This article describes a hands-on geometric tiling art activity used in two third-grade classes and four fifth-grade classes in a rural public elementary school with class sizes of around 20 students each. The lesson investigates concepts in geometry, number sense, and probability. Examples of student work and takeaways for other teachers…

This Study Snapshot highlights key findings from a study on why students often experience a decline in academic achievement as they transition to middle school. Academic mindsets, such as a belief in the malleability of ability (growth mindset) or a reluctance to engage academically because of embarrassment or a fear of failure (performance…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

This guide was created as a resource to help families better understand "Measures of Academic Progress"® (MAP®), and their child's results. The guide provides answers to a variety of questions such as: "What is MAP?"; "What does MAP measure?"; "How do schools and teachers use MAP scores?"; "Can MAP tell…

This Framework builds upon the foundation of the 2010 Massachusetts Curriculum Framework for Mathematics as well as versions of the Massachusetts Mathematics Framework published since 1995. The current Framework incorporates improvements suggested by Massachusetts educators after six years of experience in implementing the 2010 standards in their…

Preparation for college and careers begins when students are young, yet, it can be difficult for middle grade educators to know how best to prepare these students for future success. Middle grade practitioners need to know what to pay attention to and who needs additional support. Without knowing how to identify students who are on-track for high…

As a fifth-grade mathematics teacher, the author tries to create authentic problem-solving activities that connect to the world in which his students live. He discovered a natural connection to his students' real world at a computer camp. A friend introduced him to Alice, a computer application developed at Carnegie Mellon, under the leadership of…

Using sequences of coin flips as a model of serial independent events, we asked schoolchildren in grades 1 through 5 to estimate the likelihood of the next flip. Most children in each grade expected short patterns to continue.

Inspired by the research of Reading and Shaughnessy (2004), we modified an existing lesson from the National Council of Teachers of Mathematics. This lesson, a variation on the "Gumball Task", gives students the opportunity to explore and discuss the variation which occurs in sampling. This paper describes our experience using this lesson as an…

It is important to use rich problem-solving tasks to develop students' understanding of important mathematical ideas (NCTM 2000). Rich tasks are complex, nonalgorithmic, and nonroutine, requiring reasoning, problem solving, and communication of thinking. Evidence has shown that using rich tasks in student-centered classrooms is especially…

More than 10 percent of the students in our nation's public schools are English language learners, and this number grows each year. Many of these students are falling behind in math. "Supporting English Language Learners in Math Class, Grades 3-5" outlines the challenges ELL students face when learning math and provides a wealth of specific…

Every student should understand and use all concepts and skills from the previous grade levels. The standard is designed so that new learning builds on preceding skills. Communications, Problem-solving, Reasoning & Proof, Connections, and Representation are the process standards that are embedded throughout the teaching and learning of all…

New capabilities in "TinkerPlots 2.0" supported the conceptual development of fifth- and sixth-grade students as they pursued several weeks of instruction that emphasized data modeling. The instruction highlighted links between data analysis, chance, and modeling in the context of describing and explaining the distributions of measures that result…

Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…

"Differentiating Instruction With Menus Grades 3-5" offers teachers everything they need to create a student-centered learning environment based on choice. Addressing the four main subject areas (language arts, math, science, and social studies) and the major concepts taught within these areas, these books provide a number of different types of…