Portraying mathematics teachers’ knowledge for teaching the addition of fractions through representations

Abstract

eaching the concept of fractions to students stays challenging, yet representations define an effective strategy to overcome such a challenge. Considering the impact of teachers’ knowledge on students’ achievement, this study aimed at portraying mathematics teachers’ knowledge for teaching fractions through representations, precisely, the addition process that remains a prerequisite to other operations. Hence, a purposefully selected sample of novice mathematics teachers was asked to propose a pedagogical activity through which the addition of fractions could be taught to early-age students. Later, their responses were analyzed through the study framework, which was developed by combining the five interrelated constructs of fractions with the types of activities used when teaching the addition of fractions. As a result, teachers’ knowledge was crystallized into three principal categories of utilizing the Part-whole, Measure, and Operator constructs. Furthermore, the related concepts of the unit and proportional equivalence, the fractional unit, including the iteration process, and the connection between addition and subtraction were discussed. Also, manners of representing (1) the added fractions and the result through two distinct models, (2) the added fractions and the result jointly in one model, and (3) only the added fractions emerged. These results provide a foundation for the professional development of mathematics teachers.