Teaching deeper learning involves cultivating the critical thinking, problem-solving, and collaboration skills that students need to be successful in their college, career, and civic life. It also involves encouraging students to be active participants in their learning. Public schools across the United States often work to help students develop…

Proportionality can be considered among the most important mathematical notions in the middle school math curriculum (grades 5 to 8). It is the capstone of elementary arithmetic, number, and measurement concepts, and at the same time one of the most elementary understandings one needs for more advanced mathematics. Understanding proportionality is…

Consider that colorful photographs, eye-catching illustrations, and captivating images intended to make textbooks more appealing may actually distract students from the lesson at hand. Or that asking students to simply solve math problems might not be as effective as having them explain the steps of solutions that are already worked out--even some…

In early November 2013, the authors started talking about visiting the Hurley School, a dual-language school in Boston, Massachusetts. The Hurley School had spent considerable time transitioning to the Common Core State Standards on literacy, but little time addressing the shifts in math. They worried that math classes were no longer rigorous…

Middle schools take on a higher purpose by making every effort to empower all of their students to attain their highest potential. This article rediscovers the "substance of soul" in the 21st century middle schools. The author stresses that returning to one's substance of soul goes beyond merely revisiting what educators truly value and then…

This book introduces students to the types of problems and processes used throughout the "Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts and challenge their own assumptions. Additionally, by providing opportunities to give and follow…

Discusses the place of problem posing in mathematics education. Shares some approaches to implementing problem posing and critiquing in the classroom. (ASK)

This curriculum is based on the peaceable classroom model, which emphasizes cooperation, communication, appreciation of diversity, the healthy expression of feelings, responsible decision-making, and conflict resolution. This guide presents over 150 activities and tools to help middle school students learn to effectively handle the conflict that…

Argues that the way in which students solve a particular problem can be analyzed to gain insight into how students think about the mathematics involved. Discusses the use of knowledge gained from listening to student conversations about their strategies to orchestrate classroom discussions. (ASK)

This multidisciplinary guide provides middle and high school teachers and students with inquiry-based tools to support their exploration of emerging local, national, international, and transboundary security issues. Students are introduced to critical thinking, problem solving, and peacemaking strategies that will help them better understand…

This book introduces concepts of geometry that students use throughout middle-grade and higher-level mathematics courses. These concepts, presented through the study of transformations, provide a framework for other important topics such as number, measurement, proportional reasoning, and graphing on the coordinate plane. The book is designed for…

Independent study for gifted and talented middle-level students progresses through five stages, from the affective sensing of a problem to be solved through assessing both product and process. J. Renzulli's Enrichment Triad model can serve as a framework for independent study, which must be carefully structured and guided. (CL)

Describes a fifth-grade student solving the "Food for Thought" problem featured in the February 1998 issue. (ASK)

Discusses the advantages of teaching with open-ended tasks and compares students' responses to open-ended, closed-area, and perimeter tasks. (ASK)

Discusses ways to help students improve their problem-solving skills. Presents some mathematics problems to be used in classrooms. (ASK)