In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence.

Among the most urgent matters in contemporary education discourses are those that delve into the justice issues related to diversity, equity, and inclusion. Colleges of Education are critical sites for such discourse. In particular, the teaching methods course is where candidates are to acquire tools to take up such issues. Success of justice…

To provide appropriate and effective instructional supports to students with disabilities, special education preservice teachers require development of expertise in the design and delivery of specially designed lessons. It is critical that special education preservice education programs provide students ample opportunities to learn how to evaluate…

In this article, we describe the experiences of two preservice teachers (PSTs) who served as teaching assistants (TAs) in a secondary mathematics teaching methods course. As TAs, the PSTs approximated practice by being independently responsible for a learning environment and leading discussions with groups of students. Although the PSTs felt…

In this article, we share design guidelines for the development and use of online, video-based "teaching playgrounds," which provide opportunities for prospective teachers to engage in professional noticing of teaching practices. Through teaching playgrounds, we provide an instantiation of the Presence+Experience framework, which…

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 provides concrete critical and ethical responses to dominant educational policies promoting the teaching of STEM fields. Recognizing how dominant discourses of modernity (Martusewicz, et al. 2015) work discursively to constitute STEM, this paper examines and exposes how STEM education is prioritized via funding in teacher education.…

The aim of this article is to discuss key elements of a constructivist-based elementary mathematics methods course and the role of each component in enhancing elementary school teacher candidates' mathematical understanding, interest in, and confidence with learning and teaching mathematics while decreasing their math-related anxiety and fear. The…

This article describes the authors' three-component instructional sequence--a before-class activity, a during-class activity, and an after-class activity--which supports students in becoming self-regulated proof learners by actively developing class-based criteria for proof. All four authors implemented this sequence in their classrooms, and the…

Preservice teachers (PSTs) must be able to link content, effective teaching practices, and student learning; thus, it is critical for teacher educators to emphasize connections between research and practice in methods courses. Reflection plays an important role in this process. In this article, the authors discuss and illustrate a vignette…

The implementation of the Common Core's Standards for Mathematical Practice can pose a challenge to all teachers of mathematics but especially to preservice teachers. These standards require teaching in a way that often differs from what preservice teachers have experienced as learners. Standard 1--"Make sense of problems and persevere in…

We discuss an innovative task used in teacher education--Lesson Play--that involves presenting a lesson in the form of an interaction between a teacher and students. We describe the motivation for the development of this task and, through specific examples, describe the iterative design process in which the task was refined and improved. We…

Effectively engaging students in mathematics discourse is challenging, especially in a language other than the one in which you learned mathematics. Teachers must manage the academic as well as social function of language. In Spanish-English bilingual classrooms in the U.S., changing the language of instruction to Spanish may not be enough to…

Generalizing--along with conjecturing, representing, justifying, and refuting--are forms of mathematical reasoning important in all branches of mathematics (Lannin, Ellis, and Elliott 2011). Increasingly, however, generalizing is recognized as the essence of thinking in algebra (Mason, Graham, and Johnston-Wilder 2010; Kaput, Carraher, and Blanton…

This article describes the development of the authors' understanding of the contradictions in their mathematics teacher education practice. This understanding emerged from contrasting analyses of the impact of the authors' practices in mathematics content courses versus mathematics methods courses. Examples of the authors' work with two students,…