We present an investigation of the infinite sequences of numbers formed by calculating the pairwise averages of three given numbers. The problem has an interesting geometric interpretation related to the sequence of triangles with equal perimeters which tend to an equilateral triangle. Investigative activities of the problem are carried out in…

Teachers can make number talks more ambitious and increase learning opportunities for students by debugging errors, promoting multi-student thinking, and orienting to make connections. This article describes the basic number talks routine and examines some common tendencies, such as "Serial Sharing." It concludes with a vignette to…

This study examined how elementary preservice teachers attend to precision and how exposure to engaging tasks and activities impacted the development of this Standard for Mathematical Practice. Additionally, the study aimed to understand how the experiences of this study impacted participants' perspectives toward implementing SMP 6: Attend to…

This literature review examines how mathematics education uses the Technology, pedagogy, and content knowledge (TPACK). This study examines how TPACK affects mathematics classroom instruction, student engagement, and learning outcomes. A detailed examination and synthesis of pertinent publications over the last decade will accomplish this. The…

An asset-based perspective on math education means starting with what students already know instead of focusing on what is missing. This approach elevates student thinking and reasoning skills. In this way, educators acknowledge that all students bring prior experiences, strengths, talents, and resources to the learning process and can contribute…

Practice-based teacher education has increasingly been adopted as an alternative to more traditional, conceptually-focused pedagogies, yet the field lacks causal evidence regarding the relative efficacy of these approaches. To address this issue, we randomly assigned 185 college students to one of three experimental conditions reflective of common…

The purpose of this resource is to help math teachers unpack, understand, and implement the current math content and practice standards. This resource describes the progressions of learning within each course and provides content support, which includes broad ideas about effective instruction as well as practical instructional strategies. Math…

Research has shown that the ways in which teachers engage in professional development activities vary widely. identified three levels of teacher appropriation within professional development, with their inquiry stance indicative of teachers engaging in self-sustaining practices. In our project, we modified the demonstration lesson format so that…

This timely book provides support for secondary mathematics teachers learning how to enact high-quality, equitable math instruction with dynamic, mathematics-specific technologies. Using practical advice from their own work as well as from interviews with 23 exceptional technology-using math teachers, the authors develop a vision of teaching with…

This practitioner article describes a lesson carried out in a high school classroom at the conclusion of a unit on exponential growth. Two teachers use a series of music-related activities to engage students in using and connecting multiple representations of exponential growth while exploring musical frequencies on a piano.

In the late 1800s and early 1900s, increases in metallurgic technology and better manufacturing methods made naval artillery a more powerful force. Guns could fire more powerful shells that could travel farther and hit a target with much greater accuracy. Torpedoes represented a major threat to even the most powerful of warships, forcing captains…

Across nearly 20 years working as a secondary mathematics teacher, the author noticed two overarching goals that most teachers of mathematics consider to be important in their practice: (1) students knowing and understanding the content; and (2) students engaging with the learning and enjoying their time in class. However, in practice, attaining…

This article introduces basic strategies for teachers initiating translanguaging pedagogy for emergent bilingual students in mathematics classrooms to support linguistic identities, create inclusive environments, and enhance learning. The authors collaborated with Algebra 1 teachers who exclusively taught emergent bilingual students, implementing…

Discover a bold new vision for high school mathematics that empowers students through engaging, real-world learning. For decades, mathematics education has been guided by the visionary efforts of educators and leaders who recognized the importance of making math relevant, engaging, and accessible to all students. From the foundational principles…

The Association of Mathematics Teacher Educators recommends that well-prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics…