Cognitive Research On Complex Mathematic Problem Solving Of Higher Graders In Elementary Schools

Closely connected to the developments of learning theories, CPS (complex problem solving) is an outgrowth from the development of the field of problem solving. It started from the inquiries on why problems are difficult to be solved in the early 1900s. Until the 1960s and 1970s, CPS had been dealing with some relatively simple and knowledge-lean problems. The researchers began to show their interests in how the subjects solved the knowledge-rich problems from the 1970s, and extended their studies to more areas in the 1980s, including reading, writing, calculation and lawyers reasoning. Since the mid-1980s, with the rise of situated cognition and learning theory, the experts from CTGV (Cognition and Technology Group at Vanderbilt University) have become interested in cultivating students' capacity of CPS and brought the research into a new phase by developing the famous Jasper Series. With the mathematics of elementary schools as a vehicle, the Series ground on situated cognition and learning theory and function in virtue of multimedia and network technology.Within the framework of problem solving phases deriving from the present cognitive psychology research, this dissertation focuses on cognitive research on CPS of higher graders in elementary schools concerned with the mathematics basing upon situated cognition and learning theory, while referring to the related studies of CTGV's Jasper Series.Specifically, situated cognition and learning theory is the underpinning of this dissertation. In order to make readers understand why situated cognition and learning theory rises inevitably, this research places it in the grand context of three revolutions of learning theory during the past century. And then, this dissertation defines the concerned core concepts, describes the development history of situated cognition and learning theory, explains its essential viewpoints from the competence perspective and introduces its practical application, i.e. the principal features and design principles of Jasper Series developed by CTGV. All of these consist of the literature review of this dissertation.The empirical study of this dissertation comprises three logically inseparable sub-studies. The first one surveys the perceptions of higher graders in elementary schools on solving mathematic problems. Both domestic and overseas relative studies indicate that most of them focus on perceptions on mathematics, while only few of them are pertinent to perceptions on mathematic problems solving specially. On the basis of literature reviews, this study investigated 412 sixth-grade students of an elementary school in Jin Hua, a city of Zhejiang Province by a questionnaire compiled by myself. The data shows that comparing with analogous studies, this study finds the subjects' perceptions on problems solving are inclined to what are considered appropriate on the whole. It is an exciting finding. Furthermore, this study surveys children's perceptions on the authenticity of problems to be solved, and finds more students think the problems are authentic than those in the domestic and overseas analogous researches. The reason resulted is most likely concerned with the new ideas proposed by the recent curriculum reform conducted in China.The second one is a cognitive analysis on students' mathematic CPS in higher grades of elementary schools, which is also the keystone of the research. The specially-designed testing questions are applied to 37 sixth-grade students of an ordinary elementary school in Jin Hua, and observations and post-test interviews are adopted to collect cognitive indexes. Generally speaking, all of the subjects can not achieve the desired scores, indicating these students who have been trained by solving simple problems for a long time are at a loss when they encounter complex problems. Specifically speaking, the top students (with excellent academic performances) are found to spend more time in solving complex problems than the middle ones who leave out more steps. Moreover, nearly one third of subjects including the top and the m...