Mathematical composition about decimal point, and some mathematical knowledge.

Formalization is a prominent feature of mathematical science, but if it is pursued excessively in primary and secondary school mathematics courses, it will go to the other side of the problem: it pays attention to the "accuracy" of concept expression (whether it is really accurate or not is unknown), but ignores its essence and practical background; It emphasizes the careful consideration of definitions and theorems, but ignores the process of their occurrence and development and the basic facts and phenomena reflected; It emphasizes the strictness of deductive reasoning, but ignores the mathematical creativity of sensible reasoning and other informal thinking (such as intuition, association, epiphany, etc.). In particular, it is difficult to achieve the goals of "understanding the close relationship between mathematics and nature and human beings, understanding the value of mathematics, enhancing the understanding of mathematics and confidence in learning mathematics well" and "having a preliminary innovative spirit and practical ability, and being fully developed in emotional attitude and general ability". ①

In fact, mathematics is developed through human activities-problem solving, reasoning, representation, communication and evaluation. Children have gradually developed quite complicated informal ideas about numbers, formulas, shapes, data and sizes through their daily life experiences since childhood. It can be said that there is a lot of informal knowledge in the minds of students of all ages. Informal mathematics has many carriers. In practice, I found that "Mathematical Composition" with its unique form, eclectic material selection requirements and flexible expression can provide students with a broad mathematical stage and promote the realization of multiple goals in mathematics.

Try to practice (1)

So, I used the opportunity of assigning winter vacation homework (Grade Four) in 23 to assign students the task of writing a math story or a math composition. In the guidance, I explained the math composition as follows: "The content of math composition is combined with the learning content of this semester and the problems encountered in learning. It refers to a unique solution to a problem (both inside and outside the textbook) (it is required to be simpler than the original solution and suitable for similar problems), or the perception of mathematics learning, or the interesting and stupid things in mathematics. " .

It seems that the children are very enthusiastic about this homework. During the winter vacation, some students sent it to me by E-mail one after another, asking me to help me revise it. After the winter vacation, I summarized the students' math stories and math compositions, and several children's works were quite childlike. I tried to put the works of two students into the "inter-school exchange" of "Uptown Education Information Port", but they were quickly posted online. Considering that the children have spent a lot of effort, I chose some of my classmates' works, compiled a Mathematics Composition Report (Winter Holiday) and sent it to each classmate. The children looked at their hands and thought about the next time. Some asked: Can I write next time? Some asked: Why can't my article be found in the newspaper? .....

When I analyzed the articles handed in by students, I found the following characteristics:

1. There are many mathematical fairy tales. I didn't define what a math story is when I assigned my homework, but I gave them a math story "Naughty Parenthesis" and "7 and 1" written by a student under my guidance in advance, which was written in anthropomorphic form and should be regarded as a math fairy tale. As a result, almost all the math fairy tales and jokes that gave life to numbers and symbols were handed in. Of course, it is an easy way to give life to the carriers of mathematical knowledge-numbers, symbols, etc. and let them explain their mathematical knowledge themselves, so students are willing to adopt it.

2. There are quite a few students who are biased in their understanding and understanding of math stories and math compositions. Some students understand a math story as: a story with numbers is a math story. One student renamed the hero of a folk story a decimal point, and then organized it in his own language and handed it in, thinking it was a math story. Others think that a composition related to a math class is a math composition. A classmate describes the process of a math class and thinks it is a math composition.

according to the students' homework, I realize that: for students, math fairy tales and math stories are the same thing, while math composition is a little ignorant.

What exactly are math fairy tales, math stories and math compositions? After looking up some materials, I found that since the late 197s, some mathematics researchers, represented by Li Yupei, a famous popular mathematics writer, have published many popular mathematics works, such as Wonderful Curve, etc. Among them, the battle between rational numbers and irrational numbers, Sleepwalking in Kingdom and other fairy tales that illustrate and express mathematical knowledge or characteristics in vivid fairy tales, which Miss Li herself calls: mathematical fairy tales and mathematical stories. At the same time, there are similar works abroad (which should be earlier than ours). For example, there is a particularly famous math popular science book in the United States called Aha! A brainwave, in which there is a hero named Professor Quibell, who always has some interesting problems and solves them. In the 198s, China often published similar works in newspapers and magazines for students, often taking the images of Pig Bajie and the Monkey King, wise old man, and Xiao Lingli as the protagonists, and engaged in activities such as crossing the border and traveling. During the activities, some interesting mathematical problems will be encountered and then solved in interesting ways. At present, this form of works can still be found frequently. Strictly speaking, these works are popular works of mathematics, but they can also be regarded as mathematical stories or fairy tales, because the purpose of these works is to let readers learn or understand some mathematical knowledge.

And we can often see math compositions in some children's newspapers and magazines, but the authors are often adults, who explain a certain knowledge to students in the form of analysis, analogy and classification, with the aim of promoting readers' understanding of the knowledge.

Based on the above situation, I think that mathematics composition is first understood from the part of speech, which is a kind of composition. Therefore, all means of composition can be used in terms of genre and rhetoric, but the content must be the process of understanding, feeling, questioning and innovation in the process of mathematics learning, as well as the mathematical association of things and phenomena in life or the process of solving them by mathematical methods. Mathematical fairy tales and mathematical stories can be used as one of the forms of mathematical composition, just as fairy tales and stories are one of the primary school compositions.

Try to practice (2)

Based on the above understanding, after the start of school, I began to systematically guide and ask students to do math composition. According to the actual situation of students, I first put the cutting point on the question of "what to write in math composition".

First, what to write in a math composition

As mentioned above, a math composition is first and foremost a composition, and its genre and rhetoric should be the embodiment of the instrumental characteristics of Chinese class, that is, how to write a math composition is not the task of math class, but what to write is the core issue of math composition. The first thing to do is to let the students separate the math composition from the general composition after accepting the new term, that is, the math composition handed over by the students to the math teacher must contain mathematics that is not found in the general composition. The typical non-mathematical compositions and mathematical fairy tales with clear characteristics in the sorted composition can be distributed to students as model essays, so that students can make it clear in comparison, analysis and discussion that the mathematics of mathematical composition comes from the understanding, discovery, understanding, feeling, questioning and creation of mathematical knowledge in the article, instead of just replacing the name of the protagonist in ordinary composition with mathematical nouns, it is a mathematical composition. Similarly, if the word "mathematics" in an composition is used, others will be used. Therefore, if you want to write a good math composition, you should be a conscientious person, always pay attention to the math problems you are interested in inside and outside the class, pay attention to the process of observing, operating, discussing, communicating, guessing, summarizing, analyzing and sorting out in your math study and practice, and pay attention to how you experience, discover, explore and innovate, and reflect them in your math composition.

after such comparison and communication, I assigned interested students to hand in an article every month. See the following table:

March (articles) April (articles) May (articles) June (articles)

Class 1 (33 persons) 28 26 25 11

Class 2 (34 persons) 18 23 2 3

Subtotal 46 49 45 14

Total 1. 54

From the content, in March, there are still many introductions to a certain mathematical knowledge or the application of a certain mathematical skill, such as Naughty , Great Decimal Point, Simple Calculation (in fact, only an additive exchange rate is introduced), etc., while in April, the content is concentrated in mathematical thesis, such as Counting Soybeans, How many soybeans are there in a kilogram, etc. It can be seen that through a period of attempts, students can not only write mathematical compositions, but also gradually increase the scope of content and broaden their thinking.

In fact, since May, most students have made a clear definition of mathematical composition. So how can we attract students to go back to their desks to write mathematical compositions after school?

Second, let students feel the happiness of independence

Math composition is, after all, a sideline for students after school. If students don't want to write, they just hand it in reluctantly, and the quality is definitely not guaranteed. Therefore, in order to make children happy to write, it is necessary to take the following measures: < P > 1. Combine guidance with letting go.

The premise of writing mathematical composition is to get rid of the restrictions and constraints on students (perhaps this is the biggest advantage compared with ordinary composition, which requires an outline after all, while mathematical composition does not), so that students can draw up their own topics, choose their own materials, customize their own writing methods, write whatever they want, and write whatever they want, regardless of length and form, and let them express themselves freely and give full play. In May and June, some students really got a lot of good articles at their fingertips, covering a variety of topics, such as Experimental Report-Calculating the Difference between the Estimated Word Count and the Actual Word Count of The Romance of the Gods, and Six? I "The Expenditure of Children's Day", "The Mathematical Problem of Buying Clothes", "Extra Conditions" and "I'm in Charge Today" are both reasonable and reasonable, and mathematics must not be regretted in the article. There are fairy tales, experimental reports, jingles and narratives in the form, and the enthusiasm and ability of students to create are amazing. This fully shows that mathematics can really help children to "initially learn to use mathematical thinking mode to observe and analyze the real society, to solve problems in daily life and other disciplines and sciences, and to enhance their awareness of applying mathematics", and mathematical composition can let us clearly see that this goal of mathematics has been achieved by these children.

However, some students are insensitive and careless in observing mathematical problems. We should pay attention to guiding these students to discover the theme of mathematical composition in peacetime, and it is best to discuss the writing form together. Usually, the students' speech or performance in a certain part of the class is particularly wonderful, the dispute over a certain problem is particularly great, and a certain problem is creatively solved ... and so on, it can be mentioned that this is a good subject for mathematical composition. For example, Report on Counting Soybeans, Interesting Calculations, Crying of Numbers and Calculators, Regular or Calculator, etc. are all students' thoughts after class. When you get along with your classmates outside class, once you encounter something that can or must be solved with mathematical knowledge, you should spare no effort to remind and help: what mathematical knowledge can be used to solve this matter, how to solve it, and how to express it in mathematical composition. For example, calculating the total distance skillfully, going to my sister's house, calculating the departure time, and whether this is economical or not are all excavated in chatting and laughing with students. In addition, before the third weekend of each month, students are reminded that it is almost the time to collect mathematical compositions once a month. Although there is no proposition or indefinite requirement, students can be consciously reminded that some "tidbits" and fragments in mathematics classes this month can be recorded by mathematical compositions, and which activities in schools or classes contain mathematical problems, such as "I Explain Equations", "Interesting Natural Numbers" and "Experimental Reports".

The student has written a mathematical composition under the guidance of the teacher. After being affirmed, it will greatly stimulate his interest in continuing to write, and this interest will enable him to carry on the next article with a goal and desire to finish it independently, thus forming a benign development process from scratch to many. However, we must pay great attention to the discretion of giving and helping in this process.

2. Combination of guidance and self-correction.

Students have spent their rest time and worked hard to write their math composition. As demanders, they must take it seriously. This is not only a respect for students' labor, but also an affirmation and encouragement for the quality of students' math composition. Therefore, after receiving the students' mathematical compositions, the first thing to do is to read them carefully and look for "bright spots": the theme, writing techniques and length are also ok. In short, we should find good places to fully affirm and praise them, especially for students who are hard to write, and we should publicize them in a big way to be worthy of the students' hard work. Of course, appropriate guidance is also essential. The main purpose is to further stimulate students' critical thinking consciousness, broaden their horizons and improve their thinking level. Then, according to the comments after the article, they will communicate with students individually, and on the basis of students' understanding of the teacher's views, they will negotiate to revise the article, and then let students revise it independently. If there are still problems, they will negotiate and revise it again, so as to make every math composition clear. Of course, this process will be very arduous, so generally, 6~4 students should be guided by this method every month, and three levels should be taken into account every time, so that almost every student should have at least one decent math composition after one semester. The rest is to ask students to revise carefully according to the teacher's comments and then communicate with their classmates.

3. combine presentation with communication.

Students' mathematical composition can be said to be a combination of wisdom and ability. It is certainly not enough for teachers to appreciate it. If more people can appreciate their works, they may be inspired to write more. To this end, students' works can be displayed and exchanged through the following methods.

(1) Presentation and communication in class

Students can have a platform for presentation and communication in their math compositions.

All mathematical compositions can be displayed on the wall newspaper and blackboard newspaper, and students who read them are required to evaluate them. They can either write on the displayed manuscript or communicate with the author directly. This process should improve both what they read and what they read.

some representative, typical and conditional electronic texts can be compiled into tabloids after careful comments by teachers, and printed and distributed to each student, so that the students can take them back to enjoy and comment with their parents. In addition to the parents' affirmation, they hope to get their parents' support and help ―― outside school, students can often be reminded to pay attention to the discovery and application of mathematics.

Because parents should also participate, after each math composition, the teacher's comments must be accurate, pointing out the characteristics and strengths of the article, which is convenient for parents to understand. (Attached to the text)