First, create interesting situations.
Appropriate introduction of interesting historical allusions, mathematical anecdotes and anecdotes of scientists in classroom teaching is very helpful to promote students' meaningful learning. For example, I told a story in the class "The nth Harmony in arithmetic progression":/kloc-The Taj Mahal, the Mughal emperor in the 7th century, used tens of thousands of workers to build a mausoleum with jewels in memory of his beloved wife Mutazhima. It is said that there was a triangular pattern in the mausoleum at that time, all of which were inlaid with rubies. One on the first floor, two on the second floor, three on the third floor, and so on * * * has one hundred floors. Excuse me, students, do you know how many rubies are in this triangle pattern? Because most students have heard stories like this (Gauss's reverse addition), that is, 1+2+3+…+ 100, they answered quickly. Although all the students know the result, after listening to this story, their curiosity is displayed, which stimulates their enthusiasm for learning and makes them willing to listen and participate. Student's answer: Add the first and the last, the second and the penultimate ... The fiftieth and the fifty-first add up to * * * fifty 10 1, so the result is 5050. Ask again: What if there are only ninety-nine floors? Students still add in reverse order, but only 49 10 1 are found, and there are 50 more. So the sum in this way should be divided into odd and even numbers. At this time, guide the students to draw an inverted triangle next to the triangle to form a parallelogram, so each floor is the same 10 1, * * 65438. Just divide the total by two (the two triangles have the same number of gems). If it is the 99th floor, the same treatment will do. We regard the first layer as the first term and the last layer as the last term, so that we can get the sum formula of the first n terms of arithmetic progression.
Second, the situation created should be close to life.
Hua, a famous mathematician in China, once said: "People have a dull and mysterious impression of mathematics, and one of the reasons is that they are divorced from reality." Introducing new knowledge from students' life experience can make students realize the value of mathematics, thus generating a strong thirst for knowledge.
Mathematics teaching should not only consider the characteristics of mathematics itself, but also follow students' psychological laws of learning mathematics, emphasizing the creation of life situations based on students' existing life experiences, so as to mathematize life problems (materials) and make mathematics problems live, thus arousing students' existing life accumulation and generating a sense of intimacy with mathematics, thus stimulating students' interest in learning mathematics. The creation of situation can make mathematical problems live, connect with students' real life, and make students participate in mathematical activities.
Thirdly, the created situation should start from the students' existing cognitive level.
Learning is a kind of personalized behavior, and it is a process in which students construct meaning on the original knowledge structure. Therefore, the creation of situations should fully consider learners' original knowledge and skills, learners' learning motivation and attitude, and learners' age and psychological development characteristics. On the basis of comprehensive analysis, create situations that conform to the law of learners' cognitive development and create diverse situations suitable for different learners' characteristics. It is necessary to use external stimuli in line with students' cognitive psychology to promote their assimilation and adaptation to new knowledge.
Fourth, the situation created should be thoughtful.
The problem situation should have certain mathematical connotation and sufficient mathematical information, which is conducive to students' thinking. Doubt and doubt can ignite the spark of students' thinking. The center of "learning guidance" lies in guidance, which leads to congestion and difficulties. Doing a good job of guidance can effectively promote the change of thinking state. For example, when using enumeration method to solve probability in teaching, ask: "A pair of dice, if the sum of the two heads is 265438, if the sum of the two heads is 7, then B wins;" Otherwise, no one will win. Do you think this game is fair? If you think the game is unfair, explain the reasons and design a fair rule. " In this way, students are immediately guided to a thinking situation.
Fifth, the created situation should be exploratory and challenging.
Situation is created to help learners understand and internalize the learning content. Different types of teaching content need different expressions and learning methods. At the same time, different types of situations have different effects on learning different types of content. For example, when explaining the pyramids in the course of "Simple Space Geometry", a scene is designed: with the help of multimedia, students can enjoy the pictures of Egyptian pyramids as tourists; In order to further arouse students' interest, this paper introduces the "magic power" of pyramids: more than 80 pyramids in Egypt have a mysterious power, which makes people or other objects produce strange effects. The temperature in the pyramid is very high, but the biological remains in it are not rotted, but dehydrated and dry. Some scientists went in to investigate, and after they went in, their electronic instruments broke down. Some scholars have also found that staying in the tower for a long time will make people insane. Blurred consciousness. Many scholars have done interesting experiments. They divided the same milk into two cups, one in the homemade pyramid model and the other outside. Two days later, the milk in the model was as dry as cheese, but the other cup was broken. The researchers later changed the experimental method, reduced the pyramid model, placed many models side by side on the table, and then put the experiment on the top of the model instead of inside. Observe the results again. Put a bottle of wine on it first, and it will taste sweeter after 8 hours. Then put a cigarette on it, it will smell better after 1 hour. Finally, do an experiment with orange juice, and it will change after 3 hours. After 5 hours, the orange juice will be deacidified and sweet. After 72 hours, the orange juice will be divided into three distinct layers, the upper layer is transparent, the middle layer is translucent, and the lower layer has sediment. The pyramids do exist. Why is it strong? So the students are talking about it, but our existing knowledge has nothing to do with pyramids, so we successfully introduced the research content of this lesson: pyramids. I think this design can make students learn and discuss independently, truly change the traditional indoctrination teaching into students' independent teaching, pay attention to students' hobbies, and cultivate their hands-on and brain-using abilities.
Mr. Ye Shengtao said, "Know what they need and like, discuss with them and solve the problems they face." In the teaching process, teachers should create practical teaching situations according to teaching needs, guide students at different levels to actively participate in the teaching process, organize and standardize classroom teaching with situations as the main line, fully mobilize students' initiative in learning, and promote the formation and development of students' inquiry ability. This is a very effective teaching method.