2.Literature review

 The concept of constructivism

Constructivism is a branch of cognitive psychology, and it is first introduced by Swiss psychologist Piaget in the 1960s. Meanwhile, constructivism also scoop the essence of various theories of learning theory, such as historical and cultural psychology theory of Lev Vygotsky, the meaning learning theory of Ausubel, and the discovery learning theory of Bruner and so on. Thus, it reveals the cognitive law of the human learning process quite well.

By referring to the relevant literature, we can identify some main principles of the constructivism as follows: firstly, Vgotsky(1978) stresses that constructivism takes students to the center, students are the main body of learning, the main body of cognition and information processing, and the active constructors of the meaning of knowledge. The amount of knowledge that students acquire depends on the learner's ability to construct knowledge based on their own experience. As a teacher, their mission is to help and promote student’s learning. Secondly, constructivism includes problem-solving: Doing mathematics does not mean only knowing to directly apply definitions, theorems and properties, but engaging in activities which require solving problems by utilizing these definitions, theorems and properties. Problem-solving allows students to construct concepts and to apply them to problematic situations. This therefore gives them an opportunity to go beyond given information or to develop their own ideas. The problem situations designed for students should reflect the real life outside the classroom. If its degree is well adjusted, students can easily use their abilities in other problem-solving situations. Thirdly, constructivism asks students to interpret and elaborate, this means that the learners should not be contented with being an active processor of knowledge, but they should interpret and elaborate upon the knowledge. What is expected from the students is to internalize knowledge by processing, but not to have the knowledge by accumulating.