Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

# Browse

### Blake E. Peterson, Shari L. Stockero, Keith R. Leatham, and Laura R. Van Zoest

Do your students ever share ideas that are only peripherally related to the discussion you are having? We discuss ways to minimize and deal with such contributions.

### Carrie Plank and Sarah Roller Dyess

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

### Amanda L. Cullen

Any ability grouping in mathematics education is an inequitable structure that perpetuates privilege for a few and marginality for others. Ability grouping practices often occur with good intentions; we want to understand children’s learning needs and then tailor the content,

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

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

### Sarah A. Roberts, Zandra de Araujo, Craig Willey, and William Zahner

Enacting these considerations supports integrated thinking about how to attend to both mathematics content and language development.

### Carybeth Hobbs

This article describes how fortuitous mathematical moments should be noticed, encouraged, embraced, and capitalized upon.

### 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.

### Chunlian Jiang and Eunmi Joung

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners’ growth as problem solvers across their years of school mathematics.

### Amanda T. Sugimoto

Mathematics standards and practices highlight the vital role that language plays in mathematics education. However, there remains a common misconception that mathematics is somehow language-free or less linguistically demanding than other content areas. This qualitative study describes an intervention implemented in six elementary mathematics methods courses. The intervention was designed to attune prospective teachers’ noticing to the language modalities and supports in mathematics teaching and learning. The intervention began with an observation tool that prospective teachers completed in their field placement classrooms. This article classifies prospective teachers’ noticings and explicates how these noticing became a pedagogical catalyst for further learning and discussion in subsequent mathematics methods classes.