A Cognitive Study About Open-ended Mathematical Applied Problem Solving Of Primary School Students

Modern education emphasizes the combination of education and life,mathematics application problem is based on the life practice background, canbest embody the combination of education and life. The world has attached greatimportance to the mathematical applied problems. The mathematics applicationand practice become the basic trend in the reform of international mathematicscurriculum. The open-ended mathematical applied problems also emerge in theinternational trends as the times require with the promulgation ina new roundof education reform and the implementation of new curriculum standards inChina,the modern mathematical education in primary schools pay more attentionto the cognitive psychology of individual learning, the relation betweenmathematics and reality, and advocate reflected the applied value on mathematicsbegan with students’ life experience. Therefore, the open-end mathematicalapplied problems appear more and more in mathematical teaching materials and allkinds of test. However, students solve the open-ended mathematical appliedproblems is lack of systematic research. Thus, the teaching in open-endmathematical applied problems is not optimistic, which emerged the phenomenonthat“teacher is difficult to teach while student is difficult to learn”.Learning open-ended application problems is helpful for students to cultivatedivergent thinking and creative thinking. As a teacher, we should make a beneficialexploration in teaching the open-ended mathematical problems. This thesis bases on the primary school students in eastern region ofGuangdong where has profound cultural background but backward economy andeducation. Through testing the students by five open-ended mathematical problems,we can analyze the cognitive characteristics of Guangdong students who solve theopen-ended problems from four cognitive processes which are the problemrepresentation, pattern recognition, problem solving transfer, problem solvingmonitoring. The major research findings as follows:1. A few students with good problem solving ability can fully experiencethe problem representation,pattern recognition, problem solving transfer,problemsolving monitoring these cognitive processes.2. Most of students’ comprehension ability is generally low, problemrepresentation is the weakest link in solving the problem, can not correctlycharacterize caused nearly half number of problem solving to failure.3. Most of the students’ problem solving thinking is not open,with theincreasing of the growth of the age and knowledge, increase students’ problemsolving strategies.4. Most of the students’ problem solving control ability is weak,they arenot good at self inspection and evaluation in the problem solving processthemselves.5. The primary influence factors of solving open-ended problem are cognitivefactors of students’ knowledge basics,the reading ability,problem solvingthinking and strategy and non-cognitive factors including mathematicalbeliefs,emotional attitude.Finally,in allusion to students’cognitive characteristics of solvingopen-ended application problems,this thesis sums up some teaching suggestionsand coping strategies.It is worth to mention is that due to the lack of theory and practicalteaching,this thesis still needs to be researched and developed more.