Reasoning about fraction magnitude is an important topic in elementary mathematics because it lays the foundations for meaningful reasoning about fraction operations. Much of the research literature has reported deficits in preservice elementary teachers' (PSTs) knowledge of fractions and has given little attention to the productive resources that…

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…

This paper examines the implementation of an instructional module on Preservice Elementary Teachers' (PSETs) professional noticing of children's mathematical thinking as defined by Jacobs, Lamb, and Philipp (2010). The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video…

Proportional reasoning is important to the field of mathematics education because it lies at the crossroads of additive reasoning in the elementary school and multiplicative reasoning needed for more advanced mathematics. This research reports on the representations used by pre-service teachers (PSTs) as they responded to tasks involving…

Numerous studies, including our own, have documented that teacher noticing interventions can be effective in developing teachers' abilities to notice salient aspects of the mathematics classroom. In this study, we explore how specific aspects of one such intervention may have supported three prospective teachers in learning to notice…

Effectively launching a task involves surfacing and addressing misconceptions so that students can make progress on the task. Launching a task is supported by teachers' noticing (interpreting and responding to students' thinking). We investigated the degree to which an intervention supported improvements in pre-service secondary teachers' (PSTs')…

This paper reports two prospective teachers' and a mathematician's ways of identifying similar triangles and hexagons through the analysis of routines, a characteristic of geometric discourse. The findings show that visual recognition was a common approach for the mathematician as well as the two prospective teachers. However, when asked for…

To interpret in detail the meaning-making in the classroom and the corresponding teacher semiotic mediation, we have resorted to Peirce's triadic ign theory, interpreted by Sáenz-Ludlow and Zellweger. We present an example of the use of a few elements of that theory in the analysis of a classroom episode in which meaning is constructed with the…

The study investigates the characteristics of prospective teachers' geometric discourses at the van Hiele model of thinking (1959/1985), using Sfard's (2008) discursive framework. In this report, I align two prospective teachers' pre- and post-van Hiele geometry test (Usiskin, 1982) results with the analyses of their geometric discourses from…

As creating and critiquing arguments becomes more of a focus in mathematics classes, teachers need to develop their abilities to facilitate productive arguments. Toulmin's (1958/2003) model of argumentation has been useful in analyzing arguments in mathematics education research, raising the question whether it would assist mathematics teachers as…

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…

A critical practice in teaching elementary mathematics is posing problems that build on children's mathematical thinking. As such, teacher educators must provide pre-service teachers (PSTs) with a set of learning experiences to support PSTs in this practice. In this study, we present our analyses of PSTs' responses to a sequence of three methods…

This paper presents partial results of a completed study which investigated the experience of teaching mathematics content courses to preservice elementary teachers. Interviews with ten mathematics instructors who teach these courses revealed several major tensions, including one that arises as instructors strive to set priorities and balance…

This study developed twelve instructional modules based on the National Assessment of Educational Progress for mathematics content and methods courses for preservice elementary and middle school teachers and examined their impact on PSTs' mathematical content knowledge and self-efficacy beliefs about teaching mathematics. The modules help…

While understanding children's mathematical thinking is an important part of what teachers need to know in order to be effective in the classroom, preservice coursework often fails to provide learning opportunities focused on this aspect of teaching. Using a videocase curriculum focused on children's mathematical thinking, the authors examined…