Research On Mathematical Representation Means For Low Grade Students

To express problems is a chief approach to solve the problems, enhance students'abilities of mathematical representations is one of effective means to enhance their abilities to solve problems. And representation problems become one of the main subjects of researching human perceiving process.At present, domestic research on mathematical representations mainly concentrate on"problem representation", but how can a junior high school students use various representation manners to solve specific mathematical problems, the situation they master various representational manners, and researches on how to convert various representational manners between one another are rare. This paper integrate current home and abroad researches about primary classification of mathematical representations and actual situations of middle school junior students, classify mathematic representations into: word representation, symbol representation, figure representation and table representation. Investigate on grade six students'mathematical representation custom, diverse representation manners and choices of mathematical representation manners.The main problems of this paper's research are:1. Investigating research on grade six students'mathematical representation custom.2. What is the relationship between mathematic results and levels of representation manners.3. Whether levels of mathematical representation manners among top students, average students and bottom students vary obviously.4. What properties do top students and bottom students have respectively on representation manners.Collect original data via survey on grade six students'mathematical representation custom, diverse representation manners and choices of mathematical representation manners, then after doing analysis and statistics on the solutions of every question in every questionnaire, getting the following conclusions:1. During the processes of solving middle school junior students'math questions, the abilities of diverse mathematical representation manners affect the abilities to solve problems.2. Cultivate students'mastery of figure representation and table representation, forming good cognitive structure and mastery of thinking strategies of express problems.3. In general, top students'diverse mathematical representation bear more virtues, bottom students bear more deficiencies. Which means math scores and mathematical representations scores have strong connection, they link each other nearly. Math scores and mathematical representation scores affects and promotes each other, and cause and effect. Either the math scores affects levels of diverse representation or levels of diverse representation manners affects math scores, no matter which one does, the top one, average one and bottom one any two between the three groups play significant role in each other.Within the fundamental research, we bring the following teaching suggestions forward:1. Enhance students'abilities of mathematical representation have to combine with specific teaching behavior.2. Notice that use diverse cognitive theory to tutor students.3. Notice that the application of vision principle in teaching.4. Multidisciplinary along with the cultivation of abilities of mathematical representations.5. Teachers need to strength their own abilities.