Cognitive Test Instruments to Measure Student Mathematics Ability in Elementary School: Rasch Analysis

Abstract

The purpose of this study was to describe the quality of cognitive instruments to measure students' ability in mathematics at the elementary school level. Quantitative type research to validate the mathematical test instrument on fractional arithmetic operations material which has 22 items. The purposive sampling technique was obtained by respondents totaling 65 students from 3 elementary schools in Yogyakarta, Indonesia. The Rasch Model analysis reveals that item validity corresponds to the MNSQ outfit (0.59 to 1.57), ZSTD outfit (-1.04 to 1.65), and Pt Measure Corr. (0.50 to 0.70) are met. The reliability of the instrument was fulfilled based on the aspects of person reliability (0.83; 2.23), item reliability (0.82; 2.15), and CA (0.93). There are two questions with high difficulty Q7 (δ = 1.42) and Q12 (δ = 1.09), 17 questions in the medium category, two questions in the easy category, namely Q22 (δ = -1.20) and Q8 (δ = -1.72), and one question very easy category, namely Q12 (δ = -2.14). The DIF analysis showed that all items did not contain a gender bias (ρ = 0.057-1.00), so there was no difference in the level of difficulty between men and women working on cognitive test questions. Cognitive test instruments are prepared according to national competency standards for grade five elementary school material levels that can be used as good quality question banks.