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…

This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

In this study, the middle school mathematics teachers' knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case…

Microcredentials are a promising means for expanding teacher access to high quality professional development. This study examined the effectiveness of online, self-paced microcredential courses designed for teachers working in underserved rural communities. The content of these competency-based microcredentials centered on recommended…

Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we…

In order to provide a transforming way of knowing for teachers' professional learning, this paper uses narrative to present the knowledge emerging from teachers as participants in a concept study derived from complexity science. There are three components in the narrative: what knowledge emerged from concept study; what has been changed for the…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient)…

This study investigates the problems posed by Turkish pre-service primary teachers and explores the issues they encountered while posing problems related to fractions. A free problem-posing task was administered to 98 pre-service primary teachers who are in sixth academic term, and task-based interviews were conducted with eight volunteered…

This research study, carried out in South Africa and the United States of America, investigated issues that may hamper prospective primary school teachers from writing acceptable problem posing scenarios involving the addition of fractions. Pre-service teachers (n=44) were asked to compose real life problems involving the addition of two fractions…

Discusses an attempt to promote the development of prospective elementary teachers' own subject-matter knowledge of the division of fractions as well as their awareness of nature and likely sources of related common misconceptions held by children. Indicates that before the described mathematics methods course, most participants knew how to divide…

Current reform documents in mathematics education recommend that teachers help students develop both conceptual and procedural understandings; however, teachers often do not possess the in-depth mathematical reasoning abilities necessary to accomplish this goal. Describes one way in which preservice teachers can come to better understand the…

Investigates preservice elementary school teachers' content knowledge and pedagogical content knowledge of decimal numeration. Indicates that most preservice teachers were aware of longer-is-larger misconceptions in students but had little awareness of shorter-is-larger misconceptions. Emphasizes content knowledge that integrates different aspects…