In a multi-institutional study, the authors examine elementary preservice teachers' (PSTs') noticing skills before and after their engagement in a mathematics methods course. In particular, the authors examine their use of "Cognitively Guided Instruction" (CGI) as a means of supporting the development of PSTs' "professional noticing…

As mathematics teacher educators (MTEs), we enact teaching practices in our mathematics methods courses as instantiations of practice for PTs. Questioning is a core practice in teaching (and learning to teach) mathematics that interacts with relationships between MTEs and prospective teachers (PTs). We engaged in a collaborative self-study to…

Secondary mathematics teachers are frequently required to take a large number of mathematics courses -- including advanced mathematics courses such as abstract algebra -- as part of their initial teacher preparation program and/or their continuing professional development. The content areas of advanced and secondary mathematics are closely…

Mathematics and science have similar learning processes (SLPs) and it has been proposed that courses focused on these and other similarities promote transfer across disciplines. However, it is not known how the use of these processes in lessons taught to children change throughout a preservice teacher education course or which are most likely to…

The goal of this study is to analyze undergraduate elementary school pre-service teachers' conceptions and misconceptions of physical and virtual manipulative materials using an interpretive "framework." The "framework" involved the use of the "Concrete," "Pictorial" and "Abstract cognitive levels"…

In this article, we share results from a field experience model in which junior-year methods classes were held in an elementary school and preservice teachers (PSTs) worked with a single student (a "Math Buddy") on mathematics for 30 minutes per day. We focus on the development of PSTs' skills for exploring children's thinking and the…

Race-focused teacher education has centered on changing preservice teachers' racial beliefs and attitudes. In this article, we build on this work by exploring how preservice teachers identify and address issues of race and racism in the everyday work of teaching and learning. To conceptualize these processes, we propose the theoretical framework…

The COVID-19-induced closure of K-12 schools significantly impacted the field experiences of students enrolled in teacher preparation programs. We addressed this ongoing challenge by adapting an early field experience model for secondary teachers that shifted online mid-semester. The University Teaching Experience model deploys a cohort of…

This paper discusses the ways in which teacher educators can effectively engage prospective teachers (PTs) in lesson study during mathematics methods courses. Evidence from this work suggests that engagement in lesson study provides PTs with opportunities to strengthen their knowledge about mathematics, students, and pedagogy. More specifically,…

Methods for teaching early childhood mathematics and science are often addressed in a single, dual-content course. Approaches to teaching this type of course include integrating the content and the pedagogy of both subjects, or keeping the subject areas distinct. In this article, the authors discuss and illustrate their approach to such a combined…

This article explores the personal identities of two prospective elementary teachers as they progressed from mathematics methods coursework into their capstone student teaching semester. Results indicate that both prospective teachers perceived contrasting obligations of effective mathematics teaching in the teacher education and student teaching…

Gestures have been shown to play a key role in mathematical reasoning and to be an indicator that mathematical understanding is "embodied" -- inherently linked to action, perception, and the physical body. As learners collaborate and engage in mathematical discussions, they use discourse practices like explaining, refuting, and building…

This research report explores relationships between fractions' task representations (discrete, rectangular, or circular) and elementary prospective teachers' (PTs) fractions conceptions. Studies show PTs' conceptions of fractions are centered on a part-whole understanding, which may be problematic when teaching children about improper fractions.…

This article suggests the use of presentation technologies and electronic books as ways in which to employ Universal Design for Learning (UDL) principles in the mathematics classroom. In particular, the focus is on using easily accessible technologies to assist students with print and language difficulties in comprehending and reasoning with…

Fifty-seven students in mathematical content and secondary mathematics methods courses from four U.S. universities participated in an instructional sequence to generate communal criteria defining mathematical proof within their respective classrooms. Participants completed a proof-related task before class, worked together in small groups to…