This extensively updated teaching resource provides over 100 engaging, full-color visuals with explanations of how they can be used to stimulate mathematics learning, to explain mathematical concepts, and to assess students' mathematical understanding in grades K-8. Readers are provided with a strong mathematical background, downloadable copies of…

Abstract concepts, such as gravity, may provide the perfect opportunity to bring phenomena into the classroom. As a knowledge generation strategy, summarizing can foster that opportunity. Using phenomena and summary writing together might help student learning since it requires making connections between their ideas and words to explain the…

"Elementary and Middle School Mathematics" illustrates how children in PreK to 8th grade learn math, and then shows the most effective methods of teaching math using problem-based activities. Examples of real student work and common challenges help you visualize developmentally appropriate mathematics instruction and assessment that…

"High Yield Routines 2nd Edition, Grades K-8," is an essential resource for elementary and middle school mathematics teachers seeking to enhance their instructional practices and optimize classroom time. Authored by experienced educators, this book presents effective mathematical routines designed to integrate seamlessly into everyday…

This book provides an introduction to what it means to be numerate, and how numeracy can best be developed and nurtured in children and in adults. It also presents a cohesive coverage of numeracy development from early childhood to adulthood. This book draws on international research and practice to provide a comprehensive overview on the topic.…

Instructional discussion is a teaching method used in many classrooms across grade levels. In fact, the Common Core State Standards promote the use of instructional discussion in secondary classrooms (Common Core State Standards Initiative, 2018a). Students, however, are not always taught best practices for engaging in a discussion and may feel…

Do your students say that one object is "bigger" than another without attending more precisely to the attribute they are comparing? Do they have difficulty naming numbers from 11 to 19? Do some students still count all while their classmates are counting on or counting by tens? What tasks can you offer--what questions can you ask--to…

This column includes activities inspired by children's literature. This month's issue has students experience nature by examining how seeds are transported from one location to another or consider what it takes for organisms to survive in an environment. Both activities allow elementary-age children to think about how outdoor spaces can be…

Recognizing the challenges that students face when they may lack background and experiential knowledge with regard to coins is important so that teachers can address this during instruction. Exposure to coins is one of the basic necessities to learning about the coins, but that is just the initial part of the learning sequence. Unless students are…

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

The Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) propose a new vision for the mathematics classroom with updated content standards and Standards for Mathematical Practice (SMP). These practices are founded on NCTM processes (Problem Solving, Reasoning and Proof, Communication, Representation, and Connections) and abilities…

Imagine a mathematics classroom in which students engage in sharing ideas and reasoning through solutions to interesting mathematical problems. They are excited about mathematics and working on challenging problems that encourage collaboration and critical thinking. These are things that teachers want, but sometimes they do not know how to achieve…

Twenty years ago when the author was student teaching, he quickly learned what geometry teachers and researchers (e.g., Senk 1985) have long known: High school geometry students struggle with proof. Throughout his career, he has tried to create instructional materials to make proof more accessible to his students. From field-testing materials with…

In this practical guide, literacy experts show teachers how to use project-based inquiry to build students' discipline-specific skills and knowledge in grades 6-12. The authors present a five-phase framework that incorporates their professional development experience working with over 3,000 teachers. By making the intuitive practices of the…