that the basic skills are not solid.
(3) It is easier to master than to do.
This kind of problem is reflected in the arrangement of data. The teacher only needs to say it once, and the students can master it, but it is very laborious to do it. Mainly in drawing statistical maps, primary school students can do it, but many students are still short of money to make statistical maps complete and beautiful, which reflects the practical problem of unskilled basic operation and is also a weakness of students now.
(4) Difficult to master but difficult to do
This kind of topic reflects the problems of long-term memory and instantaneous memory. In probability statistics, some topics are not pure probability statistics, but also involve other mathematical problems, which need to be considered comprehensively. The teacher should practice immediately after explaining, and the students can finish it. After a period of time, students are ambiguous and have no way to start. To achieve long-term memory, only by doing more and practicing more, and analyzing problems should be combined with reality, can we break through such problems.
Combined with the problems that students are prone to, and the examination questions over the years, it is not difficult to find that the examination questions are moving from the most basic double-base examination to a high-level problem-solving level, and the flexible use of statistics and probability is reflected in the examination questions, so statistics and probability can no longer be treated as simple questions, so it is particularly important to review them well. I think we should grasp the foundation, consolidate and find skills in review, and strive to let students overcome these common problems.
Reflection on the Teaching of Statistics and Probability Chapter 9 listened to a wonderful lecture by Chen Chuanrong on "Improving Students' Statistics and Probability Awareness by Connecting with Life". After several days of online research, I have a deeper understanding and knowledge of the new course "Statistics and Probability".
"Statistics and Probability" is one of the four learning areas in the compulsory education mathematics curriculum standard. The curriculum standard also takes "statistical concept" as one of the important goals for the first time, and puts forward that students should "experience the process of describing information, inferring and developing statistical concepts with data." The main reason for this situation is that "statistics and probability" are too closely related to people's daily work and social life. In the modern society based on information and technology, people are faced with more opportunities and choices. It is often necessary to make reasonable decisions based on a large number of data under uncertain circumstances, which is the basic quality that all citizens should have in the new era. Statistics provides basis and suggestions for people to make better decisions by collecting, sorting and analyzing data.
First, how to understand the concept of statistics:
I used to think: Isn't statistics just calculating the average and drawing statistical charts? Calculators and computers can do these things well. Is it necessary to start learning at an early age? Indeed, in today's information technology is so developed, calculating the average and drawing statistical charts should not take up too much time for students. In fact, they are far from the core of statistical learning. In the compulsory education stage, the core goal of students' learning statistics is to cultivate their own "statistical concepts". Speaking of "concept" is not equivalent to simple skills such as calculation and drawing, but a feeling that needs to be cultivated in the process of personal experience, so some people label "statistical concept" as "data sense" or "information concept". No matter what vocabulary is used, it reflects the train of thought triggered by a set of data, the possible results inferred, and the conscious thought of using statistical methods to solve related problems.
Second, the interpretation of statistical data:
Modern Chinese Dictionary has two interpretations of "statistics": (1) refers to the collection, collation, calculation and analysis of data related to a certain phenomenon; (2) Summarize the calculation. It is not difficult to see that the first explanation describes "statistics" as a process, including a series of activities such as collecting data, sorting out data, calculating data, and finally analyzing data. This explanation provides a basis for us to teach simple statistics, that is, we should not divide the teaching of statistical knowledge into knowledge points, but pay attention to the process knowledge of statistics, that is, when it comes to statistics, it will inevitably involve the whole process of statistics: finding and asking questions-using appropriate methods to collect and sort out data-using appropriate statistical charts and statistics to display data-analyzing data to make decisions-and communicating and communicating our own results.
In this process, students learn how to count and why to count. So it can be said that statistics is a process.
The second explanation shows us that "statistics" is also a method and strategy to solve problems. In the information society, data is undoubtedly one of the important information. How to face the data and get information from it requires statistical methods. For example, when we study surnames, I ask students to count how many surnames there are in the class. When there are several people in each class, the students make a small statistics in the class, first write the names, then make statistics.
The description of "statistics" in the mathematics curriculum standard is as follows: "Statistics and probability mainly study the data in real life and random phenomena in the objective world. By collecting, sorting, describing and analyzing data, it depicts the possibility of events and helps everyone make reasonable inferences and predictions. " This sentence also highlights its value in the statistical process.
Third, the embodiment of statistical concepts:
1, understand the role of statistics in decision-making and think about data-related issues from the perspective of statistics.
The first aspect of cultivating students' "statistical concept" is to cultivate them to consciously think about related problems from the perspective of statistics, that is, when encountering related problems, they can think of collecting data and analyzing data.
For example, if you have nothing to do and go out for a walk, you will see many drivers passing by. Ask you what cars pass by this street for a long time? You can't draw conclusions just because you just saw it. You should observe it for a long time, collect certain data and analyze it at the same time, so as to judge what kind of car passes by.
2. Be able to make reasonable decisions through the process of collecting, describing and analyzing data.
Students should not only have the consciousness of thinking from a statistical point of view, but also experience the process of collecting, describing and analyzing data and make reasonable judgments based on the data.
Taking "What kind of car passes by" as an example, students not only realize the need to collect data to solve this problem, but also discuss what data to collect and how to collect it, and also sort out the collected data clearly, so as to make a reasonable judgment.
Four, the problems that should be paid attention to in the implementation:
The general goal of the first section of the mathematics curriculum standard points out: experience the statistical process of data, master some simple methods of collecting, sorting and describing data, answer some simple questions according to the statistical results, and initially feel the uncertainty and possibility of events.
Students in this period pay attention to the novelty and interest of things, so the study of statistics and probability should pay attention to the initial feelings and experiences, and avoid treating them as simple calculations without paying attention to students' experiences and activities.
1. Experience in data collection, collation, description and analysis.
It is difficult for students in the first phase to understand the whole process of statistics. Therefore, teachers should consciously design some statistical activities in the teaching process, such as: "How many groups do we have in our class to carry out special training?" In order to answer this question, children will want to do a survey, which leads to the necessity of statistics, and then think about specific statistical methods. Only in this way can children be exposed to more and more problems that need to be solved by statistics, so that they will not only teach knowledge but ignore experience.
2. Ask and answer simple questions according to the data in the statistical chart, and exchange your ideas with your peers.
In teaching, teachers should ask questions to promote students' analysis and interpretation of data. Specifically, it includes the following three aspects:
First, judge whether the statistical chart can express the original problem. For example, whether there are several super-long classes, which super-long classes are attended by more people and which super-long classes are attended by fewer people can be judged by statistical charts.
Second, judge whether the statistical chart can display other information. Mainly guide students to answer two questions: ① descriptive questions, such as "How many people are there in the art class?" ② Comparative questions, such as "How many people are there in the art class than in the calligraphy class?"
Thirdly, make reasonable inference according to statistical charts and guide students to exchange their experience in reading pictures.
In short, statistics learning in compulsory education stage should help students understand the basic ideas and functions of statistics, which can not only solve some problems consciously and correctly, but also rationally analyze other people's statistical data and make reasonable judgments and predictions.
Reflections on the Teaching of Statistics and Probability 10 In this lesson, two activities are arranged in the textbook. Activity 1, ask about the possibility. Activity 2: Experimental activity to experience the possibility. Activity 1: Students don't feel any difficulty in finding possible solutions, but some students still don't have a good grasp of distinguishing the composite numbers of prime numbers. In activity 2, some students didn't bring small cubes according to the teacher's requirements, so they had to use some students' experimental data for statistics. The frequency of results with the sum of 5-9 is much greater than that with the sum of 2,3, 1 1, 12. Why is there such a result? Students' curiosity is aroused, and they are urgently needed to explore the possibility of all the results. The students put forward various methods: list method, formula method and enumeration method ... All of them come to a conclusion: the possibility of sum being 2, 12 is 1/36, and the possibility of sum being 3, 1 1 is 65438+. The probability that the sum is 4, 10 is12, the probability that the sum is 5,9 is 1/9, the probability that the sum is 6,8 is 5/36, and the probability that the sum is 7 is 1/6. The doubts in my heart were solved, the children's brows were relaxed, and I smiled.
Through the review of statistics and probability, students' knowledge is consolidated, and the methods and strategies to solve practical problems by using what they have learned are learned. Their awareness of applying mathematics to solve practical problems has been strengthened and their practical ability has been continuously improved. I believe that for them, the benefits are huge. For teachers, each student will leave a different learning experience, and teachers also feel that they have benefited a lot.