Answer: According to some examples that have appeared in mathematics teaching, there are the following basic types:

(1) intuitive. This is a common method for junior students. Ausubel thinks: "The essence of meaningful learning process is to establish a non-artificial and substantive connection between new knowledge represented by symbols and the existing appropriate concepts in the cognitive structure of learning." The so-called substantive connection refers to the connection between symbols and their concepts and the existing representations or concepts of learners.

When the experience or representation required by new knowledge is lacking by students, or it is too complicated to be clearly expressed in language, it is most appropriate to introduce it in an intuitive way.

(2) question type. The problem is a kind of contradiction, which naturally arises in the teaching process. This is the imbalance between students' cognitive structure and external stimuli. Although students have the psychological tendency to reverse the imbalance, they have no rational thinking and need the guidance and inspiration of teachers' questions.

(3) New and old contact types. The solution of a new mathematical problem is often inseparable from the old mathematical knowledge. The introduction of classroom teaching is a transition from mastering old knowledge to acquiring new knowledge, and also a transition from known to unknown. Therefore, deriving new lessons on the basis of reviewing old knowledge and establishing the connection between the old and the new are the most commonly used types of lead-in in middle school classrooms.

(4) interesting. Interest is the psychological tendency and motivation to know something and an activity, and it is the premise to start students' thinking. Guided by interesting stories or examples, students can be quickly grasped and brought into the artistic conception of the new curriculum.