Development and Rasch Validation of a Mathematical Communication Skills Test for Indonesian Elementary School Students

In the world of education, a test is only as good as the questions it asks. For decades, teachers and researchers have relied on standard methods to judge how well a student understands a subject. These traditional methods work well for counting right answers, but they often struggle to measure something more subtle: the ability to explain why an answer is right. This is the realm of mathematical communication. It is not just about solving a problem; it is about the capacity to draw a picture of a situation, turn a real-world story into a set of numbers, and write down the logic that connects them. Without a way to measure these skills accurately, educators might miss the specific hurdles a child faces when trying to translate their thoughts into math. If a student can solve an equation but cannot explain the steps, or if they can draw a diagram but cannot link it to a formula, the standard test might simply mark them as "correct" or "incorrect" without revealing the true nature of their thinking.

A team of researchers in Indonesia set out to build a better tool for this specific challenge. They wanted to create a test that could reliably measure how elementary school students communicate mathematical ideas, using a sophisticated statistical approach known as the Rasch model. This method acts like a precise ruler that measures both the difficulty of the questions and the ability of the students on the same scale, ensuring that the results are fair and consistent regardless of which group of children takes the test. The researchers developed a twenty-five-question multiple-choice test designed for fifth and sixth graders. The questions were carefully crafted to cover three main areas: representing situations through pictures or tables, translating stories into mathematical symbols, and selecting the right written explanation for a solution. To see if this new tool worked, they administered it to 529 students across three schools in Southeast Sulawesi, ranging from boys and girls in fifth grade to those in sixth grade.

The results of the study were promising. The analysis showed that the test functioned as a single, unified measure of mathematical communication, rather than a confusing mix of unrelated skills. The questions were generally well-suited to the students' abilities, with the test proving highly reliable in distinguishing between different levels of skill. The researchers found that the test was fair; it did not favor boys over girls or sixth graders over fifth graders, meaning that a student's score reflected their actual ability rather than their gender or grade level. However, the data also revealed a specific gap. While the students performed well on questions that asked them to match pictures to stories or use simple symbols, they struggled more with the tasks that required them to build complex mathematical models or write out detailed explanations of their reasoning. The test was slightly easier than the average student in the sample, suggesting that while it could identify high-achieving students, it might need more challenging questions to fully stretch the abilities of the most advanced learners.

The researchers noted that two of the more difficult questions behaved a bit unpredictably, likely because they were so hard that students guessed or got confused, but these items were kept because they represented important, complex skills. Overall, the study concluded that this new instrument provides a solid foundation for assessing mathematical communication in Indonesian primary schools. It offers teachers a way to diagnose not just whether a child can get the right answer, but whether they can represent, model, and explain the math behind it. By identifying that students are stronger at simple visual tasks than at complex written explanations, the test points directly to where instruction needs to improve. The researchers suggest that future versions of the test should include easier questions to help identify struggling students and more difficult ones to challenge the advanced ones, but the current version stands as a validated, fair, and useful step forward in understanding how children learn to speak the language of mathematics.