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Teaching practice and thinking of life estimation
"Mathematics Curriculum Standard" points out: "Estimation is widely used in daily life and mathematics learning. It is of great value to cultivate students' estimation consciousness, develop students' estimation ability and give students a good sense of numbers. " In the first stage of teaching, it is very important for students to establish the concept of number and the initial concept and estimation of number. Rousseau believes that in order to let students acquire knowledge, experience and development, they must be taught to participate in various practical activities. So, I tried to take a practical activity class of "Estimation in Life". In order to let students experience the whole process of estimation and learn the method of estimation; Let students improve their ability to explore and solve problems through observation, operation, discussion, communication, speculation and verification; Understand the role of estimation in daily life and cultivate estimation consciousness.
[Active Clip]
Activity 1: pre-class investigation and classroom information exchange.
Teacher: A few days ago, the teacher asked you to investigate the estimation used in life and completed a questionnaire on "Estimation in Life". Now, please share your survey results in the group first, tell your own estimation methods and reasons, choose the one you are most interested in, and report to class later.
Student 1: I found that there are 32 classes in our school, with about 50 students in each class. Using "class size × class size", I calculated that there are about 1600 students in our school.
Student 2: Through investigation, I know that our school has 25 kilograms of recyclable garbage every day. According to this calculation, there is about 10000 kg of recyclable garbage in 365 days a year, which is equivalent to 10 ton. This not only protects the environment, but also recycles the waste. What a kill two birds with one stone!
Teacher: When can I use estimation in my daily life?
Health: Estimates can be used to calculate how many people can live in a building.
Student: We can use estimation when calculating the distance between my home and school.
Health: When calculating how much water a bottle can hold, you can use an estimate. ...
Teacher: Through investigation, students know that estimation is often used in our daily life. It seems that it has played a big role!
Activity 2: Estimate the number of words in a newspaper.
Teacher: Have you ever noticed your reading speed? How many words can you read per minute when you are reading?
Health 1: I can read about 1 80 words in1minute.
Health 2: I can read about 1 50 words in1minute.
S3: I can read about 250 words in 1 minute.
Teacher: Why is there such a big difference in the number of words read in 1 minute?
Health 4: Because of the two of them (Health 2 and Health 3), one reads fast and the other reads slowly. czsxz.com
Teacher: Yes, the number of words read per minute will be very different between fast reading and slow chewing. I'll give you a minute now. Please choose an article in the third edition of Light of Shen Hours to read and try how many words you can read at normal speed.
At the sound of "Start", the whole class began to read aloud. Just after the "stop", I heard that a large number of students below could not wait long. They have started counting, 1, 2, 3, 4 ... After a while, a dozen hands were raised. Wait a minute, I see that most students have raised their hands. )
Teacher: 1 min. How many words did you read? What method did you use?
Health 5: I counted from the topics to the places I read. I read the word 193 in one breath.
Teacher: You count them one by one. Do other students have a better way?
(A dozen people who count quickly raise their hands again. )
Health 6: I counted about 20 words per line first, and then counted 9 lines, so I read about 1 minute. czsxz.com
Teacher: What do you think of this method?
Student: It's much simpler than a word, because we don't need to know how many words 1 minute can be read. We just need to know how many words can be read in 1 minute.
Teacher: Yes, the teacher thinks so. According to your reading speed, how many words can you read in 10 minute? And tell your deskmate your calculation results.
Teacher: Estimate, can you finish reading the 1 version of this newspaper in 10 minutes? Why? what do you think? Students guess that there are two possibilities, one can finish reading and the other can't finish reading. )
Teacher: Who estimated it more accurately? We have to estimate how many words there are in this version first, right? If necessary, you can also work at the same table or in groups.
Health 7: I first estimate the number of words in an article, and then count the number of articles, and work out that the third edition is about 2500 words.
Health 8: I think the number of words in the third edition is more than he estimated, because the article he estimated is much shorter than others. I counted 60 words per line, then 80 lines, and finally estimated that 1 version * * * has 4,800 words with "words per line × lines".
Health 9: I think my method is relatively simple. I'll first convert this version into 16 and work out a copy of about 300 words, and 16 copies of about 4800 words.
Teacher: Your method is great! Now, who says how many minutes it will take you to finish reading this edition?
……
Activity 3: Estimate the number of sheets of a dozen blank sheets.
Teacher: The teacher found that the students in our class have very strong estimation ability. Now each group has more than a dozen pieces of white paper. Can you estimate how many pieces of paper there are?
Health:100,200,500, 1000 ...
Teacher: Who estimated it more accurately? If you use a ruler, can you verify it? (Yes)
Let's conduct verification activities in groups. I hope to pay attention to the following two points: a, the group students discuss the verification method first, and cooperate together at the beginning of the operation; B, fill in the estimate report, check whether the calculation is correct, and prepare the report.
(Now the students are very busy, some take a ruler to measure, some count paper, some count, some record ...)
Teacher: Please report your report concisely, explain the advantages of your group's report, listen carefully to the reports of other groups and make a reasonable evaluation.
Group 1: paper quantity estimation report
Estimation step
First measure 5 mm, count 55 sheets, and then measure the whole dozen sheets to be 2 cm, that is, there are 4 sheets in 55 sheets.
Tools used
rule
assessment result
55×4=220 sheets
The second group: "1 group method needs to count too many sheets, which wastes time." First measure 1mm, then count 10, and then measure the whole dozen pieces to 2cm, that is, there are 20 pieces of 10, that is, 200 pieces. (table omitted)
Group 3: The number of groups 2 is incorrect. We counted 1 mm, and there was 13.
S: It's not necessarily that the two sets of numbers are wrong, because some are loose and some are tight when measuring.
T: "that's good. In order to measure as accurately as possible, we can stack the paper neatly, measure it several times, count the number of sheets and calculate the average. "
The fourth group: first, 10 paper is 1mm, and then the whole dozen pieces are 2cm, so there are about 200 pieces of paper.
Teacher: Were you right just now? The student "yeah" cried with joy. The students seem to be cheering for their success. ) Can you work out the thickness of 1200 sheets of paper? Make a gesture.
Health: Wow, 1200 sheets of paper is so thick!
……
Reflection:
I have learned a lot from our vision and practice, and the deepest is the following three points:
1, let students do mathematics in the prototype of life experience mathematics.
Real life is the destination of learning mathematics. "Mathematics Curriculum Standards" points out in the implementation plan: "Teachers should make full use of students' existing life experience, guide students to apply what they have learned to reality at any time, solve mathematical problems around them, and realize the application value of mathematics in real life. "In teaching, we should pay attention to providing students with more practical opportunities, guiding students to observe and understand things around them with a mathematical eye, guiding students to solve practical problems with their own mathematical knowledge, making students realize the role of mathematical knowledge in real life and its connection with real life in practical activities, and cultivating students' mathematical consciousness and practical ability. The practical activity class focuses on highlighting students' activities, and the selected materials must be personally felt by students. Teachers should be good at guiding students to become mathematical knowledge through their own practice and reflection, that is, let students experience a "mathematization" process in doing mathematics, so that students can truly gain dynamic mathematical knowledge and experience the endless fun of mathematical creation. Before this class, I asked the students to make a survey and give them free space and time to play. In the process of investigation, students must think about many problems, where to use estimation in life and how to estimate it. This enables students to associate facts in life with mathematics. At the same time, the information collected by students increases the sense of the scene. Through the information exchange meeting, students can feel the practical significance and role of estimation and understand the preliminary application of mathematics. What is more valuable is that students go out of the classroom and cultivate their hands-on ability and brain ability.
2. Let students learn to practice and experience the production process of knowledge.
There is a sign in front of the national library in Washington, USA, which reads: "I have heard of it, but I may forget it;" I may think of it when I see it; I did, and I really mastered it. "A remarkable feature of the new curriculum standard is that it puts forward the process goal. Modern mathematics teaching should pay attention to students' inquiry process, students' emotions and emotional experiences, and let students devote themselves to colorful and energetic mathematics learning, so as to give full play to students' main role.
The cognitive process of scientists is a process of producing new knowledge, while the cognitive process of primary school students is a process of reproducing knowledge. In this process, practical operation is one of the most basic and important means and methods to learn knowledge. In order to let students learn to practice, teachers should always guide students to practice, so that students can gradually form a sense of seeking knowledge in the process of experiencing knowledge production. I remember an old man named Bing Xin said, "Let children grow freely like weeds." Only by giving students the space, time, stage and world to explore freely can they give full play to their potential, display their individuality and cultivate their innovative consciousness. In this class, I consciously take activities such as operation practice, independent exploration, cooperation and exchange, and positive thinking, so that students can feel and understand the generation and development of knowledge and taste the success of discovering truth. For example, in the activity of estimating the number of dozens of blank sheets, I first asked each student to estimate the number of blank sheets by himself and told my deskmate the estimated results. Then I asked the students to cooperate in groups and verify their initial guesses through experimental activities such as measurement, counting and calculation. In this way, students not only experienced the process of "inquiry", but also experienced the process of knowledge generation. For another example, when students have a certain feeling about the thickness of a dozen of 200 sheets of paper through operation exercises, I will ask students to guess how thick 1200 sheets of paper are. Through this kind of guessing and their use of estimation strategies, students feel the meaning of numbers, master the size of numbers and develop their sense of numbers.
3. Let students learn to communicate and cooperate to show their talents.
The math classroom is a little homophonic, so it should be a place for members of the same body to exchange mathematical ideas. In math class, students should learn to express their views, dare to think, dare to say and dare to ask; Learn to listen carefully to each other's thoughts and ideas; Learn to communicate and cooperate. Students learn to communicate and cooperate, which will make the process of exploring knowledge full of excitement, make mathematics classroom a learning paradise full of flowers and birds and flowers, and become a stage for students to fully express and give play to their personal talents. For example, in the activity of estimating the number of words in a newspaper, students know that there are many ways to estimate the number of words in a newspaper, such as: ① first count the number of words in an article and then multiply it by the total number of articles; (2) count the number of words in each line, and then multiply it by the number of lines; ③ First, fold it into 16, estimate the number of words in a copy, and then multiply it by 16. In the process of communication, students can experience that different methods can get the same result, thus promoting the development of students' thinking. Another example is: the activity of estimating the number of dozens of blank sheets highlights the cooperation and communication between students and between teachers and students, which is manifested in that students are very good at listening to the reports of other groups of students, and can make a reasonable evaluation of the results of their own reports and supplement and improve them; Dare to put forward different opinions and methods. This not only shows students' talents, but also makes students' personalities fly and makes the whole class look colorful.