Although research has delved into the challenges faced by mathematics teachers and students across various educational levels when working with fractions, these challenges persist. Fractions are an important but difficult content area in elementary school mathematics, and many future elementary teachers enter teacher education with limited knowledge of fractions. This lack of prior knowledge, combined with diverse experiences and attitudes toward the teaching and learning of mathematics, presents a challenge for teacher education programs aiming at enhancing prospective teachers’ knowledge to enable them to teach fractions effectively. Teacher education is a crucial time to attain a comprehensive pedagogical knowledge of mathematics, and this thesis characterizes prospective elementary teachers’ (n = 61) knowledge for teaching fractions as an outcome of Swedish teacher education. Through four empirical studies, the thesis also addresses the concept of mathematical identity and investigates the topic in light of the Mathematical Knowledge for Teaching framework.

The findings highlight substantial differences between the participants in the subject matter and pedagogical content knowledge domain of fractions, revealing difficulties in both their procedural and conceptual knowledge. Challenges also arise in analyzing different fraction solutions and combining knowledge of fraction content with knowledge about elementary students, teaching, and the national curriculum document. This difficulty can be a hindrance for the quality teaching of fractions. Moreover, incoherent fraction knowledge occurs across the different knowledge categories included in the Mathematical Knowledge for Teaching framework. The findings also reveal uncertainty in relation to work with fractions and prospective teachers’ mathematical identities. A new framework for the analysis of different aspects of fractions is also presented in the thesis, and the findings are discussed considering the context of Swedish teacher education and the Mathematical Knowledge for Teaching framework.