APOS Theory-Based Learning: Impact on Mathematical Problem-Solving Skills

Learning is a fundamental process aimed at enhancing students' cognitive abilities, with particular emphasis on the development of problem-solving skills in the context of 21stcentury education. One instructional approach that supports this objective is the APOS theorybased learning model. The APOS theory, consisting of the components Action, Process, Object, and Schema, provides a framework for understanding how students construct mathematical knowledge. The present study seeks to investigate the effect of APOS theorybased learning on students’ problem-solving abilities in the domain of probability. Employing a quantitative research design with a pretest-posttest approach, the study involved 31 eighthgrade students from Class VIII A at SMPN 4 Yogyakarta. The learning material focused on probability, and a set of test items was utilized to assess the students' problem-solving skills. Data were analyzed using the N-Gain statistical hypothesis test to evaluate the extent of improvement in the students' performance. The results of the study indicate a statistically significant positive effect of APOS theory-based learning on the students' problem-solving capabilities. Post-intervention, students exhibited a deeper conceptual understanding of probability and demonstrated a more structured approach to problem-solving. These findings suggest that APOS theory-based learning can be an effective pedagogical strategy for enhancing students' problem-solving skills, particularly in mathematics. Consequently, the integration of APOS theory in teaching probability offers a viable instructional model that not only promotes mathematical comprehension but also fosters critical thinking skills essential for academic and real-life problem-solving.