Study On The Relationship Between Geometric Cognitive Structure And Geometric Reasoning Ability Of Ninth-grade Students

As a specific embodiment of the core competence of mathematics education in compulsory education at the junior high school stage,reasoning ability has always been one of the crucial competences pursued by China’s mathematics education,as well as a focus of other countries’ mathematics education and international large-scale assessment projects.Geometric reasoning ability,which is an essential dimension of mathematical core literacy,plays a significant role in the development of junior high school students’ mathematical abilities.By summarizing previous researches on reasoning ability,we notice that there are comparatively few empirical studies on factors influencing reasoning ability.Reasoning activities have to occur with mathematical knowledge,as an organic integration between cognitive structure and mathematical knowledge,the subjects of whether geometric cognitive structure has an impact on geometric reasoning ability and whether reasoning ability can be cultivated from geometric cognitive structure are worth exploring.This study contributes to the existing research on reasoning abilities and cognitive structures by focusing on the field of geometry and graphics.A framework was constructed for evaluating geometry reasoning abilities among junior high school students,which was used to create a Geometry Reasoning Ability Test Paper.Additionally,a Geometry Cognitive Structure Test Paper was developed using the CPFS structure theory proposed by Yu Ping.This study examines 129 ninth-grade students from a middle school in Zhengzhou.The data collected from the tests is analyzed using IBM SPSS Statistics 27 software so as to explore the level of geometry reasoning ability and the status of geometry cognitive structures among the subjects,as well as the correlation between the two factors.Through the qualitative analysis of responses situation,the thinking tendency and geometric cognitive structure characteristics of the ninth-grade students are judged when faced with geometric problems.Based on the findings,the study proposes educational strategies and design cases to enhance the development of geometry reasoning ability from the perspective of geometry cognitive structure.The conclusions drawn from this study are as follows:(1)The geometrical reasoning ability of the ninth-grade students is generally at an intermediate level,and there are obvious differences among different groups;the geometrical thinking of the ninth-grade students is between the informal deductive thinking level and the formal deductive thinking level of Van Hiele’s geometrical thinking theory;gender is not a significant factor affecting the ninth-graders’ geometric reasoning ability,but the reasoning achievement span of the girls is wider than that of the boys,and the performance variability of the girls within the low reasoning level group is significant;the ninth grade students are more inclined to use the properties of graphics to solve geometry problems,and the number and accuracy of problem-solving methods have a certain relationship with the students’ geometrical thinking level,but it is more likely to be expressed in the medium and low reasoning levels.(2)The vast majority of the ninth-graders’ geometrical cognitive structure is at an average level,and there are apparent distinctions among different individual students;the average scores and standard deviations of the cognitive structure of the ninth-graders’ boys are slightly higher than those of girls,but there is no remarkable difference between boys and girls in the overall difference comparison and the difference comparison of cognitive structures within different groups;the geometric cognitive structure knowledge reserve of ninth-grade students is not extensive and has a limited hierarchical,but lacking in wholeness.(3)There is a significant positive correlation between the geometrical cognitive structure and geometrical reasoning ability of ninth-grade students;the performance of geometric cognitive structure has a predictive effect on the performance of geometric reasoning ability,and the better the geometric cognitive structure,the better the performance in geometric reasoning.The regression equation between geometrical cognitive structure and geometrical reasoning ability of the ninth-grade students is Y = 0.548 X + 32.019.Some suggestions for improving geometric reasoning skills based on geometric cognitive structure can be given as follows:(1)In the process of teaching mathematics,the connotations of concepts shall be revealed from multiple backgrounds,aspects,dimensions and structures,and students ought to be guided to think in a multi-dimensional way,complete concept filed;(2)Sufficiently expose the process of mathematical thinking,enhance the horizontal and vertical connections between knowledge,and train students to think in a holistic way;(3)Based on geometric cognitive structure,guide students to think in a developmental perspective to improve their reasoning ability;(4)Innovating the format of reviewing lessons,changing from " emphasizing conclusion" to "process-oriented".The innovations of this paper are:(1)The framework for assessing geometric reasoning ability in junior high school students was constructed based on Van Hill’s geometric thinking theory and the objective requirements of the Compulsory Education Mathematics Curriculum Standards(2022 Edition)for fourth-grade graphics and geometry.(2)This study aimed to investigate the relationship between geometric reasoning ability and geometric cognitive structure by developing the Geometric Reasoning Ability Test Paper using the framework.(3)The study proposes a set of educational strategies and design cases to enhance the development of geometry reasoning ability from the perspective of geometry cognitive structure.