A Study Of Geometrical Reasoning Ability Of Eight-grade Students

Students’ geometrical reasoning ability is receiving increasing attention from mathematics education at home and abroad, and mathematics teaching has attached importance to developing students’ comprehensive reasoning skills in geometry curriculum. The purpose of this study is to discuss the performance of eight-grade students in our country in geometrical reasoning level. This study uses "Usiskin test" and a self-developed "formulaic geometrical reasoning test" as research tools, choosing as study subjects371eight-grade students from several districts in China. We use percentage change, one-sample t-test, independent-sample t-test, two-way ANOVA, interaction effects, Chi-Square Test, etc, to shed some lights on students’ performance in the test and distributions in the geometrical reasoning level, in order to study the differences of the geometrical reasoning ability of students from various schools as well as of different genders in the test and to analyze students’performance in formulaic geometrical reasoning level in depth.The conclusions are as follows:1. The geometrical reasoning level from Level3to Level5express informal deduction,formal deduction and rigor respectively, and the total correct response rate of geometrical reasoning test of them, were:78.17%,46.74%and25.08%, with no discernible discrepancy between male and female students, while an obvious distinction between urban and rural origins is observed.2. The total distribution of the eight-grade students in the geometrical reasoning level exceeds Level3but not Level4, between the informal deduction and formal deduction. The distribution from Level3to Level5, were:48.79%,30.46%and6.47%,with5.93%belong to Jumping Level. Most distributions of the geometrical reasoning of students in Level4were of School A and D, while almost all in Level5were of School C. 3. Distributions of the geometrical reasoning level varies distinctively for students from3schools, in all three Levels. However, gender does not affect the distributions of the geometrical reasoning level.4. In the "formulaic geometrical reasoning test", the eight-grade students have low awareness of deductive argument. The pass rate for the subject with longer narration which requires careful demonstration is lower on the one hand, and the pass rate for the subject of reasoning about the nature and determination of special quadrilateral and reasoning about the relationship between different quadrilaterals is higher on the other.5. School and gender do not interact with each other in the "formulaic geometrical reasoning test", but the differences between schools are obvious. School C performs significantly better than the other schools, followed by School D, and School A is at the bottom of the list. But the differences among School A, B, D are not significant.An obvious distinction between urban and rural origins is observed while no obvious distinctions between different genders.