Coaching teachers is complex work as coaches must navigate multiple and competing roles of expert and colleague. Within mathematics education, there is a lack of research exploring how coaches enact their stance for coaching, balancing the roles of expert and colleague, in ways that best support teacher learning. Furthermore, little is known about…

Students with autism spectrum disorder (ASD) are included in the general education classroom more often than ever before. Despite mathematical strengths and early success, these students experience poor outcomes (academic and employment) compared to their typically developing peers. The language of mathematics increases in complexity, use, and…

Mathematics traditionally has been taught in a way that reifies the cultural belief that it is discrete in nature and, therefore, irrelevant to other content areas and the real world. National Council of Teachers of Mathematics, inclusive of mathematics teacher educators, views this belief as unproductive to learning and has stressed the need for…

We contribute to the understanding of teacher noticing by focusing on what a teacher may notice in students' mathematical contributions in the context of problem-based lessons. Complementing approaches to research on noticing that focus on individual teachers' perceptual, cognitive, or situated skills, this conceptual article offers four…

Quantitative measures in mathematics education have informed policies and practices for over a century. Thus, it is critical that such measures in mathematics education have sufficient validity evidence to improve mathematics experiences for students. This article provides a systematic review of the validity evidence related to measures used in…

The challenge posed by algebra story problems creates a significant hurdle for many students, transcending both the mathematical content of the problem and the specific instructional background received. This study offers a distinctive contribution to the existing literature by focusing on the cognitive conditions essential for comprehension in…

Providing opportunities for students to talk directly with their peers is a critical dimension to facilitating discussions in mathematics and science, including argumentation-focused discussions in which students construct arguments and critique others' arguments. Research suggests that supporting student-to-student talk and facilitating…

We conducted a literature review to describe the conceptual use of "noticing" in pivotal mathematics and science education publications from 2002 to 2022 by tracing the language and ideas used to describe and study teacher noticing. Results from 12 highly cited or recently written publications indicated substantial differences in the…

This paper details a literature review of mathematics vocabulary intervention studies for students with mathematics difficulty. The primary aim was to identify instructional practices that support mathematics vocabulary development. We conducted a database search to identify mathematics intervention studies either focused exclusively on vocabulary…

Co-teaching is described as the pairing of a general education teacher and a special education teacher in the general education classroom for the shared instruction of students with and without disabilities. Many teachers struggle to form unified partnerships, especially in mathematics classrooms. The MathMATES project was developed to address a…

Teacher noticing has been identified as central to enacting responsive and equitable mathematics instruction. Mathematics teachers' noticing is shaped by institutional and sociopolitical narratives and ideologies that persistently marginalize culturally, socially, linguistically, and neuro-diverse learners. Gaining insight into how one's noticing…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

In our mathematics methods courses for elementary preservice teachers, we work to uncover and confront students' understandings as well as misconceptions about important mathematical topics. Karp and colleagues' ("Teaching Children Mathematics", 21(1), 18-25) "13 Rules That Expire" article has been a useful resource for us to…

We investigated what high school mathematics teachers and their students noticed about students' mathematical engagement to develop a framework for teachers' and students' noticing of mathematical engagement. This framework offers clarity about the complexity of engagement, and it includes three elements: evaluations of the valence of engagement…

We further conceptualize the work of responsive teaching by contrasting it with a type of teaching we call endorsing. We define responsive teaching as a type of teaching in which the teacher: (a) ensures students' ideas are the genesis of ways of reasoning that are eventually taken up by the classroom community; and (b) continually assesses and…