Teachers and teacher educators have been sharing strategies and resources for implementing mathematics routines in National Council of Teachers of Mathematics (NCTM) journals for years. A less commonly shared mathematics routine, especially with young learners, is "Clothesline Math" (Shore, 2017, 2018). In this routine, teachers create…

Researchers in educational measurement use Differential Item Functioning (DIF) to examine whether test items are functioning uniquely across subgroups of test participants while taking into account their ability level. DIF is essential for test validity arguments, thus making it a necessary part of validity studies. This study examines DIF across…

This study aimed to examine whether a computational thinking (CT) intervention related to (a) number knowledge and arithmetic (b) algebra, and (c) geometry impacts students' learning performance in primary schools. To this end, a quasi-experimental, nonequivalent group design was employed, with 61 students assigned to the experimental group and 47…

This study investigated how six Year Four (9-10 years old) students interacted with a dynamic (zoomable) digital number line to demonstrate knowledge and understandings of decimal fractions. Results from a task-based interview indicated that the zoomable number line is able to assist students in developing conceptual understandings of decimal…

Teachers and mathematicians hold different perspectives on the teaching and learning of whole number arithmetic. Though these perspectives may be complementary, sharing them across communities is challenging. An unusual professional development course for primary school teachers, initiated and taught by research mathematicians, provided a setting…

This study examined cognitive precursors of hierarchical mathematical development. Six-year-old children (n = 258) were assessed on number skills, cognitive skills, and arithmetic 1 year prior to school entry. Skills in advanced arithmetic and advanced mathematics were assessed in Grades 3 and 6, respectively. Path analyses were computed and…

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…

This article reports on a study in which researchers asked children to "make up as story and a picture about marbles for this number sentence: 3 x 5 = 15." Students in this study came from pre - dominantly low- to average-income families living in three distinct geographical areas within the United States. A similar division task was…

The aim of the present study was to investigate the cognitive profiles of primary school children (age 82-133 months) on a battery of basic number processing and calculation tasks. The sample consisted of four groups matched for age and IQ: arithmetic disorder only (AD; n = 20), reading disorder only (RD; n = 40), a comorbid group (n = 27), and an…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

Math relies on mastery and integration of a wide range of simpler numerical processes and concepts. Recent work has identified several numerical competencies that predict variation in math ability. We examined the unique relations between eight basic numerical skills and early arithmetic ability in a large sample (N = 1391) of children across…

Upper primary school students' difficulties with decimal place value are widely recognised due largely to the availability of assessment tools that accurately identify students' misconceptions in this domain. Yet, many students' decimal difficulties seem to stem from a lack of understanding of whole number place value for which there are few, if…

A comprehensive working memory battery and tests of mathematical skills were administered to 90 children--41 in Year 1 (5-6 years of age) and 49 in Year 3 (7-8 years of age). Working memory could explain statistically significant variance in number writing, magnitude judgment, and single-digit arithmetic, but the different components of working…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…