We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

This paper reports an ongoing effort to address the problem of instructional capacity for high school geometry from a systems improvement perspective. In an effort to understand the system that contains the high school geometry instructional capacity problem, we identified key stakeholders and conducted preliminary interviews to learn about the…

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…

Mathematics teaching is an inherently social activity, highly dependent on the lived experiences of its members. Drawing on sociocultural perspectives, we explore the mathematical lives of Latinx paraeducators to better understand the ways in which their backgrounds might influence their attitudes toward mathematics and mathematics teaching.…

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…

These proceedings are a written record of the research presented at the 41st annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) held in St. Louis, Missouri, November 14-17, 2019. This year's conference theme is "...against a new horizon." The papers comprise 67…

This paper reports on an ongoing project aimed at developing an inter-institutional system of professional support for the improvement of the Geometry for Teachers (GeT) courses that mathematics departments teach to preservice secondary teachers. In alignment with the literature on improvement science (see Bryk et al., 2015; Lewis, 2015), it is…

This working group addresses the challenge and opportunity presented by the use of simulations of teaching practice as an educative tool for preservice and practicing teachers. We focus particularly on the development of teachers' skills in enacting the content-intensive work of teaching, including how simulations may be able to cultivate or…

This study explores preservice teachers engaging in a ratio activity connecting the wages of men and women to the number of men and women in government positions. Mathematical learning expands the critical literacy framework reading and writing the word situating mathematics as the world itself. Furthermore, the bridging of mathematics, the self…

Although research and policy documents provide recommendations to inform secondary mathematics teacher preparation, no single study has addressed the "big ideas" of courses in multiple programs and how those big ideas may be interpreted through the lens of recent research and policy documents. To answer this need, we focused on big ideas…

Professional noticing of student thinking is considered a useful construct to investigate instructional decisions and activity made by teachers to support learning. This paper highlights the findings from one component of a multi-university (United States & Australia) research project focused on improving pre-service secondary mathematics…

Embracing the theme of this year's meeting, we seek as a community to consider the role of expansion, displacement, and growth in mathematics education in the privileging of some and marginalizing of others. Following on the topics discussed at the Working Group between 2009- 2018, this year the focus is on balancing the need to reflect and…

The emerging use of approximations of practice in teacher education calls for ways to document teacher candidates' (TCs') skill from their enactments and to determine how TCs' skill develops through such pedagogies. We highlight two cases of secondary mathematics TC development, connecting analyses of two types of approximations--coached…

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…