Development of a test instrument to measure mathematical communication skills on the topics of three-variable linear equations and two-variable linear inequalities

Abstract

Mathematical communication skills are essential in helping students express, interpret, and solve mathematical problems. However, these skills are often underdeveloped due to a lack of targeted test instruments aligned with relevant mathematical content. This study aims to develop a valid and reliable test instrument to measure mathematical communication skills in the context of three-variable linear equations and two-variable linear inequalities. Using a development research approach with preliminary and formative evaluation stages adapted from Tessmer's model, the instrument was systematically designed, validated, and tested. Data were collected through expert reviews, student responses, and field testing involving 30 participants. Internal validation results indicated a very high validity score (92.80%), while field testing showed that 12 of the 13 developed items were externally valid. The reliability coefficient was 0.80, categorized as very high. The final test set included one easy item, nine medium items, and two difficult items, with discriminating power ranging from sufficient to very good. These findings demonstrate that the developed test instrument is both valid and reliable, and it effectively assesses mathematical communication skills with an appropriate balance of difficulty and item discrimination.