This article shares a mathematics discourse technique adapted from literacy instruction and designed to prepare students' engagement in a mathematics task by model mathematical thinking. The Math Think Aloud is used during the launch of a lesson to provide access to the mathematics and help students make sense of the task so they are able to work on the task and share their mathematical thinking. Successes, challenges, and tips for effective implementation are shared. 

This article describes a mathematics professional development program for elementary school teachers focused on improving mathematics discourse for all students, in particular emergent multilingual learners. Frameworks, such as the Math Discourse Matrix (Sztajn, Heck, & Malzahn, 2020) that characterizes four types of discourse (correcting, eliciting, probing, responsive) and other resources aimed at planning and implementing lessons that support emergent multilingual learners' engagement in productive mathematical discussions are shared. 

In this paper, we engage in an analysis of professional development design, examining professional development activities and the sequencing of professional learning tasks. We use a theoretical framework typically used in pre-service teacher education to understand the design of one professional development program. Our overarching goal is to theorize about how to design professional development and sequence professional learning tasks for practicing teachers.

In this chapter, we use the Framework for Teaching Practice (Grossman, Compton, Igra, Ronfeldt, Shahan, & Williamson, 2009) as a conceptual tool for analyzing the design of professional development. Although initially developed to examine the education of prospective teachers, we contend that this framework is appropriate for analyzing and supporting the design of professional development. The framework consists of three elements: decompositions, representations, and approximations of practice.

Many mathematics teachers agree that engaging students in high-quality discourse is important for their conceptual learning, but successfully promoting such discourse in elementary classrooms—with attention to the needs of every learner—can be a challenge.