An Investigation On Multi-Representations And It’s Transformation During Mathematics Problem Solving

Research on multi-representations has become a hot topic in fields of cognitive science, education, etc. Especially in the learning of mathematics, it is valued universally as an important part in the psychology of mathematics education. Problem solving is an effective way of cultivating students’ innovative spirit and practical ability. As for mathematics, proper representation and transformation is the key to resolve problems successfully. Therefore, it’s worthwhile studying the situation of multi-representations and transformation when students solve mathematics problems.Based on the research review, this paper reckon that there are mainly 3 representation types in the mathematics problem-solving of function part in compulsory module 1: literal representation, symbolic representation, and graphic representation. Representational transformation is divided into direct transformation and indirect transformation. Based on this, in the direct transformation, this paper mainly studied the transformation between each two of the three types; in the indirect transformation, it studied the essential process of problem solving which chose one of the three representation types as the intermediate presentation. Through student questionnaire and investigation on teachers and students, this paper concluded that:Whether direct or indirect transformation in mathematics problems solving, students have the preliminary ability of representation and transformation. Their performance has two features. On the one hand, transformation from symbolic representation into graphic representation performs better than transformation from graphic representation into symbolic representation in the direct transformation; while in the indirect transformation, they are not good at solving mathematics problems which involve graphic representation. On the other, their transformations lack equivalence. Students mainly have two different wrong ways. One is that they cannot understand the problem; the other is they cannot fully grasp the information reflected by the problem.In view of the current situation, combining with the data of the interview, this paper probed the reasons from the perspectives of students’ metacognition and teaching. Finally, it provided some commendations: we should strengthen teachers’ conscious and ability of using multi-representations and transformation, train students to use different ways of representation, and focus on equivalent transformation between them.