Decimal numbers are generally assumed to be a straightforward extension of the base-ten system for whole numbers given their shared place value structure. However, in decimal notation, unlike whole numbers, the same magnitude can be expressed in multiple ways (e.g., 0.8, 0.80, 0.800, etc.). Here, we used a number line task with carefully selected…

In the primary grades, engaging in counting collections provides students with regular opportunities to make sense of numbers in dynamic ways, build social skills, and communicate about mathematics. This article aims to guide elementary educators through a team's process of planning and implementing counting collections in kindergarten. Counting…

Our study on 328 five- to six-year-old kindergarteners (mainly White European living in France, 152 girls) shows that children who do not count on their fingers and undergo finger counting training exhibit drastic improvement in their addition skills from pre-test to post-test (i.e., accuracy from 37.3% to 77.1%) compared to a passive control…

Children learn the cardinalities of the first numbers one, two, three and four before they learn how counting tracks cardinality for all numbers. It may be that when children start to understand counting, they also discover how numbers relate to one another in a structured number system. Do children who understand that the cardinality of a set is…

To understand the ways that manipulatives might support changes in students' reasoning about algebraic generalizations, a constructivist teaching experiment was conducted with two sixth-grade students. The students interpreted numerical situations with units of one and could construct units of units in mental activity. Initially, the students'…

Background and objectives: An early understanding of numerosity is crucial to developing proficiency in arithmetic, and rapid pattern recognition via subitizing is key in this process. The training app "LORE" specifically targets and cultivates pattern recognition skills from the beginning of formal schooling. This study investigated…

A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…

This longitudinal study tested the notion of a hierarchy of maths skill development by examining whether the development of later acquired arithmetic skills rely on development of earlier acquired arithmetic skills. The scores of 307 children on single-digit arithmetic, multi-digit calculation, arithmetic word problem-solving, and reading…

This article illustrates how teachers can use number lines to support students with or at risk for learning disabilities (LD) in mathematics. Number lines can be strategically used to help students understand relations among numbers, approach number combinations (i.e., basic facts), as well as represent and solve addition and subtraction problems.…

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…

Perceptual learning theory suggests that perceptual grouping in mathematical expressions can direct students' attention toward specific parts of problems, thus impacting their mathematical reasoning. Using in-lab eye tracking and a sample of 85 undergraduates from a STEM-focused university, we investigated how higher-order operator position (HOO;…

This study investigated the effects of working memory load (WML) and automaticity on mental addition through an examination of both task and individual characteristics within the framework of cognitive load theory. Results from 73 fourth graders showed that WML, automaticity, and their interaction had significant effects on mental addition.…

Previous research has demonstrated a link between children's ability to name canonical finger configurations and their mathematical abilities. This study aimed to investigate the nature of this association, specifically exploring whether the relationship is skill and handshape specific and identifying the underlying mechanisms involved.…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

Evidence of positive associations between the frequency of home math activities and preschool children's math skills is mixed, and the operationalization of home math activities varies across studies. We test whether home math activities can be grouped by activity factors based on the math subdomain they target (i.e., counting and cardinality,…