Analisis Miskonsepsi Ungkapan Algebra melalui Ujian Diagnostik Kognitif Dua-Peringkat berasaskan Model Rasch (Analysis of Misconceptions in Algebraic Expressions through a Two-Tier Cognitive Diagnostic Test using the Rasch Model)
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Abstract
The Distractor Analysis based on Option Probability Curves (OPC) represents a systematic approach to identify students' misconceptions in basic operations of algebraic expressions. The cognitive diagnostic test was used in this study as an instrument to collect research data. The research instrument consists of 24 multiple-choice items in two-tier format. This study employed a survey method involving 1,029 Form One students from 10 secondary schools in Penang state. The content validity and construct validity of the research instrument recorded the lowest Item Content Validity Index (I-CVI) value of .83, Scale Content Validity Index/Average (S-CVI/Ave) value of .99, Scale Content Validity Index/Universal Agreement (S-CVI/UA) value of .96, with all 24 items (100%) and 18 items (75%) meeting the MNSQ infit and outfit requirements, standardised residual variance (PCA) recording 59.0%, PTMEA CORR values between .49 to .78, DIF contrast (Differential Item Functioning) values within the range of –.25 to +.26 logits, scale validity with the lowest observed count of 24 observations, instrument respondent distribution between –2.5 to +5.0 logits, and item difficulty distribution between –1.0 to +1.0 logits. The results of Rasch OPC misconception analysis revealed that among students demonstrating misconceptions in the basic operations of algebraic expressions, the majority experienced misconceptions in using algebra, and low-ability students did not understand concepts. This proves that most students faced assimilation pseudo-conceptions involving students' failures in basic operations between algebraic terms. The reliability indices of respondents (.92), items (.99) and Cronbach Alpha (KR-20) (.96) in this study demonstrate a very high level of instrument reliability and validity. Nevertheless, the findings of this study have limitations in terms of scope, time, and the topographical context of its implementation. In addition, the use of objective-type instruments may also restrict the types of student misconceptions identified in algebraic expressions.
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