Validating the Cognitive Diagnostic Assessment and Assessing Students’ Mastery of ‘Parallel and Perpendicular Lines’ Using the Rasch Model

Abstract

‘Parallel and Perpendicular Lines’ is an important topic that serves as a basis for the learning of a more advanced geometric concept in later years. Yet, this topic is hard to master by the students. To pinpoint students’ weaknesses in this topic, this study sought to develop a cognitive diagnostic assessment (CDA) to assess students’ mastery of ‘Parallel and Perpendicular Lines’. The validation of the CDA and the use of CDA in measuring students’ mastery of ‘Parallel and Perpendicular Lines’ was documented in this article. The content validation involved two subject matter experts, while the pilot test involved 154 Year Four students from Kedah state of Malaysia selected using cluster sampling. The experts' consensus on the relevancy of test items was captured by calculating the content validity index. The psychometric properties of items and reliability of assessment were analysed based on Rasch Measurement Model. The validity of the assessment content was supported with an acceptable content validity index of 1.00 (>.80). The findings of Rasch analysis span across all ranges of abilities level and hence fit students’ competence well. With an acceptable person separation index of 1.58 (> 1.50), person separation reliability of .74 (>.70), and KR-20 coefficient of .78 (>.70), the CDA developed is reliable. The findings of assessing students’ mastery level highlighted their weaknesses in defining the properties of perpendicular lines and drawing perpendicular lines. The findings of this study would encourage practitioners to utilise it in the mathematics classroom for diagnosing students’ weaknesses and hence plan for remedial instruction.