Adapting and measuring mathematical problem-solving ability among secondary school students: a Rasch model analysis

Abstract

Problem-solving ability are essential competencies that students need to develop from elementary education to higher education. However, in developing countries such as Indonesia, the assessment of process-based problem-solving skills remains limited. Educational practices in Indonesia still focus more on outcome-based assessment rather than evaluating the problem-solving process itself. Therefore, this study aimed to develop and validate an instrument for assessing process-based problem-solving abilities among lower and upper secondary school students. This study employed an instrument development and validation research design using a quantitative approach. The instrument was adapted from textbooks aligned with the Merdeka Curriculum, Indonesia's current national curriculum. After the validation stage, the instrument was tested on 322 secondary school students from three schools located in a city on the island of Java. The collected data were analyzed using the Rasch model. The results showed that all adapted items fit the Rasch model and demonstrated good validity and reliability. Item reliability was high, while person reliability was sufficiently consistent in capturing differences in student responses. Item difficulty levels were classified into easy (28.7%), moderate (28.7%) and difficult (42.86%) categories. Lower secondary students generally succeeded in answering moderate items, whereas upper secondary students were more capable of solving difficult items. Student abilities were grouped into low (4.66%), moderate (87.26%) and high (8.07%) levels. The instrument showed no gender bias, although most items displayed bias across grade levels, likely due to differences in students’ learning experiences. Overall, the Rasch model explained 44.7% of the variance, indicating that the instrument is unidimensional, valid and reliable for measuring process-based problem-solving ability that the instrument is suitable for research and assessment in mathematics education.