Preservice teachers’ proficiency in fraction subconstructs as predictors of conceptual understanding in fraction arithmetic

The study aimed to determine whether the Kieren-Behr model holds true when examining the relationship between knowledge of fraction subconstructs and conceptual understanding of fraction arithmetic. Specifically, the study argued that the proficiency of pre-service teachers in fraction subconstructs can contribute to the development of conceptual knowledge in fraction arithmetic. It asserted that performance in problem-posing tasks, which reflect conceptual understanding, is significantly related to proficiency in different subconstructs of fractions. The proficiency of pre-service teachers in fraction subconstructs and their problem-posing performance were assessed using the expert-validated Fraction Subconstruct Test (FST) and Problem-Posing Test (PPT). The collected data were analyzed using descriptive statistics and standard multiple linear regression. Overall, the pre-service teachers only achieved a “beginning level” of proficiency in fraction subconstructs and performed unsatisfactorily in the PPT. Their proficiency in the measure subconstruct predicted conceptual understanding of adding fractions; their proficiency in the quotient subconstruct predicted conceptual understanding of subtracting fractions; their proficiency in the operator and quotient subconstructs predicted conceptual understanding of multiplying fractions; and their proficiency in the part-whole subconstruct predicted conceptual understanding of dividing fractions. The study suggests that teacher education institutions should develop intervention and enrichment programs to enhance the numerical competency of pre-service teachers, particularly in fractions. Additionally, curriculum writers are encouraged to emphasize mastery of each fraction subconstruct in order to promote successful development of conceptual understanding.