Given the centrality of angle in mathematics curricula and scarcity of research in this area, we investigated 64 PTs' assimilatory domains of angularity by analyzing the angles they indicated when presented with four segments mutually sharing an endpoint. In both interview and written settings, we found PTs were more likely to recognize convex…

This paper examines the possibilities of designing a formative assessment that gathers information about novice elementary teachers' skills with modeling content and makes sense of such information. A decomposition of the practice of modeling content was developed and used to design the assessment. Participants included ten first-year teachers who…

This paper reports on a study of learners' use of immersive spatial diagrams to make arguments about three-dimensional geometric figures. Immersive spatial diagrams allow learners to use the movement of their bodies to control their point of view, while immersed in three-dimensional digital renderings. We present analysis of two pairs of…

Fraction proficiency continues to be a challenge for many learners of mathematics. Valid and reliable methods for assessing fraction understanding are critical tools in the pursuit of meeting this challenge. Written assessments have been widely used with K-12 students to assess fraction understanding, including units coordination. However, using…

Multiplication and division are vital topics in upper level elementary school. A teacher's pedagogical content knowledge (PCK) influences both instruction and students' learning. However, there is currently little research examining teachers' PCK within this domain, particularly regarding professional education of future teachers. To help address…

Increasingly, mathematics is being positioned as a tool to support students' understandings of social (in)justice and their own unique social positioning in the world. To this end, this study analyzes the impact of curricular reform efforts in an elementary mathematics content course. The course focused on fractions and statistics, and the course…

This research report describes a study that explored the intersections of professional noticing of children's mathematical thinking (PN), pedagogical content knowledge (PCK), and affective domains with preservice elementary teachers (PSETs). An instructional module on professional noticing, as defined by Jacobs, Lamb, and Philipp (2010), included…

As a component of a course on geometry for preservice elementary teachers (PSTs), we derive area formulas for a variety of polygons including triangles, quadrilaterals, and both regular and irregular shapes whose areas can be measured empirically using decomposition. Decomposing a circle to justify why its area can be measured using the standard…

In this paper, we describe an experience within mathematics teacher preparation that engages preservice teachers (PSTs) in Making and design practices that we hypothesized would inform their conceptual and pedagogical thinking. With a focus on the design of new tools to support mathematics teaching and learning, this Learning by Design experience…

We present a story of a teacher educator's response to a 'disturbance' and describe how her experience enhanced her personal mathematical knowledge and influenced her teaching. In our analysis we attend to different levels of awareness that support a teacher educator's work and illuminate the qualities of a teacher educator's knowledge, in…

The purpose of this review was to examine the 25-year period of research on elementary prospective teachers (EPTs) in mathematics content courses since publication of the "Curriculum and Evaluation Standards for School Mathematics" (NCTM, 1989). Analysis included an extensive electronic search and a manual search of 11 well-respected…

This study explored the problem solving experience of pre-service teachers in finding the greatest common factor and the least common multiple using many different approaches. In particular, it examined the effect of pre-service teachers' mathematics content knowledge on how they chose their preferred approach and how they valued the most…

Mewborn and Stinson (2007) explored three tasks implemented in a preservice teacher education program, which supported awareness of beliefs and reflection on teaching practice. In this study, we investigated one of these tasks, a single student mathematical field experience, to study its impact on learning and to determine its effects over time.…

This study explores the hypothesis that experience with children's mathematical thinking facilitates the development of teachers' professional knowledge. Multilevel models of a data set representative of US public institutions preparing K-6 teachers from the Teacher Education and Development Survey in Mathematics (Brese & Tatto, 2012)…

This paper describes a synthesis conducted to determine what research says regarding preservice teachers' understanding of fractions and identify the gaps in their existing knowledge basis. Specifically, this paper will address a smaller portion of the synthesis and report the findings from fraction multiplication and division topics. Results…