Analysis of Misconceptions in Algebraic Expressions through a Two-Tier Cognitive Diagnostic Test using the Rasch Model Wei Seng Khong, Hooi Lian Lim, Xiao Xue Liu Asia Pacific Journal of Educators and Education, 2025 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.
Misconception analysis for integer numbers by using rasch model , Wei Seng Khong, Hooi Lian Lim, and Asia Pacific Journal of Educators and Education, 2019 Diagnostic Test for Operations Subtraction of Negative Integer Number (UDOPNIN) is constructed to identify misconceptions among form one students on subtraction operations involving negative integer numbers. Distractor analysis in Option Probability Curves (OPC) through RASCH model in this study was to identify types of misconceptions among form one students based on students' ability. The survey research method is used in this study to determine the achievement of the objectives of the study. A sample of 572 Form one students from 11 secondary schools in Penang state involved in this study, consisted of 298 boys and 274 girls. The analysis validity and reliability of UDOPNIN instrument by RASCH model showed standardised residual variance (PCA) is 70.4%, the PTMEA CORR is between 0.12 to 0.68 provide the item can contribute to identify misconceptions of the respondents, 38 items (95%) is fulfil the requirement in MNSQ infit and 35 items (87.5%) is fulfil the requirement in MNSQ outfit, the result of t-test in Differential Item Functioning (DIF) for 40 items is between -2.0 to +2.0, and the value of Content Validity Index (CVI) for UDOPNIN instrument is 0.80. The OPC of 40 items in UDOPNIN instrument showed among the students' misconceptions on subtraction operations of negative integer numbers, majority of students who had problems of symbol misconceptions was because of pseudo-conception accommodation. The result of Winsteps version 3.57.2 showed that the item reliability index is 0.99 and the respondent reliability
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