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

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### Deanna Pecaski McLennan

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

### Katherine Baker, Scott A. Morrison, and Mirella F. Cisneros Perez

Integrating mathematics and nature offers students benefits for physical and mental health and enriches their learning.

### Alice Aspinall

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

### Lara K. Dick, Mollie H. Appelgate, Dittika Gupta, and Melissa M. Soto

A group of mathematics teacher educators (MTEs) began a lesson study to develop a research-based lesson to engage elementary preservice teachers with professional teacher noticing within the context of multidigit multiplication. Afterward, MTEs continued teaching and revising the lesson, developing an integrated process that combined lesson study with the continuous improvement model. This article introduces the continuous improvement lesson study process, shares an example of how the process was used, and discusses how the process serves as a collaborative professional development model for MTEs across institutions.

### Megan H. Wickstrom

Preservice elementary teachers (PSTs) often enter their teacher preparation programs with procedural and underdeveloped understandings of area measurement and its applications. This is problematic given that area and the area model are used throughout K–Grade 12 to develop flexibility in students’ mathematical understanding and to provide them with a visual interpretation of numerical ideas. This study describes an intervention aimed at bolstering PSTs’ understanding of area and area units with respect to measurement and number and operations. Following the intervention, results indicate that PSTs had both an improved ability to solve area tiling tasks as well as increased flexibility in the strategies they implemented. The results indicate that PSTs, similar to elementary students, develop a conceptual understanding of area from the use of tangible tools and are able to leverage visualizations to make sense of multiplicative structure across different strategies.

### Jere Confrey, Meetal Shah, and Alan Maloney

Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.

### Dorothy Y. White

Use this activity to support students in working together, recognizing one another’s contributions, and leveraging their mathematical strengths to solve challenging problems.

### Corinne Thatcher Day

This hands-on task, featuring differentiation and open-ended learning, sets up students to discover area models for themselves. Organized around NCTM’s eight teaching practices from *Principles to Actions*, this article describes the task’s setup and implementation.

### Katherine Baker, Scott A. Morrison, and Alyssa Herrmann

This article features a third-grade multiplication exploration that integrates materials from nature and outside spaces. Teaching and learning mathematics with and in nature foster connections—mathematical, interpersonal, and with the natural world.