Characterization Of Middle School Students Math Problem-solving Research

Problem is the heart of mathematics. The key purpose of mathematical education is to develop the students' ability to solve the mathematical problems. In this article, firstly we won't only analyze the background of problem solving's production, but also sum up the domestic and international relevant theories in problem solving. We'll elaborate the importance and necessity of problem solving in our country's mathematical education reform and the significance of mathematical problem solving. Among them, problem representation is the core and key of problem solving, which is a hot topic in subject problem solving in recent years. In this article, the definition of problem representation is given. It explains the importance of problem representation and summarizes many scholars' achievements on subject problem representation and points out existent problems and shortages in mathematical course.According to Liao Bo-qin's & Xu Xing-chun's theory, a hypothesis is made on the representation system in the process of mathematical problem solving. With senior students as the subjects and using Protocol analysis, the study explores the dynamic character of mathematical problem solving and further studies the difference of problem representation between successful students and unsuccessful students. For finding out the condition of the students in mathematics learning, questionnaire and talking method are adopted. We have concluded the results as follows:1. The mathematical problem solving pattern of the students accords to the general pattern of problem solving, which have four stages: information feeling, situation representation, mathematical representation and operations.2. The representations for difficult problems of unsuccessful students are lack of efficiency.3. For the students with good knowledge structure, the representation speed is quicker while solving mathematics problems and the proper ratio is higher than others.4. For the simple problem, whether scene is acquaint or not, the senior students resolve effectively, and for the difficult problem, the diversity of problem representation is obvious between successful students and unsuccessful students.5. Many senior students are lack of interest in mathematical learning.Finally based on the above research, we analyze the influential factors of problem solving, and propose some teaching advices to improve students' abilities of mathematics problem solving.