Cognitive diagnosis assessment of senior high second grade students’ mastery in learning the concept of plane equation

• Main Authors: Wei Kuang Liang, 魏光亮
• Other Authors: 蔡蓉青
• Format: Others
• Language: zh-TW
• Published: 2011
• Online Access: http://ndltd.ncl.edu.tw/handle/13922520716738343610

碩士 === 國立臺灣師範大學 === 數學系在職進修碩士班 === 100 === The purpose of this study is to use the cognitive diagnosis model to analyze the assessment data, so as to understand the senior high second grade students’ mastery of the concept of plane equation. Meanwhile, it is to investigate if there are significant differences between students of different genders and majors in terms of their mastery of each attribute. We further analyze how students with different numbers of mastered attributes perform in the mastery of each attribute, in order to conclude which concepts should be further strengthened for students with different levels of mastery. Finally, the students are clustered based on their cognitive mastery status to construct the hierarchical relationship between the attributes of cognitive learning in plane equation. We also investigate if there are differences in the hierarchy of learning cognitive concepts between students of different genders and majors. The sample of this study is 20 classes of second grade students, numbered 660 in total, in a senior high school in Taipei City, and these students are ranked PR92 in senior high school entrance exam. The main conclusions of this study are as follows: 1. About senior high school second grade students’ mastery of the related attributes of plane equation: (1) The performance of reciting the formula of the concept is better than that of understanding the concept. (2) The performance of the concept of perpendicular is better than that of the concept of parallel. (3) There is no significant difference between male and female students in their mastery of various attributes. (4) There is no significant difference between students with different majors in their mastery of “the representation of plane equation”. However, as to the rest of the attributes, the mastery of natural science majors is significantly better than that of the social science majors. 2. About the distribution of the number of plane equation concept attributes that senior high school second grade students master and the kind of concept attributes that different levels of students master: (1) Among the 11 concepts covered in testing, the largest proportion of the students fall in the mastery group of 10 attributes, and more than 80% of the students master more than half of the attributes of plane equation. (2) As for the following two attributes, “representation of the plane equation” and “The plane normal vector is vertical of the plane.” , the proportion of mastery does not increase for students with larger number of mastered attributes. (3) The concepts that students are expected to familiarize should be ordered. In remedial instruction, teachers should strengthen or prioritize the mastery of the concepts differently according to students’ various levels. 3. Hierarchical relationship between the concept attributes of plane equation: In this study, the first step is to construct a hierarchical relationship between the concept attributes of plane equation, and to find the different learning patterns in concept mastery of plane equation for students of different genders and majors. Finally, the study puts forward suggestions for senior high school teachers and future studies based on its main findings.