Research has established that executive functions, the skills required to monitor and control thought and action, are related to achievement in mathematics. Until recently research has focused on working memory, but studies are beginning to show that inhibition skills--the ability to suppress distracting information and unwanted responses--are…

From a curricular stand point, the traditional invert and multiply algorithm for division of fractions provides few affordances for linking to a rich understanding of fractions. On the other hand, an alternative algorithm, called common denominator algorithm, has many such affordances. The current study serves as an argument for shifting…

Teaching statistics meaningfully at school level requires that mathematics teachers conduct classroom discussions in ways that give statistical meaning to mathematical concepts and enable learners to develop integrated statistical thinking. Key to statistical discourse are narratives about variation within and between distributions of measurements…

Fitness trackers can provide primary students with exciting opportunities to calculate, measure time and distance, graph, make sense of data, and improve their activity levels. This article suggests ways to use fitness trackers in the classroom.

Researchers suggest students in early elementary grade levels are active learners and creators and need to be exposed to science, technology, engineering, and mathematics (STEM) curriculum. The need for student understanding in STEM curriculum is well-documented, and positive results in robotics and computer programming are leading researchers and…

The aim of this qualitative case study is to investigate prospective mathematics teachers' subject matter knowledge of the underlying concepts of standard and nonstandard algorithms used to solve the problems with whole numbers. Twenty three prospective mathematics teachers enrolled in the Elementary Mathematics Education Program of one of the…

Several detours prompted me to find time in an overcrowded school day to incorporate important, powerful, daily, whole-class application of fact strategies. A few years ago, I embarked on a journey with my second graders, a journey through the strategies for mental computation of addition and subtraction facts. The focus of that journey was to…

Why would anyone think of teaching and learning mathematics directly from primary historical sources? We aim to answer this question while sharing our own experiences, and those of our students across several decades. We will first describe the evolution of our motivation for teaching with primary sources, and our current view of the advantages…

This article takes the position that teachers can use simple manipulative materials to model relatively complex situations and in doing so scaffold the development of students' number sense and early algebra skills. While students' early experiences are usually dominated by the cardinal aspect of number (i.e., counting the number of items in a…

How does the visual system recognize images of a novel object after a single observation despite possible variations in the viewpoint of that object relative to the observer? One possibility is comparing the image with a prototype for invariance over a relevant transformation set (e.g., translations and dilations). However, invariance over…

In general, researchers attempt to quantify cognitive load using physiologic and psychometric measures. Although the construct measured by both of these metrics is thought to represent overall cognitive load, there is a paucity of studies that compares these techniques to one another. The authors compared data obtained from one physiologic tool…

Benchmarking is an important strategy for comparing the size of fractions. In addition, knowing whether a given fraction is greater or less than a particular benchmark (e.g., one-half) can support students with accurately locating the fraction on a number line. This article offers a game-based activity that engages students in discussions around…

Difficulties with rational numbers have been explained by a natural number bias, where concepts of natural numbers are inappropriately applied to rational numbers. Overcoming this difficulty may require a radical restructuring of previous knowledge. In order to capture this development, we examined third- to fifth-grade students' understanding of…

Background: This study aimed to identify the mathematical domains affected in adults with neurofibromatosis 1 (NF1) and the impact of the numerical difficulties on the patients' activities of daily living. Methods: We assessed 28 adult patients with NF1 and 28 healthy control participants. All participants completed the standardised battery of…

Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. The "specialized content knowledge" (SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations…