This paper reports selected findings from a study of number sense proficiency of students aged 13 to 16 years in a state in Malaysia. A total of 1756 students, from thirteen schools in a state in Malaysia participated in this study. A majority (74.9%) of these students obtained an A grade for their respective year-end school examinations. The…

With powerful influence on the people, taboos should be noticed with keen awareness and handled with cautious respect for international visitors in China, a traditional country in its process of modernization, if successful cross-cultural communication is to be achieved. In the ever changing and integrating world, Chinese taboos are never free…

Although elementary number theory topics are closely linked to foundational topics in number and operations and are prevalent in elementary and middle grades mathematics curricula, little is currently known about how students and teachers make sense of them. This study investigated pre-service elementary teachers' developing understanding of…

The value of a consideration of large numbers and exponentiation in primary and early secondary school should not be underrated. In Indian history of mathematics, consistent naming of, and working with large numbers, including powers of ten, appears to have provided the impetus for the development of a place value system. While today's students do…

This study investigates how 217 students in Years 5, 6 and 7 from three schools in Nanjing, China, link number and algebra (called relational thinking in this study). It categorizes their performances in terms of five levels, and uses these levels to create profiles of algebraic thinking across Years 5, 6, and 7. The study examines the…

For at least 2000 years people have been trying to calculate the value of [pi], the ratio of the circumference to the diameter of a circle. People know that [pi] is an irrational number; its decimal representation goes on forever. Early methods were geometric, involving the use of inscribed and circumscribed polygons of a circle. However, real…

In this article we contribute a perspective on mathematical embodied cognition consistent with a phenomenological understanding of perception and body motion. It is based on the analysis of 4 selected episodes in 1 session of an undergraduate mathematics class. The theme of this particular class session was the geometric interpretation of the…

The Common Core State Standards for Mathematics (CCSSM) were "designed to be robust and relevant to the real world, reflecting the knowledge and skills that young people need for success in college and careers" (CCSSI 2010). For the first time in U.S. history, a set of standards is established that will be taught in nearly every state. Forty-four…

A randomized evaluation of a 9-month comprehensive math program for preprimary Bangladeshi school children addressed skills such as numbers, measurement, shapes, patterns, and space. Nine schools were randomly selected for the Intervention group and nine for the Control group, with 12 children randomly selected from each to participate in testing.…

This study examined how four domain-specific skills (arithmetic procedural skills, number fact retrieval, place value concept, and number sense) and two domain-general processing skills (working memory and processing speed) may account for Chinese children's mathematics learning difficulties. Children with mathematics difficulties (MD) of two age…

Number relationships, which go far beyond counting skills, refer to the ability to represent a quantity in multiple, flexible ways. It is arguably among the most important mathematics concepts in number and quantity. The current study examined the effectiveness of number relationships instruction in preschool classrooms. Participants included 73…

In this study, we directly contrast two approaches that have been proposed to explain the SNARC effect. The traditional direct mapping account suggests that a direct association exists between the position of a number on the mental number line and the location of the response. On the other hand, accounts are considered that propose an intermediate…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

This study aims to determine the influence of teaching Fibonacci numbers and golden ratio through history of mathematics on student achievement and the opinions of students regarding this issue. This study was carried out by case study method with 30 students who attended the 8th grade of an elementary school in Erzincan in spring term of…

The goal of this study was to understand errors that student make when simplifying exponential expressions. College students enrolled in four college mathematics courses were asked to simplify and compare such expressions. Quantitative analysis identified three persistent errors: interpreting negative bases, negative exponents, and parentheses.…