This study focuses on the knowledge base that Swedish elementary student teachers demonstrate in their solutions for six routine fraction tasks. The paper investigates the student teachers’ common content knowledge of fractions and discusses the implications of the findings. Fraction knowledge that student teachers bring to teacher education has been rarely investigated in the Swedish context. Thus, this study broadens the international view in the field and gives an opportunity to see some worldwide similarities as well as national challenges in student teachers’ fraction knowledge. The findings in this study reveal uncertainty and wide differences between the student teachers when solving fraction tasks that they were already familiar with; two of the 59 participants solved correctly all tasks, whereas some of them gave only one or not any correct answer. Moreover, the data indicate general limitations in the participants’ basic knowledge in mathematics. For example, many of them make errors in using mathematical symbol writing and different representation forms, and they do not recognize unreasonable answers and incorrect statements. Some participants also seemed to guess at an algorithm to use when they did not remember or understand the correct solution method.

Fractions are core content of elementary school mathematics, and conceptual knowledge of fractions is essential when developing a comprehensive understanding of fractions. Previous research, however, has indicated  limitations in student teachers' fraction knowledge. This study investigated 57 Swedish elementary school student teachers' conceptions of fractions. The data were collected using a paper-and-pencil questionnaire and analysed with an analytical framework building on previous research on four core components of fractions. Using the devised analytical framework, we were able to characterise the conceptual content shown in the student teachers' answers and identify gaps in their fraction knowledge. The most severe gaps were identified in relation to interpretations of fractions, where only the part-whole and the quotient interpretations were identified; the measure, operator, rate, ratio, and number interpretations were missing completely. Aspects of fractions related to representations and procedures were better represented in the participants' conceptions of fractions, but we also illustrate substantial differences between the student teachers. In addition to this quantitative description, we provide qualitative examples. The results raise some questions and implications to be addressed in teacher education programs when developing student teachers' fraction knowledge.

This study investigates the pedagogical content knowledge identified in six prospective elementary teachers’ written teacher practicum reports. Focusing on the three categories of pedagogical content knowledge included in the Mathematical Knowledge for Teaching framework, the study analyzes the prospective teachers’ descriptions and combines their knowledge of fraction content with knowing about students, teaching, and curriculum. The results indicate that prospective teachers describe teaching and learning of fractions mainly on a general pedagogical level. Moreover, they do not differentiate characteristics for elementary students’ fraction difficulties and misunderstandings as well as fraction core contents in the curriculum. The findings are discussed in relation to the Swedish teacher education context in which the study was conducted. Implications for teacher education are also discussed.

This study investigates four Swedish prospective elementary mathematics teachers’ mathematical knowledge for teaching fractions. Using narrative inquiry, the study focuses on the prospective teachers’ reflections upon their mathematical identity and their analyses of six different solutions for a fraction division task. The results show that there are substantial differences between the prospective teachers in their mathematical content knowledge, pedagogical content knowledge, and in their attitudes towards mathematics teaching at the time of their graduation. Moreover, the prospective teachers expressed that teacher education did not respond to all their needs in their development as mathematics teachers. Thus, some implications for teacher education are also discussed in this paper.