PEMBINAAN UJIAN DIAGNOSTIK KOGNITIF BERBENTUK DUA-PERINGKAT UNTUK MENGENAL PASTI MISKONSEPSI OPERASI MUDAH UNGKAPAN ALGEBRA (Development of a Two-Tier Cognitive Diagnostic Test to Identify Misconceptions of Basic Operations of Algebraic Expression)
DOI:
https://doi.org/10.32890/mjli2026.23.1.9Keywords:
CDA (Cognitive Diagnostic Assessment), miskonsepsi, rasch, two-tier diagnostic test, ungkapan algebra, instrumen UDKOMUAAbstract
Tujuan – Kajian ini bertujuan untuk membina instrumen Ujian Diagnostik Kognitif Operasi Mudah Ungkapan Algebra (UDKOMUA) berbentuk dua-peringkat (two-tier). Matlamatnya adalah untuk mengenal pasti miskonsepsi operasi mudah (+, ‒, ×, & ÷) ungkapan algebra dalam kalangan murid tingkatan satu.
Metodologi – Kajian kuantitatif ini menggunakan kaedah tinjauan. Peserta kajian melibatkan seramai 107 orang murid tingkatan satu di sebuah sekolah menengah di Pulau Pinang. Model CDA (Cognitive Diagnostic Assessment) diaplikasi dalam proses pembinaan instrumen UDKOMUA bersama dengan Item Response Theory (IRT). Instrumen UDKOMUA mengandungi 24 item aneka pilihan dua-peringkat menunjukkan kesahan kandungan yang tinggi. Data murid dikumpulkan dengan menggunakan ujian UDKOMUA yang berkaitan dengan latar belakang dan item aneka pilihan ungkapan algebra berdasarkan empat operasi mudah (+, −, ×, & ÷). Data dianalisis dengan menggunakan model Rasch, untuk menentukan kesahan dan kebolehpercayaan instrumen UDKOMUA.
Dapatan – Analisis model Rasch perisian Winsteps menunjukkan instrumen UDKOMUA mempunyai 23 item (95.8%) dan 21 item (87.5%) mencapai keperluan MNSQ infit dan outfit. Varians reja terpiawai (PCA) mencatat 60.8% dan nilai polariti item (PTMEA CORR) dalam lingkungan .41 hingga .73 berjaya membezakan kemampuan antara responden. Nilai ujian-t dalam DIF (Differential Item Functioning) dalam lingkungan −1.75 hingga +1.47 menunjukkan tidak berlakunya bias dan skala kadar yang digunakan agak bagus dengan kiraan pemerhatian (observed count) paling rendah 13 pemerhatian. Indeks kebolehpercayaan responden, item dan Cronbach Alpha (KR-20) masing-masing bernilai .88, .92, dan .95 telah membuktikan instrumen UDKOMUA yang dibina mempunyai kesahan dan kebolehpercayaan.
Signifikan – Instrumen UDKOMUA yang dibina dalam kajian ini dapat digunakan dan dimanfaatkan dalam kalangan guru matematik tingkatan satu.
ABSTRACT
Purpose – This study aims to develop a two-tier Cognitive Diagnostic Test Instrument for Basic Algebraic Expressions Operations (UDKOMUA). The purpose is to identify misconceptions related to the basic operations (+, ‒, ×, & ÷) of algebraic expressions among Form One students.
Methodology – This quantitative study employed a survey method. The study involved 107 Form One students from a secondary school in Penang state. The Cognitive Diagnostic Assessment (CDA) model was applied in the development process of the UDKOMUA instrument, along with Item Response Theory (IRT). The UDKOMUA instrument consists of 24 two-tier multiple-choice items, and has demonstrated high content validity. Student data were collected using the UDKOMUA test, which included background information and multiple-choice items on algebraic expressions based on the four basic operations (+, −, ×, & ÷). Data were analysed using the Rasch model to determine the validity and reliability of the UDKOMUA instrument.
Finding – Analysis using the Rasch model of Winsteps showed that 23 items (95.8%) and 21 items (87.5%) had fulfilled the requirements in MNSQ infit and outfit. The standardized residual variance (PCA) was 60.8% and the item polarity value (PTMEA CORR) was between .41 to .73, which successfully differentiated the ability of respondents. The result of t-test in DIF (Differential Item Functioning) was between −1.75 to +1.47, which means showing no bias, and the rate scale used was quite good with the lowest observed count of 13 observations. The reliability index of respondents, items, and Cronbach Alpha (KR-20) was .88, .92, and .95 respectively. This has confirmed that the UDKOMUA and the result of study are reliable and valid.
Significance – The UDKOMUA instrument built in this study can be used and utilized among Form One mathematics teachers.
Keywords: CDA (Cognitive Diagnostic Assessment), misconceptions, rasch, two-tier diagnostic test, algebraic expression, UDKOMUA instrument.
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