This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

In this article, the author describes strategies to support students in conjecturing in ways that promote their agency. Conjecturing involves justifying (i.e., a practice that promotes epistemic agency and engages students in mathematical reasoning to defend their claims; Bieda & Staples, 2020) by which a conjecture becomes proven, modified,…

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…

In their commentary, "Toward a Framework for Research Linking Equitable Teaching with the Standards for Mathematical Practice," Bartell et al. (2017) provide a stepping-stone into the challenge of clarifying the interface between equity and standards setting in mathematics education by devising a framework that relates the "Common…

"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…

Despite the introduction of Common Core State Standards and the National Council of Teachers of Mathematics urging educators to explore fundamental concepts in mathematics at a deeper level, the majority of mathematics education has remained aimed at initial skill acquisition. The result has led to students learning to mimic a standard set of…

Teachers are constantly looking for new ways to make mathematical procedures such as radical simplification meaningful for students. In classes, teachers discovered what researchers have long known, that students who only memorize a set of steps get confused when their steps do not match a new problem or scenario perfectly. The area and side…

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.…

Facilitating meaningful discourse directly supports what students should be able to do with respect to the third of the eight Standards for Mathematical Practice (SMP 3) in the Common Core State Standards for Mathematics (NGA Center and CCSSO 2010): "Construct viable arguments and critique the reasoning of others" (p. 6). Following best…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

The Common Core State Standards for Mathematics emphasize the importance of developing students' conceptual understanding, mathematical reasoning, and problem solving skills. This is a shift from the traditional approach to teaching mathematics and many teachers rely on curriculum resources to help them meet these new standards and expectations.…

Implementation of the Common Core Mathematical Standards and Practices (CCSS) has emphasized the importance of instruction that develops both procedural knowledge and conceptual understanding. Novice teachers have experienced the implementation of the CCSS during their PreK-12 experience, as well as within their teacher preparation program. It may…

Natural disasters often receive massive media attention. The headlines can engage students to think mathematically and scientifically about the world around them. 'Principles and Standards for School Mathematics' explicitly encourages instruction where students "recognize and apply mathematics in contexts outside of mathematics" (NCTM…

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…

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…