In this article, we review research literature concerning number sense from several related fields. Whereas other authors have pointed to difficulty defining number sense or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: three constructs given the same name. Our purpose is to clarify the…

Students exhibiting mature number sense make sense of numbers and operations, use reasoning to notice patterns, and flexibly select the most effective and efficient problem-solving strategies (McIntosh et al., 1997; Reys et al., 1999; Yang, 2005). Despite being highlighted in national standards and policy documents (CCSS, 2010; NCTM, 2000, 2014),…

Number line models provide a visual aid for students to examine the relationship of integers with each other and facilitate learning of integers and integer operations. Such models are typically used when students are asked real-life problems. This study employs a qualitative case study design to perform an in-depth analysis of how middle grade…

In this meta-analysis of 54 longitudinal studies with over 58,000 students in kindergarten through 12th grade, we examined the predictive nature of early numeracy measured at or before the first year of formal schooling in relation to later mathematics. Results showed that early numeracy significantly predicted mathematics measured after 6 months…

Despite the importance of computational estimation skill for the improvement of number sense, little research exists on preservice teachers' estimation skills and their view on estimation in the US context. This study examined the computational estimation skill of 58 preservice elementary teachers (PSTs) and its relationship to their views of the…

The aim of this study was to investigate second-grade elementary school students' performance related to their counting skills, place value understanding, and addition operation in natural numbers. A total of 205 second-grade elementary school students from Turkey participated in this study. The data were collected through a 'Personal Information…

The number line estimation task is widely used to investigate mathematical learning and development. The present meta-analysis statistically synthesized the extensive evidence on the correlation between number line estimation and broader mathematical competence. Averaged over 263 effect sizes with 10,576 participants with sample mean ages from 4…

Instruction in an introductory programming course is typically designed to introduce new concepts and to review and integrate the more recent concepts with what was previously learned in the course. Therefore, most exam questions in an introductory programming course require students to write lines of code that contain syntactic elements…

We review research literature concerning "number sense" from several related fields. Whereas other authors have pointed to difficulty defining "number sense" or to some degree of inconsistency in the literature, we argue instead that this is a case of polysemy: There are 3 different constructs that go by the same name. In this…

Mental rotation is positively related to arithmetic ability; however, the mechanism underlying this relationship remains unclear. The possible roles of working memory, place-value concept, and number line estimation in the correlation between mental rotation and whole-number computation were investigated. One hundred and fifty-five first-grade…

This study examined the role of initial skill in moderating intervention effects of a 50 lesson mathematics intervention program, ROOTS, for at risk kindergarten students focused on developing whole number concepts and skills. The study utilized a randomized block design with at-risk students (n = 592) within classrooms (n = 60) randomly assigned…

This study examined the role of initial skill in moderating intervention effects of a 50-lesson mathematics intervention program, ROOTS, for at-risk kindergarten students focused on developing whole-number concepts and skills. The study utilized a randomized block design with at-risk students (n = 592) within classrooms (n = 60) randomly assigned…

In recent studies, test-score increases have been shown in rule-based intelligence test tasks, such as number series, after watching a corresponding video tutorial. An open question remains regarding the mechanisms involved. Specifically, taking notes to describe the relations between numbers might be linked to test scores, and is hypothesized to…

It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of…

A 1 h classroom activity is presented, aimed at consolidating the concepts of microstates and Russell-Saunders energy terms in transition metal atoms and coordination complexes. The unconventional approach, based on logic and intuition rather than rigorous mathematics, is designed to stimulate discussion and enhance familiarity with quantum…