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…

Reading comprehension and arithmetic skills are essential abilities for children, particularly at the early career. Examine the link between language proficiency and numeral information process amongst primary school children. This study examines numeral comprehension in 600 Chinese primary second graders with different levels of decoding and…

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.…

State Early Learning Standards (ELS) are multi-function tools that inform early childhood instruction and practices. Using an established framework of early numerical development, this study assessed the prevalence of number, number relations, and number operations indicators in ELS, specifically indicators of counting, numeral knowledge,…

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…

Number sense is fundamental to the development of numerical problem-solving skills. In early childhood, children establish associations between non-symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non-symbolic and symbolic…

The study investigates the knowledge profiles of elementary pre-service teachers (PST) concerning numbers and operations before their professional classroom practice. By validating an instrument through exploratory and confirmatory factor analyses, it identifies and categorizes the PST' performance into distinct profiles based on the mathematical…

Equal representation as a social issue is about the participation of one social group, in a particular context, in proportion to the numbers in the group within the total population. The proportion of women in parliament, and of the participation rate of students of lower socioeconomic status in higher education, are examples. The aims of this…

Rational numbers, such as fractions and decimals, are harder to understand than natural numbers. Moreover, individuals struggle with fractions more than with decimals. The present study sought to disentangle the extent to which two potential sources of difficulty affect secondary-school students' numerical magnitude understanding: number type…

Integer arithmetic is difficult for students worldwide. Although students' integer thinking has frequently been studied, little is known about typical instructional practice for this difficult topic. Thus, to investigate what resources teachers use, we surveyed U.S. middle-grade teachers who teach negative numbers. About half the teachers said…

Competence with rational numbers is essential for mathematics proficiency in secondary mathematics. However, many students struggle with rational number concepts, and students with mathematics difficulties struggle even more. The purpose of this study was to examine the effects of an intervention that incorporated the use of explicit instruction…

In this study, we investigated how secondary students interpret algebraic expressions that contain literal symbols to stand for variables. We hypothesized that the natural number bias (i.e., the tendency to over-rely on knowledge and experiences based on natural numbers) would affect students to think that the literal symbols stand for natural…

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.…

The study set out to explore different mathematical difficulties among 877 second-grade children and to test the effect of memorization versus conceptual practices with number combinations. It used a latent profile analysis of baseline measurements of digit writing speed, number combination fluency, multidigit calculation, and number sense skills…

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…