高中二年級學生在平面方程式概念學習之認知診斷分析
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2011
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本研究旨在利用認知診斷模型來分析評量資料，以了解高中二年級學生在學習平面方程式的概念之精熟情形，並探討不同性別與不同類組的學生在各概念屬性的精熟是否有顯著差異。再依學生所精熟的概念個數，進一步分析程度不同的學生在各個概念屬性的精熟上有何差異，以了解哪些是他們下一步應該強化的概念。最後將學生依其認知屬性精熟狀況進行分群，以建構學習平面方程式的認知概念間的階層關係，並探討性別或類組不同的子群體是否在學習的認知概念階層有所不同。本研究選取台北市的一所高中二年級共二十個班級為樣本，學生素質為PR92，共計660個學生。
本研究的主要結果為：
一、高中二年級學生在平面方程式相關概念屬性的精熟情形
1.可透過公式的背誦去記憶的概念表現優於需要理解之概念的表現。
2.垂直概念的表現優於平行概念的表現。
3.男女學生在各概念屬性精熟度無顯著差異。
4.不同類組的學生除了在平面方程式的表示法的概念無顯著差異外，其餘各屬性自然組學生的精熟情形皆顯著優於社會組學生。
二、高中二年級學生在平面方程式概念屬性精熟個數的分布及程度不同學生在各概念屬性的精熟情形
1.在測驗所涵蓋的十一個概念中，精熟十個概念屬性的群體人數比例最多，超過八成的學生精熟平面方程式一半以上的概念屬性。
2.「平面方程式的表示法」及「與平面垂直的向量為平面法向量」這兩個概念屬性的精熟比例，不因學生所精熟的概念個數增加而有所提升。
3.學生對於概念的精熟應有順序性，對於程度不同的學生，教師進行補救教學時進行強化或優先精熟的概念應該有所不同。
三、平面方程式相關概念屬性的階層關係
本研究首先建構平面方程式的概念屬性間的階層關係，並發現不同性別及不同類組的學生在平面方程式單元的概念精熟過程不盡相同。
最後根據本研究的結果，提出有關教師在平面方程式單元的教學及未來研究的建議，以供參考。
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.
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.
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Keywords
概念屬性, 精熟程度, 精熟組型, 概念階層, attribute, level of mastery, mastery pattern, and hierarchy of attributes