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…

This study presents the preliminary qualitative results of a larger mixed methods study. The qualitative phase utilized task-based clinical interviews to examine the non-symbolic and symbolic linear generalizations of middle-grades students. This investigation identified similarities and differences in the students' generalizations, and…

What is the nature of the relationship between different lower-level numerical skills and their role in developing arithmetic skills? We consider the hypothesis of a reciprocal relationship between the development of symbolic (e.g., Arabic numerals) and nonsymbolic (e.g., arrays of objects) numerical magnitude processing. Evidence for…

Background: Early numeracy skills are associated with academic and life-long outcomes. Children from low-income backgrounds typically have poorer maths outcomes, and their learning can already be disadvantaged before they begin formal schooling. Understanding the relationship between the skills that support the acquisition of early maths skills…

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0-20 and NLA 0-100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test-retest reliability. The NLA 0-20 had low and the…

People frequently encounter numeric information in medical and health contexts. In this paper, we investigated the math factors that are associated with decision-making accuracy in health and non-health contexts. This is an important endeavor given that there is relatively little cross-talk between math cognition researchers and those studying…

This manuscript presents the results from a study to investigate the technical characteristics of two versions of a number line assessment (NLA 0-20 and NLA 0-100). The sample consisted of 60 kindergarten and 46 first grade students. Both number line versions had sufficient alternate form and test-retest reliability. The NLA 0-20 had low and the…

Background: Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in…

Little is known about whether and how parents can foster their children's spontaneous focus on number, an unprompted measure of attention to small numbers of objects that predicts later math achievement. In the current study, we asked 54 preschool-aged children and their parents to play together in a children's museum exhibit using either a…

This study investigated the relationship between kindergartners' Spontaneous Focusing on Numerosity (SFON) and their number-related utterances during numerical picture book reading. Forty-eight 4- to 5-year-olds were individually interviewed via a SFON Imitation Task and a numerical picture book reading activity. We expected differences in the…

Research Findings: Young children develop numeracy competencies during interactions with more knowledgeable others. Such interactions typically occur in the home numeracy environment (HNE). In this study a nonintensive intervention procedure was developed to improve both the HNE and numerical competencies. All parents of 113 Australian children…

The relationship between letter and numeral identification is reviewed to determine whether early identification of these symbols impact upon both literacy and numeracy development. Numerals and letters share similar perceptual properties such as geometric features and arbitrary labels. Through early socio-cultural experiences with surrounding…

Are there differential benefits of training sequential number knowledge versus spatial skills for children's numerical and spatial performance? Three- to five-year-old children (N = 84) participated in 1 session of either sequential training (e.g., what comes before and after the number 5?) or non-numerical spatial training (i.e., decomposition of…

One crucial issue in mathematics development is how children come to spontaneously apply arithmetical principles (e.g. commutativity). According to expertise research, well-integrated conceptual and procedural knowledge is required. Here, we report a method composed of two independent tasks that assessed in an unobtrusive manner the spontaneous…

Validating the structure of informal numeracy skills is critical to understanding the developmental trajectories of mathematics skills at early ages; however, little research has been devoted to construct evaluation of the Numbering, Relations, and Arithmetic Operations domains. This study was designed to address this knowledge gap by examining…