1. Comparison between mathematics teaching and traditional teaching under the environment of modern information technology: Mathematics teaching under the guidance of cognitive construction concept has been strongly supported by modern information technology, which makes it possible for it to develop from an auxiliary teaching method to a cognitive tool for learners.

We can gain richer experience and more intuitive and concrete conceptual images in mathematical activities, which also provides better conditions for the reorganization of knowledge. There are many advantages in using information technology in mathematics teaching, but the problems that were difficult to solve with chalk and blackboard before are easy to solve. Using information technology can replace part of the blackboard writing of mathematical information, save drawing and writing time, increase classroom density, improve the efficiency of teaching and learning, and let teachers and students have more time to communicate.

Using the powerful computing function of the computer, a large number of data can be enumerated, so that students can fully understand its laws, guess correctly and find a solution.

Second, using modern information technology, plus teachers' elaborate lectures and inspiration, combined with students' independent exploration, questioning, questioning and discussion, students can draw correct conclusions through on-site intuitive feelings and careful observation, thus changing the past form of relying solely on teachers to "irrigate" and students' passive acceptance, effectively stimulating students' interest in learning;

The application of information technology can present the course contents that were difficult to present in previous teaching, and turn abstract knowledge into concrete and vivid knowledge. First, put forward the teaching objectives in class: ① make power function images when the index takes different rational numbers, and summarize the types of power function images;

② Induce the properties of power function. Drawing with geometric sketchpad is convenient and quick. As long as the students say the value of the index, images will appear immediately when using the courseware. After a while, various images appeared on the computer, and the students were very interested.

Soon, some students found that odd and even indexed images showed different types; Through their own experiments, students communicate and discuss with each other, and quickly find the law. On the basis of group cooperative learning, they revise it repeatedly, and correctly write out the period, value range and monotonous interval of the function. In this way, students not only gain knowledge, but also have more and more rich inquiry experience, and their ability of analysis and induction has also been effectively cultivated. This kind of inquiry activity is difficult to realize with traditional teaching methods.