Mathematics experiment is an important way of learning, which is required by the new mathematics curriculum standard 20 1 1. This fully affirmed the importance of mathematics experiment as a learning strategy. It is precisely because of hands-on operation, repeated observation and independent thinking that embodied thinking (action thinking) is started, which promotes the smooth development of image thinking and abstract thinking. Yu Ping, a professor at Nanjing Normal University, believes that the image thinking produced by sensory perception and the development of abstract thinking, the core literacy, are inseparable from action thinking. Embodied thinking is also called embodied learning, which is inseparable from hands-on operation, experimental verification and practical activities, and is the result of repeated use of hands and brains, operational observation and meaningful thinking. Action thinking is inseparable from the active participation and coordinated development of various senses, and the concrete and sensible cognitive imagination formed on this basis is inseparable from practical activities, which is embodied thinking. It can be seen that the process of mathematical experimental learning not only accumulates the experience of mathematical activities, understands the formation process of mathematical thinking methods and mathematical knowledge, but also lays the foundation for forming certain problem-solving skills, accumulating cognitive emotions, stimulating learning interest and establishing scientific learning concepts, and also makes a good start for the development of image thinking and abstract thinking. The following papers are elaborated with specific examples, and more readers are invited to think and learn.

First, mathematical experiments, meaningful understanding of concepts, properties, theorems

Mathematical experiments are generally simple, adaptable to local conditions and not restricted by conditions. As long as you are good at conscientious preparation, make full use of the conditions around you, operate with your hands and think with your head, it is very beneficial to understand mathematical concepts, properties and theorems. For example, the establishment of classical probability concept is easy to learn through simple calculation, but the connotation of probability is not so simple to understand and needs mathematical experiments. Each person throws a coin, throws a towel on the table for 20 or 40 times, draws the word "positive" to record the throwing results, then cooperates in groups, summarizes the research, communicates with the whole class, and finally counts the data of hundreds of throwing results, so that the possibility of throwing coins face up is close to half. So as to approximate and accurately express the changing and developing law of events with probability, gain a deep understanding, and fully realize the unchangeable thinking method in the change.

For another example, there are 400 kinds of pythagorean theorems, and the area proof method is the most. It is not difficult to get Pythagorean theorem by guiding students to make a "chord diagram" with four congruent triangles, constructing identities with different area calculation methods, and expanding and simplifying with multiplication formula. I feel very comfortable when I do it myself and deduce the relationship. I can use it freely, remember it unconsciously, and use Pythagorean theorem to solve problems naturally, so I have a good learning effect.

Mathematical experiments that help to understand the theorem of conceptual nature are shortcuts to teaching and not teaching, the necessity of understanding and loving mathematics, and the path to stimulate learning interest, learning mathematics and learning mathematics.

Second, mathematical experiments, meaningful mastery of mathematical thinking methods.

The purpose of learning mathematics is to meet the requirements of "four basics", to understand and master basic knowledge and skills, to understand and master basic mathematical thinking methods, and to experience basic activities. Empty preaching and simple repetition are obviously useless, and there is no need to try to create experiments. After the experimental activities, teachers should not suffer, and students will naturally get the message.

For example, the seventh edition of Suko Edition uses equations to solve practical problems. There is such a problem that Xiaohong and Grandpa run in the same direction from the same place along a 400-meter circular runway at the same time. The speed relationship between them is known, and the time of the first chase is also known, so we can find their speed. Here, the key of the equation is to construct equivalence relation, and the granddaughter runs a whole distance more than grandpa. This quantitative relationship confuses some students, so they will be grouped in groups of four on the playground to guide students to do chasing and sports experiments and remember their laps. As a result, everyone is interested in repeated experiments, not afraid of failure, not afraid of repetition, and enjoys it. In fact, some people walk, some run, some run along a circle, some run along a rectangle, and some run along a semicircle. The result is the same. Fast runners are much slower than slow runners.

Another example is profit and loss problem, who generally explains methods and sets of formulas to calculate. He knows how to do it, but he is bored and doesn't understand the principle of solving problems, which makes people very uncomfortable. The author adapted the problem into two parts and a complete scheme, and the result is easy to understand. For example, a bag of candy is given to several children, and each child has 3 pieces left; Five dollars each. Five dollars is missing. How many children and sweets? Think of it this way: when you start to divide the candy like this, everyone has 3 pieces left, and the rest of the candy will continue to be divided, and everyone will be divided into (5-3)2 pieces, which will meet the requirements of the second distribution. Let's divide the remaining three pieces first, which can be divided into 1 person. But we know that we still need to buy five pieces. When we divide them into three pieces, there is still one piece left, that is, six pieces to be divided, just enough to share.

Students' enthusiasm for learning, meaningful understanding of mathematics, analogy, transformation, logical deduction, and the combination of mathematics and thinking methods have changed their understanding of mathematics learning. They like and love math learning.

Third, mathematical experiments, meaningful discovery and problem-solving learning.

Mathematical experiments, hands-on thinking, repeated observation and emotional bedding often give birth to many unexpected teaching wisdom, which makes people feel sorry. For example, the multiplication rule of rational numbers and the understanding of "negative is positive" can guide students to operate, restore the problem situation, make mathematics problems come alive, and arouse students' curiosity and confidence in learning mathematics well at once. Everyone is standing, which is equivalent to the water level pole standing upright and moving hands up and down, which is equivalent to the fluctuation of water level. The water level rises (falls) 4 cm every day. What was the water level three days ago (after)? According to the number of centimeters that change every day, the number of centimeters that increase every day is+4 ",and -4 means the number of centimeters that decrease every day; It is not difficult to calculate the relationship from the water level change results of about 3 days.

By analogy, students are grouped to construct many formulas of negative number × negative number = positive number and negative number × positive number = negative number. Then it classifies and induces, and deduces the rational number multiplication rule, especially the rule of understanding "negative is positive". When the students were studied by their own discoveries, their eyes sparkled with joy. The efficiency of effective learning in class is very high.

We should carry out mathematical experiments, let embodied thinking take root, change the implementation scheme of indoctrination teaching, persistently and effectively change the way of mathematics learning, understand mathematics and master mathematics through the coordinated development of hands-on, brains and perception, so as to observe the world with mathematical eyes, think about the world with mathematical thinking and express the world with mathematical language, and finally realize the core literacy goal of Lide Shu Ren.