Preservice teachers conceptual and procedural understanding of fractions: Ethiopia as a case study

Abstract

This study investigates Ethiopian preservice teachers’ procedural and conceptual knowledge of fractions, examining their capacity to execute mathematical operations and interpret underlying principles. Despite the foundational importance of fractions in mathematics, challenges persist in bridging the gap between procedural competence and deep conceptual understanding among educators. Using APOS (actions, processes, objects, and schemas) Theory as a framework, this research examines how preservice teachers progress through the action, process, object, and schema stages when solving fraction problems. A mixed-methods design was employed, combining quantitative analysis of the test performance of 90 preservice teachers with qualitative insights from interviews and focus-group discussions involving 5 preservice teachers. The study explored preservice teachers’ understanding of fractions, revealing progression from performing procedures (Action) to recognising patterns (Process), with few reaching abstract conceptualisation (Object). This highlights cognitive gaps and emphasises the need for instruction supporting transitions across APOS stages. The participants were good at following steps, but they did not fully understand important ideas like the equivalence of fractions, division, and part-whole relationships. Common problems included confusing numerator and denominator roles, misinterpreting fraction division as the division of whole numbers, and relying on memorised algorithms without contextual understanding. These knowledge gaps were made worse by cultural and educational factors, such as a focus on memorisation and a lack of visual or real-world applications in the curriculum. Collaborative learning environments and reflective discussions are proposed to foster schema development by connecting fractional concepts to broader mathematical systems. These recommendations aim to enhance teacher preparation programmes, thus addressing Ethiopia’s systemic challenges in mathematics education and improving classroom outcomes. By highlighting the interplay between cognitive development, cultural context, and instructional practices, this research contributes to global efforts to strengthen mathematics teacher education.