The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

"Mathematical Thinking: From Assessment Items to Challenging Tasks" is a compilation of 36 problem-based lessons that encourage students to engage in productive struggle and deep thinking. Its 36 full-length lessons for grades 2-8 are each inspired by an actual test item from the National Assessment of Educational Progress (NAEP).…

The advent of dynamic geometry software has changed the way students draw, construct, and measure by using virtual tools instead of or along with physical tools. Use of technology in general and of dynamic geometry in particular has gained traction in mathematics education, as evidenced in the Common Core State Standards for Mathematics (CCSSI…

Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image--not the whole plane? Do they understand that examples--no matter how many they find--cannot prove a conjecture but one counterexample is sufficient to disprove it? "What tasks can you…

"Setting the Stage with Geometry" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards that is designed to help students in grades 6-8 build and reinforce basic geometry skills for measuring 2D and 3D shapes. Developed by The Actuarial Foundation, this program seeks to provide skill-building math…

This new addition to Math Solutions "Supporting English Language Learners in Math Class series" offers a wealth of lessons and strategies for modifying grades 6-8 instruction. Section I presents an overview of teaching math to English learners: the research, the challenges, the linguistic demands of a math lesson, and specific strategies and…

This article presents a guided investigation into the spacial relationships between the centres of the squares in a Fibonacci tiling. It is essentially a lesson in number pattern, but includes work with surds, coordinate geometry, and some elementary use of complex numbers. The investigation could be presented to students in a number of ways…

Teachers know that Differentiated Instruction (DI) helps all students to learn. Yet DI challenges teachers, and nowhere more than in mathematics. In this new book, written specifically for secondary mathematics teachers, the authors cut through the difficulties with two powerful and universal strategies that teachers can use across all math…

Using differentiated instruction in the classroom can be a challenge, especially when teaching mathematics. This book cuts through the difficulties with two powerful and universal strategies that teachers can use across all math content: Open Questions and Parallel Tasks. Specific strategies and examples for grades Kindergarten - 8 are organized…

Children who learn math fundamentals in preschool and kindergarten have the best chance of later achievement in school--but too often, children don't get the effective early math instruction that makes all the difference. Now there's a core early childhood textbook that helps current and future educators teach the most critical math concepts to…

Describes how students use crazy cars to confirm that the sum of measures of the angles of any triangle is 180 degrees. (Author)

This book contains a set of versatile enrichment exercises that cover a very broad range of mathematical topics and applications in geometry including Euclidean, post-Euclidean, and non-Euclidean geometry. Several criteria have been used in developing the activities and selecting the topics that are included. All of them bear heavily and equally…

Describes an activity in which students develop a conceptual understanding of the formulas of the circumference and area of a circle by exploring pi. (YDS)

Presents an activity in which students investigate geometric probability at a school fair. (YDS)

Provides practical applications of elementary coordinate geometry while discussing how mathematics is used to assess the security of systems. (ASK)