平均分与平均数的区别（Thedifferencebetweenthemeanandthemean）

平均分与平均数的区别（The difference between the mean and the
mean）
The difference between the average and the average: the current position: People's teaching network, 2010>> primary mathematics, teacher center, personal album, Wang Feiyun's essay, Wang Feiyun's essay
The difference between an average and an average
How do you reflect the difference between the average and the average in teaching?" This is the question I asked when I was taking part in the UC online teaching research this evening. Before trying to solve this problem, it is necessary to specify what the mean is.
What is the mean?
The new curriculum teaching under the third grade teaching note: the average number is an important concept in statistics. The average number used in elementary mathematics refers to the arithmetic mean, that is, the sum of a set of data divided by the number of sets of data. In statistics, arithmetic averages are often used to represent the general level of a statistical object. It is a statistic that describes the extent of the data set. Not only it can be used to reflect the general situation of a group of data (with the average number represents a set of data, the characteristics of intuitive and concise), also can compare different sets of data with it, can be seen between group differences.
Through learning, I learned that "the average is the amount of data that represents the trend in a set of data sets."". Of course, such a concept is impossible to speak directly to students. So how do you make the students realize the meaning of the average?
Problem raised:
In this section, students are taught to understand the meaning of the average by shifting and supplementing. Therefore, I pay great attention to the teaching design of Mr. Wang Xiuhua here today. (the instructional design is as follows:)
Teacher: we look at charts, think, when the number of participants is not at the same time, how to Bizet fair? (group discussion)
Report to the class: how many balls per person are they holding?.
T: can you judge the result in this way? Let's have a try. Ask the group to study together. How do you figure out how many balls per person per person? You can hold a swing with your hands, or start counting. One more match to see which team wins.
Team work to find out how to get the average number of ball clips for each team. The whole class exchanged discussion. The method of seeking the average number of autonomous reporting, division camera guidance. Realize the meaning of the mean.
Personal feelings: the children have not yet passed the shift
to fill the initial perception of what the average number, they asked the team to explore how to seek the average, the difficulty of the span is too large. No wonder the teaching teacher in rural primary school teaching will feel that teaching here is very poor. ]
Method 1: shift more and supplement less.
Teacher: what method did your group study? Who won? (mobile)
T: attention, careful observation. What hasn't changed during the movement? What has changed? (of course, the courseware shows more and more movement)
Teacher: please put up your little ears and listen to him (the boys averaged 5 balls, and the girls averaged 6 balls, so the girls won.)
Teacher: the impartial judges please return the original small, the girl is the final winner, congratulations to you. (applause.)
Teacher: just now the student used the method of shifting more and filling less. What hasn't changed in the process of moving? (the total number has not changed)
Teacher: the observation is really careful, the total number has not changed all the time, the shift is many, the supplement is little, only is the group interior adjustment, the influence does not affect this group's result? (no) then it is perfectly fair to judge the outcome by comparing the number of balls per
person.
T: think again, what has changed in the process of moving? (the number of people in each folder changed.)
How's everything going? (as much)
What's the number? (turned 5)
What does this 5 mean? (mean an average of 5 balls per player)
So what's the number 5? Guess, yes, it's called average.
[personal comments: teachers in multi shift less process, attaches great importance to guide the students to observe "what change", this is the total number of copies, with subsequent = average number of laid a foundation. But the question of "what has changed" has not been adequately addressed. Teachers themselves should be clear, in fact, the original number of each ball is not 5, the average does not mean that the actual number of each. Its concept is not exactly the same as that of average in the past. The average is a "virtual" number that is obtained by means of the mean. ]
Problem exploration
So, how do you help students understand the meaning of the average and show the difference between the average and the average? Because I have not yet come into contact with the new curriculum materials, so I can only talk about my own ideas on this issue.
1, how to explain the mean?
According to the age characteristics of the students of grade three, the meaning of the average can be explained by specific examples, which is more convenient for students to understand. As in the example above, teachers can be in multi shift less after summary "in total at the same time, several different numbers by multi shift less becomes as much, as many of the original number is this number with the average number of.
"And a question," then what is the average number of boys, 4, 7, 5, 4, 5?" To test the students' knowledge of the concept.
2, how to distinguish between the average and the average?
When the student replied, "the average number of boys holding a ball is 5", the teacher may ask, "the average is 5. Did you get 5 balls for each boy?"" The students thinking to the deeper level thinking, so from the "real data" to the "average" back to the "real data", let students understand the mean is the average of a set of data, realize the average number of "virtual" feature. If students can answer, "the average number is shifted more and less later.""
"The average number is not the original number per player, some boys are more than 5, and some boys are less than 5. It represents the average strength of boys," the teacher may evaluate: "yes."! The average does not mean the actual number of each item. It is not an actual number, so we use the dotted line to represent the mean. Said in the chart with "-" indicates
the value of the mean.
Here, I want the children to say, "what's the mean?" What is the difference between the average and the average?" Hearts should have the answer.
Experience
Through today's discussion and the process of writing essays, I feel deeply that the process of finding answers is more meaningful than the answer itself.
2006-08-25 original
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