Use the language of mathematics to explore diversity in kindergarten.

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### Evthokia Stephanie Saclarides, Brette Garner, Gladys Krause, Claudia Bertolone-Smith, and Jen Munson

Learning to teach mathematics is a complex endeavor, requiring sustained focus and time. Yet time is especially scarce in elementary teacher education programs, where preservice teachers (PSTs) learn all content areas. Through a collaborative self-study, five teacher educators identified three time-related tensions in elementary mathematics methods courses: (a) teaching mathematics content and pedagogy; (b) connecting theory and practice; and (c) promoting social contexts in teaching mathematics. To address these tensions, we offer three design principles and illustrative examples: (a) addressing multiple goals for each course component; (b) developing PSTs’ dispositions over time; and (c) building on PSTs’ strengths to develop understanding of mathematics. We present a reflection tool to assist mathematics teacher educators in designing their courses to maximize their instructional time.

### Carrie Plank and Sarah Roller Dyess

Use these three strategies to support student perseverance and discourse about context.

### Douglas H. Clements, Shannon S. Guss, and Julie Sarama

Learning trajectories help teachers challenge children at just the right level for their best learning.

### Susanne Prediger, Kirstin Erath, Henrike Weinert, and Kim Quabeck

Empirical evidence exists that enhancing students’ language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (*N* = 589) investigates differential effects for these extended target groups, comparing two language-responsive interventions (with or without vocabulary work) and a control group. The regression analysis reveals that all students significantly deepened their conceptual understanding in both interventions. Unlike what was anticipated, multilingual students’ growth of conceptual understanding had no significant additional benefit from integrated vocabulary work. These findings call for promoting language-responsive mathematics instruction for all students and for using a discursive rather than a vocabulary focus.

### Luz A. Maldonado Rodríguez, Naomi Jessup, Marrielle Myers, Nicole Louie, and Theodore Chao

Elementary mathematics teacher education often draws on research-based frameworks that center children as mathematical thinkers, grounding teaching in children’s mathematical strategies and ideas and as a means to attend to equity in mathematics teaching and learning. In this conceptual article, a group of critical mathematics teacher educators of color reflect on the boundaries of Cognitively Guided Instruction (CGI) as a research-based mathematical instructional framework advancing equity through a sociopolitical perspective of mathematics instruction connected to race, power, and identity. We specifically discuss CGI along the dominant and critical approaches to equity outlined by , ) framework. We present strategies used to extend our work with CGI and call for the field to continue critical conversations of examining mathematical instructional frameworks as we center equity and criticality.

### Jody Guarino, Shelbi Cole, and Michelle Sperling

In a humanized approach to assessment, the design of the instrument itself is only a small part of the overall process.

### Amanda T. Sugimoto and Heidi Meister

The authors draw on collaboration with a group of teachers to describe how three-act tasks could be (re)designed and implemented for online synchronous and asynchronous learning, identifying technological factors that teachers might consider.

### Elizabeth E. Peyser and Jessica Bobo

Because number lines are an integral part of mathematics after they are introduced in second grade, connecting number sense to a linear view of numbers establishes a foundation for number line use in all levels of mathematics.

### Larry Buschman and Introduction by: Beth Kobett

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.