The Effect Of Field Cognitive Style And Schema Level On The Geometric Problem Representation

Problem-solving has been a hot issue in the field of cognitive psychology research.Currently more and more research on problem-solving focus on discipline problems.Plane geometry is an important part of junior mathematics.The improve of problem-solving ability of the student is an important target of geometry teaching.Problem representation is the key to problem solving,and the peoblem schema level of the student is also an important factor which affect the process of problem-solving and problem representation.This study take the students of grade two in junior high school as the research object.The first study mainly investigated the schema level of plane geometry of the student in middle school,revealed the influence of field cognitive style, the way of problem-guiding and the degree of problem-processing on the schema level of the students in the process of problem-solving.Based on the first study,the second study combined field cognitive style and schema level to investigate the characteristics of the geometric problem representation.The main results of the two studies are as follows:1.In the process of geometry problem solving,compared with field-independence students,field-dependence students'schema level is more affected by the degree of problem-processing.More field-dependence students change the classification criteria and showe higher schema level when the problem with higher level of processing.2.For Students in schema guidance, the degree of problem-processing have significant effect on the schema level.The schema level scores before solving the problem are significantly lower than the scores after solving the problem. The degree of problem-processing only have little effect on the schema level for Students in conceptual guidance.3.In comparison to low-level schema group,the high-level schema group prefer to use schematic representation.There is no difference between the two in the choice of literal representation and principle representation.There is no difference between field-independence students and field-dependence students in the choice of these three representation type.4.In the process of geometric problem representation,deviation errors is the most frequent errors.The low-level schema group have more errors in the process of problem representation than high-level schema group do.The field-dependence are more susceptible to the interference of irrelevant information than the field-independence,and have more information perception errors and deviation errors,but there is no significant difference in reasoning errors and schema-start errors between the two.5.The problem-solving performance of field-independence students is significantly better than the performance of field-independence students. The problem-solving performance of high-level schema group is significantly better than the performance of low-level schema group.When it comes to the three types of representation,there is a significant positive correlation between schematic representation and the problem-solving performance,but literal representation and principle representation have no significant correlation with the problem-solving performance.