An Investigation On High School Students’ Mathematical Concept Multiple-representations

Mathematical concept is the logical starting point of mathematics, is the core of students’ mathematical thinking, so it plays a very important role on mathematical learning and teaching. The research on multiple-representations was gradually became the theme of International Group for the Psychology of Mathematics Education. Attaching great importance to mathematical concept multiple-representations is mathematics learning psychology in the current development trend. The ability of high school students’ mathematical concept multiple-representations can reflect the situation of students’ mastering mathematical concepts well. The purpose of my thesis is to research the high school students’ current situation of the ability of multiple-representations for the mathematical concept, which can provide further practical guidance for learning and teaching of mathematical concepts.This study is based on the related literature at home and abroad, uses the unstructured questionnaire method to do empirical research. Take the angle, the increasing function, the vertical, the sine function, the equation root5concepts for instance to analyse the situation of mathematical concept prototype and multiple-representations of high school students. Take the rational number and the function for instance to analyse the high school students’ mathematical concept network situation. Attempt to explore the characteristics of high school students’ mathematical concept prototype and multiple-representations, the relationship between math score and multiple-representations ability, also the mathematical concept network and multiple-representations ability.Through the investigation and analysis, we get some conclusions, and based on these, putting forward some targeted teaching suggestions. The following main conclusions are:(1) Study shows that the characteristics of high school students’ mathematical concept prototype has two aspects. The one is the most high school students’ mathematical concept prototype sticking on the level of the first touching, they may hardly jumping to the higher level with the deep learning. The other one is that the specific graphs are the most high school students’mathematical concept prototype. The mathematical result and students’ mathematical concept prototype level have low correlation. Someone’s mathematical result is high, that is not to say his mathematical concept prototype level is high and vice versa.(2) The outstanding students’ mathematical concept multiple-representations have some features:representations’ level are higher; representations are rich and comprehensive; representations are more accurate and flexible. On the opposite, the features of the poor students are that the representations’ level are lower; representations are single, not accurate and stagnant. The mathematical result and mathematical concept multiple-representations result link close each other. Generally speaking, the better your mathematical concept multiple-representations ability is, the higher your mathematical result is and vice versa.(3) The situations of high school students’ representations on mathematical concept network can be divided on three aspects:first, the knowledge points are scattered, and they don’t have formed a system; second, the students can form a system with their studied knowledge, but those points mainly come from the textbook; third, the students not only can form relatively complete knowledge system, but also have broad knowledge and strong ability of expanding.(4) The outstanding students’ mathematical concept multiple-representations have better mathematical concept network, the poor students’ concept network are unconnected. Whose mathematical concept network is bad, his concept multiple-representations ability is also bad. However, whose mathematical concept network is good, his multiple-representations ability is not necessarily good.