An analysis of the dimensionality of the SPM additional mathematics open-ended items using multidimensionality model for DIF framework
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Date
2007
Authors
Leong, Chee Kin
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Abstract
Test dimensionality is an important issue as it is related to test validity and reliability. It affects the test reliability estimates, its interpretation as well as the administration, scoring, and analysis of the data and more importantly, it affects the validity of the results obtained (Abedi, 1967). This study investigates the dimensionality of the Additional Mathematics open-ended items test. It was analysed exploratory utilizing the Principal Components Factor Analysis and model fitting in the Confirmatory Factor Analysis (CFA). The open-ended items test was verified exploratory to be multidimensional. This study then advocates the use of the Poly-SIBTEST’s Differential Test Functioning (DTF) analysis, which is based on the multidimensional and to identify the possible secondary dimensions involved. Additional Mathematics, a specialized mathematics is offered to students in Form Four and Form Five who are inclined towards the field of sciences and technology as well as social sciences (Kementerian Pendidikan Malaysia, 2001). These open-ended items are hypothesized to assess two distinct cognitive dimensions to supplement the dominant latent trait being measured, namely the mathematical communication and formal reasoning abilities besides the dominant construct, the general additional mathematics ability. This study investigates the DTF between proficient and non-proficient writers and DTF between formal reasoners and non-formal reasoners who are in Form Four and have completed their Form Four Additional Mathematics’s topics. This study also explores how the open-ended items test functions differentially for the various groups with different levels of writing proficiency and formal reasoning ability. The occurrence of DTF in these situations actually enhanced the construct validity of the test because according to the Additional Mathematics’ curriculum and syllabus, these two secondary dimensions are important components of Additional Mathematics’ ability. Both exploratory factor analysis and model fitting in the CFA as well as Poly-SIBTEST’s DTF analyses showed that the Additional Mathematics open-ended items test introduced two extra dimensions, namely the mathematical communication and formal reasoning, in addition to the general additional mathemathics ability. However, the presence of DTF influences the validity of inferences that is made on the test scores and having one test score reported leads to incorrect decisions and inferences being made about the examinees.
Description
PhD
Keywords
Education , SPM additional mathematics , open-ended items , multidimensionality model , DIF framework