Mathematics Reading Assessment Analysis Based on Clustering and Ordering of Factor Score

Yuan-Horng Lin ； Jeng-Ming Yih

《International Journal of Intelligent Technologies and Applied Statistics》 13卷2期 (2020/06) Pp. 101-113

https://doi.org/10.6148/IJITAS.202006_13(2).0001

摘要

The purpose of this study aims to diagnose the mathematics reading performance and structural features for sixth-graders. In this study, latent construct of mathematics reading includes three components which are based on the content area reading components provided by M. C. McKenna and R. D. Robinson. These three components of mathematics reading are general reading comprehension, prior knowledge of mathematics and mathematics-specific skills. The researcher develops the mathematics reading assessment with regard to real-life statistics. Based on the assessment data, the integrated methodology with three major steps are adopted to reveal students' performance and structural features on mathematics reading. The first step is the factor analysis and it shows there exists three factors with respective to the three components of mathematics reading. The second step is fuzzy clustering based on these three factor scores and it reveals that all the students are divided into four clusters properly. The final step is ordering analysis of each cluster in accordance with their factor scores to show their factor ordering structures. It indicates there are distinct features of factor ordering structures as to these four clusters. The major three findings of this study are as follow. Firstly, this study implements mathematics reading assessment based on theoretical foundation of three cognitive components. Secondly, the empirical data shows there exists four clusters on mathematics reading performance. Thirdly, there are distinct factor ordering structures so as to represent students' varied cognition of mathematics reading.

關鍵字

Clustering analysis ； Ordering theory ； Factor analysis ； Mathematics reading