Constructivism is a further development from behaviorism to cognitivism, which is developed on the basis of absorbing many learning theories, especially Piaget and Vygotsky's thoughts. Constructivism makes a scientific analysis of "what is the essence of learning activities" from a holistic and certain epistemological perspective. Although there are many schools of constructivism, we have the following understandings about students' learning: (1) Learning is an active construction process. Students do not passively accept external information, but actively and selectively perceive external information according to the previous cognitive structure to construct its meaning. (2) Textbook knowledge is not an accurate representation of reality, but an explanation and a more reliable assumption. Students' learning of this knowledge is a process of testing and adjusting these assumptions on the basis of understanding. Therefore, knowledge can be regarded as the rationalization of personal experience, rather than explaining the truth of the world. (3) The construction of knowledge in learning is not arbitrary, it has multi-directional sociality and interaction with others. In the process of knowledge construction, there should be communication and consultation, and there should be self-adjustment and correction. (4) Students' learning process is diversified. Because of the complexity and diversity of objects, the particularity of learning emotions and the uniqueness of personal experiences, students' construction of object meaning is also multidimensional. Constructivism learning theory has many meanings in guiding mathematics learning: first, we should look at mathematics from the viewpoint of constructivism. Mathematics itself is also the product of discipline construction, which should be the result of living, dynamic, open, multidimensional and not absolutely correct mathematical activities. This view of mathematics will directly lead to the change of mathematics curriculum view and teaching view.

Secondly, it needs to be emphasized that knowledge learning is a construction process, and learners' main role must be highlighted. The teacher's explanation can't directly transfer the knowledge to the students. Teachers can only make students actively participate in the whole learning process through their identities as organizers, collaborators and guides. In addition, we should pay more attention to the personalized characteristics of students' learning, so that they can get a reasonable personal experience in knowledge learning. But we should also see that the construction of knowledge is not only personal, but also social. Therefore, the interaction between teachers and students in the classroom and the activities of * * * are very important. "The formation of whole-body learning and the construction of classroom social environment and situation have become important ways to obtain mathematics learning results.

Third, several new learning ideas worth learning and learning from. Just as students' learning of knowledge is a discipline construction, people's understanding of the development law of learning psychology is also a discipline construction, which will inevitably form a diversified understanding of the development of learning psychology and promote the emergence of some new learning concepts. For example, Gardner's "theory of multiple intelligences" holds that everyone has more or less multiple intelligences (nine kinds have been put forward so far), and everyone has his own superior intelligence. It tries to promote the development of previously neglected intelligence by expanding the content field of learning and the representation of knowledge, and give full play to everyone's potential; Robert Jeffrey Sternberg's "successful intelligence theory" is successfully introduced into the scope of intelligence research, trying to evaluate intelligence from the perspective of whether the products of intellectual activities are successful in reality; "Communicative teaching theory" regards the teaching process as a communicative process, pays attention to the promotion of communication between teachers and students, and emphasizes the "self-realization" of students' personality ... All these provide us with a theoretical basis with more epochal connotation to understand the relationship between mathematics learning and physical and mental development from a newer perspective, a deeper level and a wider dimension, which is worth further study and discussion.