1. Increase the hands-on ability.
Leading students to carry out math activities often can undoubtedly improve their practical ability. In recent years, Chinese students are among the best in many international comprehensive mathematics tests, but the practical ability to solve practical problems ranks lower (How China People Learn Mathematics has a detailed introduction to this, and interested teachers can refer to it). Practical ability is also one of the mathematical abilities. Therefore, teachers should pay more attention to students' shortcomings in this respect, consciously and systematically design mathematics activities, guide students to understand the relationship between mathematics, feel the integrity of mathematics, constantly enrich problem-solving strategies, and gradually improve students' hands-on operation ability.
For example, mathematical activities can be carried out: making model trains.
(1) Requirements: Make four car models.
① Cuboid carriage, ② Cylindrical carriage, ③ Prismatic carriage, ③ Elliptical column carriage.
(2) Steps: ① Drawing: Drawing a three-dimensional diagram and a plane development diagram (determined by oneself according to a certain size); ② Copy the figure on a piece of hard paper, cut it with scissors (be careful not to leave the pasted edge), and then fold and paste it.
Homework: Complete a train model with a round roof.
For another example, students like to play the game of "clapping hands" to see who can react quickly and hit each other's palms. Teachers can set up a math activity according to this game: test reaction ability.
Content: method of grasping the ruler: work in pairs. ① Separate the thumb of one hand from the other four fingers, and prepare to hold the ruler. (2) companion will ruler upright, zero scale at the bottom, aimed at your thumb and other four fingers apart, and your thumb at the same height. Without knowing it, the companion suddenly let go and the ruler fell. You should grab the ruler as quickly as possible: ③ Record the scale on the ruler when you grab it (l cm, that is, you grabbed it after your straight foot fell l cm); (4) Repeat the experiment 10 times, record and sort out the obtained data, and take the average value (repeat the experiment to increase the sample size); ⑤ Calculate your reaction time (that is, the time from seeing the release to reacting to the ruler).
These interesting mathematical activities or problems are beyond students' original cognitive structure, but they can be solved through thinking. Moreover, hand-made mathematics can be materialized and revealed, thus making mathematics learning interesting and creative and making students taste the joy of success.
2. Enrich students' mathematics background.
The mathematical knowledge that students have learned is the result of systematic arrangement and processing. In order to meet the age characteristics of students, a lot of mathematics knowledge is omitted. Therefore, the students' mathematical background is not rich. In order to solve this problem, teachers can adapt some famous mathematical topics and classic mathematical models to design mathematical activities, which is very beneficial to enrich students' mathematical knowledge and infiltrate mathematical thinking methods.
For example, Mobius brought his students into contact in primary school, but none of them really started to study, so teachers can design math activities: exploring Mobius belt.
Objective: To perceive Mobius zone.
Requirements: (1) Cut two pieces of paper and paint both sides with red and blue colors;
(2) draw a line segment with the same color on both sides in the middle position;
(3) respectively making two pieces of paper into an endless belt and a Mobius belt;
Question: (1) What's the difference between ants crawling on two belts? Why?
(2) Cut the Mobius belt with scissors, and what do you get?
(3) What will happen if we continue to cut in two ways? Exploring ancient classical mathematical models like this can not only improve students' problem-solving ability, but also expand their mathematical knowledge and enrich their mathematical background knowledge.
3. Feel the beauty of mathematics
Teachers often say that cultivating students' mathematical aesthetic ability can be implemented concretely, but there is no feasible way, so we can only shout slogans in vain. In fact, mathematical inquiry activities are a good way for students to truly understand the beauty of mathematics. Teacher Zhang Siming, a special-grade teacher in the middle school affiliated to Peking University, has made great achievements in leading students to carry out mathematical modeling. He once mentioned an example. Ask the students in Grade One to find out 1/7,113,1/7, 1/23, 1/29,/kloc-0 with a calculator. 1428 57 142857 ..., I can see that there are only six round festivals, but by117, there are 16 round festivals, which cannot be displayed. At this time, the teacher didn't tell the students what to do, but let them explore again. Teacher Zhang did it for a week. They found some interesting laws, such as117, which is 0,0588235294117647, 16. There are round knots, and the middle is across the board. The first eight digits and the last eight digits add up to exactly eight nines. A cyclic node of 1/29 is 0.0344827520689651724137931,with 28 bits, and the middle 14 bit is cut off, which is14+. Sometimes it is like a hidden poem, such as 1/243, which is converted into decimals, and the cycle section has a sense of mathematics rhythm, which makes students feel that mathematics is beautiful.
Senior one students also put forward such a question: "Teacher, can a 99 88 square calculator count?" "But the calculator clearly shows 1, why? Is the calculator wrong? " In the process of this research, the students also wrote down their feelings, and several of them were like this-"I am very excited and excited, but I am happier. What are you happy about? I didn't do it in elementary school. Very interesting, but I really didn't know how to do it at first, and I have to study it carefully in the future. " "I think the calculator is just a few keys that everyone can use, but it's different now, so mysterious and interesting. I'll study it again." This is the motivation, attracting students to take the initiative to learn mathematics, is to feel the charm of mathematics, which is also the charm of mathematics activities.