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 provides evidence on how elementary school students from a Mexican public school move from using an operational sense, expressed in computational strategies, to a kind of relational thinking based on structure sense ideas and expressed by number decomposition. Even though the results are somewhat preliminary, they illustrate how…

In this theoretical research report we reflect on the challenges of becoming more fox-like in mathematics education work. Using a communities of practice motivating theoretical lens, we compare and discuss the differences in defining, creating, and accessing knowledge between virtual and scholarly communities of practice in mathematics education.…

As the field of professional development for mathematics graduate students evolves, there is a need for research studies that examine how mathematics graduate students develop as teachers. This study aims to fill this gap in the research by studying mathematics graduate students' experiences with teaching as they progress through their graduate…

This research report will discuss mathematics specialists and the way in which they communicate ideas of equity and social justice within a master's program that leads to a state endorsement in mathematics education leadership. Many mathematics specialist programs focus on developing their mathematical content knowledge for teaching, but these…

Formulating a mathematical model is a dynamic process, and attending to changes in students' models as they engage in modeling tasks is critical for informing pedagogical interventions. In this report, we coordinate constructs from literature on mathematical modeling, quantitative and covariational reasoning, and semiotics to characterize changes…

I discuss how three preservice mathematics teachers' (PSTs') covariational reasoning supported the mathematization of a simple energy balance model (EBM) for global warming, and how such mathematization shaped PSTs' understanding of the link CO2 pollution and global warming. I use Thompson & Carlson's (2017) levels of covariational reasoning…

In mathematics classrooms, teachers are often the authority as a knower of mathematics. To support students to develop their identity as doers of mathematics, teachers need to decenter the authority and to place students in a more powerful position as autonomous thinkers. Building on the work of Herbel-Eisenmann and colleagues (2013), this paper…

As teachers shift their practice from traditional student-to-teacher interaction patterns to collaborative discussions around rich mathematics, they often encounter instructional challenges. One such challenge is deciding when to pursue interesting and productive ideas that run contrary to the particular mathematical goal of the lesson. In this…

In response to the call for research on integrating best general practices in teaching with those that promote equity and access, we present a two-part study focused on instructional strategies that may remove learning barriers for English Language Learners. We theoretical developed and empirically explored supplemental components for traditional…

What are the substantive differences between flipped and non-flipped instruction? This study examined the instruction of two teachers who have worked together within the same school using the same Algebra 1 curriculum for years. One teacher flipped his instruction (creating lecture videos assigned as homework), while the other teacher continued…

This study was conducted to gain understanding about potential influences that learning about quadratic functions has on high school algebra students' action versus process views of linear functions. Pre/post linear functions tests were given to two classrooms of Algebra II students (N=57) immediately before and immediately after they participated…

This study examines how elementary preservice teachers notice children's mathematical thinking and how this noticing influences the evaluation of technological resources. In particular, we explore the aspects of thinking to which preservice teachers attend and how they interpret evidence about children's thinking when using the Spatial-Temporal…

Current reform efforts challenge teachers to create more student-centered classrooms focused on high quality classroom discourse (NCTM, 2014). There are difficulties, however, teachers face in bringing this vision to fruition. Over the past three years, we have worked with a group of 7-12 teachers supporting their efforts to implement high quality…

Supporting students' in-the-moment perseverance is a vital objective in mathematics education because it promotes learning with understanding. Yet, little is written about if and how student perseverance can improve over time. I examine the specific ways in which secondary students improved their perseverance as they engaged with challenging…