The Influence Of The Level Of Junior High School Students On The Representation Of Geometric Problems

This study took 183 students of grade two in a junior middle school in Nanjing as the research object. The first study mainly investigated the problem schema level characteristics of plane geometry through a questionnaire method of 183 students'two classification tests, and revealed the influence of the students' mathematics level, gender and the degree of problem-processing on the schema level in the process of problem-solving. The second study inspected the influence of the middle-school students'schema level on the problem representation of different types of geometric problem using the experimental method of 81 students' geometric test. The third study investigated the middle-school students' problem representation characterization in different auxiliary lines, using oral report method of 36 students' geometric test, and revealed the influence of students' schema level on the problem representation process, representation error and representation level.Results showed:(1) Junior middle school students' mathematics level had a significant effect on the schema level (F(2,168)=10.488, p<0.001), and the main effect of the degree of problem-processing was also significant (F(1,168)=8.779, p<0.01). While the main effect of gender was not significant.(2) Junior middle school students' schema level (F(1,79)=11.640, p<0.01) and question types (F(2,158)=11.891, p<0.001) had significant effect on the geometric problem representation score. The interaction of the schema level and question types showed significant effect on the geometric problem representation score(F(2,158)=3.212, p<0.05).(3) In the process of plane geometry problem representation, the schema level showed significant effect on the time of situational representation, principle representation and schematic representation. The main effect of the question types on the time of information perception, situational representation and principle representation was also significant.(4) In the error of plane geometry problem representation, the schema level showed significant effect on the information perception errors, reasoning errors and deviation errors. In different question types, students had no significant difference in the representation errors.The main conclusions were:(1) Junior middle school students' schema level was affected by the mathematics level and the degree of problem-processing. Middle-level and high-level mathematics students' schema level was significantly higher than that of low-level mathematics students. The deeper the problem was processed, the more students changed the classification, the higher schema level they showed.(2) Junior middle school students' schema level and question types had significant effect on the geometric problem representation. For high schema level students, the more complete the graph was, the simpler the auxiliary line was added, the higher the geometric problem representation score was obtained. Question types had little effect on the geometric problem representation score for low schema level students.(3) Junior middle school students' schema level and question types had significant effect on the geometry problem representation process and error. The higher the schema level was, the simpler the auxiliary line was added, the less time was spent and less error was made during the process of the geometry problem representation. On the contrary, students spent more time and made more errors during the process of the geometry problem representation.