For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

How can students achieve an understanding of multiplication that allows them to go beyond recall to explain their thinking? Author and mathematics education professor Juli Dixon introduces a program that teachers can seamlessly integrate into existing mathematics instruction. Learn six tactics to help you shift from an anxiety-producing,…

Reinhart's (2000) article "Never Say Anything a Kid Can Say!" shared the lessons he learned as he journeyed from a teacher-centered model of instruction to one that puts students at the center of the teaching and learning process. Within his narrative, he itemized the strategies he used and learned from, balanced recommendations with…

In grade 3, students are expected to be able to represent a fraction on a number line by first identifying the interval from 0 to 1 as the unit and by partitioning the unit as needed on the basis of the denominator. This task extends these grade 3 fraction goals stated in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010)…

In this article, the author shares the Menu Writing project, designed to promote a meaningful, real-world connection to mathematics with the lives of students. The rationale for developing this project was two-fold: (1) to connect school mathematics to students' lived experiences to encourage and sustain students' interest, motivation, and…

Do you work tirelessly to make your math lessons meaningful, challenging, accessible, and engaging? Do you spend hours you don't have searching for, adapting, and creating tasks to provide rich experiences for your students that supplement your mathematics curriculum? Help has arrived! "Classroom Ready-Rich Math Tasks for Grades 4-5"…

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…

Meaningful inclusion of quantitative reasoning into mathematics instruction requires meaningful ways to evaluate it. Few formative assessments exist to evaluate the strategies students use when reasoning mathematically. The Framework for Evaluating Quantitative Reasoning Strategies presented in this article provides teachers with categories for…

This task structure both engages students in serious, grade-level appropriate mathematical work and allows the teacher to do the intentional and purposeful work of building a collaborative classroom culture. We highlight possibilities for adapting this task structure to teach different mathematics content across grade levels 3-5.

The International Association for the Evaluation of Educational Achievement (IEA) Research for Education series represents a further effort by IEA to capitalize on it's unique datasets, so as to provide powerful information for policymakers and researchers. Each report focuses on a specific topic and is produced by a dedicated team of leading…

When the focus of instruction is on learning to use mathematical tools--such as a ruler or a calculator--as a procedure, students tend not to incorporate their own mathematical reasoning. This unreflective use of tools hinders students' questioning of the reasonableness of their answers. This article describes how children expressed their…

This math activity focuses on experimental design while connecting math with life science. It is important that the science and engineering practices (SEPs) are not taught as a separate "unit" but integrated within the curriculum wherever possible. The focus is on experimental design to teach animal behavior. Students predict and test…

Paper folding is an easy and inexpensive way to engage students artistically, culturally, and mathematically. The pinwheel base is the source for many origami playthings, from a pinwheel to a boat to a butterfly. This article explores a fourth grade activity that repurposes the pinwheel base into a rich and inexpensive manipulative for the review…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This is a companion piece to "Professional Learning Community: Improving Mathematical Problem Solving for Students in Grades 4 through 8. Facilitator's Guide. REL 2019-002" (ED595201). It contains handouts to accompany each of the sessions included in the facilitator's guide.