We describe how mathematical argumentation supports curiosity and exploration by sharing a first-grade lesson in which students explored decomposition with subtraction. We also reflect on the conditions that supported the inclusion of mathematical argumentation.

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### Deanna Pecaski McLennan

Use the language of mathematics to explore diversity in kindergarten.

### 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.

### 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.

### 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.

### Douglas H. Clements and Introduction by: Carol Matsumoto

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

### Jennifer Ward and Victoria Damjanovic

This department provides a space for current and past PK–12 teachers of mathematics to connect with other teachers of mathematics through their stories that lend personal and professional support.