This book examines the study of geometry in the middle grades as a pivotal point in the mathematical learning of students and emphasizes the geometric thinking that can develop in grades 6-8 as a result of hands-on exploration. An essay on the accompanying CD-ROM describes the van Hiele framework and how it can help improve teaching strategies and assessment. The supplemental CD-ROM also features interactive electronic activities, master copies of activity pages for students, and additional readings for teachers.

Navigating Through Geometry in Grades 6-8 (Principles and Standards for School Mathematics Navigations)

Science & Math

David K. Pugalee

Jeffrey Frykholm

Art Johnson

Hannah Slovin

Carol Malloy

Ron Preston

Mathematics

National Council of Teachers of Mathematics

This book gives teachers of students in grades 3-5 the deep understanding of geometry and measurement that they need to identify and dispel students common misconceptions, correct erroneous claims that they make, and move them forward mathematically. It prepares teachers to introduce terms from geometry and measurement in ways that not only bolster students vocabulary but also enhance their understanding of concepts and definitions. By helping teachers understand what changes or stays the same when shapes are transformed, the book equips teachers to support and extend students understanding of shapes and the space that they occupy.

Developing Essential Understanding of Geometry and Measurement for Teaching Mathematics in Grades 3–5

Barbara J. Dougherty

Rose Mary Zbiek

Richard Lehrer

NCTM

Do your students think they can model ratios with sets of discrete objects and combine them to show the addition of ratios? Do they believe that equivalent ratios are based on additive relationships rather than multiplicative ones? What tasks can you offer what questions can you ask to determine what your students know or don't know and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach ratios and proportions effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with ratios and proportions--not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of ratios and proportions. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.

Putting Essential Understanding of Ratios and Proportions into Practice in Grades 6–8

Melfried Olson

Travis A. Olson

Do your students suppose that if the perimeter of a shape increases, the area also increases? Do they think that area is the product of base and height, without understanding that this applies only to parallelograms? Do they believe that a transformation happens only on or to a particular object and not the entire plane? What tasks can you offer-what questions can you ask-to determine what they know or don't know-and move them forward in their thinking? This book focuses on the specialized pedagogical content knowledge that you need to teach geometry effectively in grades 6-8. The authors demonstrate how to use this multifaceted knowledge to address the big ideas and essential understandings that students must develop for success with geometry-not only in their current work, but also in higher-level mathematics and a myriad of real-world contexts. Explore rich, research-based strategies and tasks that show how students are reasoning about and making sense of geometry. Use the opportunities that these and similar tasks provide to build on their understanding while identifying and correcting misunderstandings that may be keeping them from taking the next steps in learning.

Putting Essential Understanding into Practice: Geometry, 6–8

Terry Crites

Karen Karp

Reshaping Mathematics for Understanding (RMU): Getting Started

Curriculum Research & Development Group

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Books by Hannah Slovin