1) the connection of teaching ideas
In the stage of senior high school education in China, exam-oriented education still occupies a dominant position, which makes the teaching thought of senior high school mathematics stagnate, only emphasizes the hard instillation of mathematical knowledge, and lacks the cultivation of students' comprehensive ability and quality.
In the stage of higher education, higher mathematics teaching has always emphasized students' all-round development and focused on cultivating students' flexible application ability of mathematics knowledge, which makes it difficult for students to adapt to the changes in teaching environment and easily reduces students' mathematics learning effect.
Second, the connection between teaching content and street.
Due to the lack of unity and coordination between senior high school mathematics curriculum reform and advanced mathematics, the teaching contents of the two are out of line and repetitive.
For example, the inverse trigonometric function is not included in the teaching plan in high school mathematics, but it is often used as a basic elementary function in higher mathematics; High school mathematics does not need column coordinates and spherical coordinates, and advanced mathematics is directly applied as known knowledge; High school mathematics hardly involves hyperbolic function, integer function, symbolic function, etc., but it is often used in higher mathematics.
In addition, there are many overlapping parts between advanced mathematics and senior high school mathematics, including limit, integral calculus of unary function and differential calculus of unary function, which easily leads to the waste of teaching hours of advanced mathematics.
Third, the street connection of teaching methods.
The characteristics of high school mathematics are closely related to China's long-term exam-oriented education. The teaching methods of senior high school teachers are mainly explanation and practice. In this way, students can deepen their understanding of mathematical concepts or theorems, so as to master relevant problem-solving methods.
At the same time, high school teachers will also guide students in their spare time and conduct tests regularly to consolidate the knowledge points that are difficult to master. Although this method can improve students' academic performance, it will lead to students gradually losing their enthusiasm and initiative in learning, which is not conducive to their all-round development.
For advanced mathematics, teachers generally adopt the teaching method of drawing an outline and point to point, which is very different from the teaching method of high school mathematics, which leads to many students' inadaptability and unsatisfactory teaching effect.
Fourthly, the convergence of learning styles.
Most senior high school students use the methods taught by teachers in the process of learning mathematics, and only a few students sum up a set of their own learning methods on the basis of continuous thinking.
However, in order to cope with all kinds of tests and exams, students have to study according to the teacher's ideas, so students are always in a passive learning state. Higher mathematics requires students to have strong autonomous learning ability, and students will inevitably be uncomfortable in the process of transition from passive learning to active learning.