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 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…

The theme of the 39th proceedings of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA) conference was "Synergy at the Crossroads: Future Directions for Theory, Research, and Practice." The metaphor of crossroads was inspired by the conference venue--the historic Indianapolis Union…

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…

Being able to effectively interpret students' thinking and respond effectively in the moment are important skills that preservice teachers (PSTs) need to learn. This study zooms in on 14 PSTs' planning, teaching, and reflections involved in number string lessons, and investigates to what extent PSTs anticipate their students' strategies and…

This paper represents research that exists at the crossroad of scholarly practice and scholarly inquiry. We share the design, enactment and empirical examination of an elementary methods course activity, Exploring and Supporting Student Thinking (ESST) which engaged 18 prospective teachers in two sessions of one on one problem posing with 3rd…

This paper explores the use of animations as an approximation of practice to provide a transformational technology experience for elementary mathematics preservice teachers. Preservice teachers in mathematics methods courses at six universities (n = 126) engaged in a practice of decomposing and approximating components of a fraction lesson. Data…

Prospective teachers must be prepared for their role in providing equitable access for learning high quality mathematics. Therefore, it is imperative that mathematics teacher educators provide opportunities to develop an equity-centered orientation in teacher preparation courses. In this study, we begin to address this issue by identifying what…

This mixed-methods study examines effects of implementing a mock edTPA task on prospective elementary teachers' perceptions of teaching effectiveness. Results from the Mathematics Teaching Efficacy Beliefs Instrument document a significant change in participants' beliefs that they can effectively teach mathematics. Qualitative results illuminate…

This project examines how prospective elementary teachers (PSTs) framed the idea of drawing on multiple mathematical knowledge bases (MMKB)--children's mathematical thinking and funds of knowledge--for diverse learners, in the context of adapting curriculum. We analyzed 47 written reflections of PSTs' analyses of an existing mathematics…

The theme of the 38th meeting of the International Group for the Psychology of Mathematics Education (PME 38) and the 36th meeting of the North American Chapter of the Psychology of Mathematics Education (PME-NA 36) was "Mathematics Education at the Edge." Academically, the theme provides opportunities to highlight and examine…

The goal of this study is to better understand preservice elementary teachers' changes in attitudes towards mathematics in connection with their participation in a module aimed at developing professional noticing capacities. This module, typically implemented in the mathematics methods course, involves practice with the three interrelated…

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…

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…