The Impact of the Pirie-Kieren Theory on Developing Fraction Understanding in Third-Grade Students

Abstract

This study aims to examine the impact of applying the Pirie-Kieren theory to enhance third-grade students' understanding of fractions in Kosovo. Fractions are a foundational concept in mathematics, essential for both mathematical competency and general education. However, comprehending fractions remains a major challenge for students, educators, and parents worldwide, including in countries with well-established traditions in mathematics education. By incorporating the Pirie-Kieren theory into the design of instructional programs and textbooks, the content is structured in a coherent and logical progression. This method ensures that each learning unit builds on previously acquired knowledge, thereby transforming present learning into a strong foundation for future understanding. In Kosovo, where the introduction of fractions begins in the third grade, our study utilized an experimental design with a control group, involving a total of 148 students - 80 from experimental classes and 68 from control classes - across three schools in different regions. We started by conducting a detailed analysis of curriculum components and textbooks related to fractions, identifying several didactic-methodological shortcomings, including disorganized content, inadequate visual representations, and material that was not age-appropriate. In the experimental phase, we created detailed lesson plans for teachers and worksheets for students in the experimental groups, ensuring they were in accordance with the principles of the Pirie-Kieren theory. These materials were refined with input from experts and reputable organizations such as UNESCO, the State Department, NCTM, and OECD. The study also designed a specialized test to evaluate outcomes in both the experimental and control groups. The results were analyzed using various statistical methods to compare the performance of the two groups. The study findings reveal that teaching and learning fraction-related content through the Pirie-Kieren theory/model is significantly more effective than traditional instructional methods.