The current study identified socioeconomic status (SES) group differences in student performance on an eighth grade mathematics assessment derived from the Third/Trends in International Mathematics and Science Study (TIMSS) 2003. Differential item functioning (DIF) methodology was applied to examine SES group differences on item performance for…

Research on learning has shown the importance of the learner's possibilities to discern what differs as well as what is similar when meeting new phenomena. But how does this kind of understanding develop when young children try to understand their environment in natural settings? The results of Tolchinsky's research (2003) about young children's…

Ordinality is--beyond numerical magnitude (i.e., quantity)--an important characteristic of the number system. There is converging empirical evidence that (intra)parietal brain regions mediate number magnitude processing. Furthermore, recent findings suggest that the human intraparietal sulcus (IPS) supports magnitude and ordinality in a…

The theory of error-correcting codes and cryptography are two relatively recent applications of mathematics to information and communication systems. The mathematical tools used in these fields generally come from algebra, elementary number theory, and combinatorics, including concepts from computational complexity. It is possible to introduce the…

How this teacher develops composition of ten with second graders was dramatically reshaped by the 2006 release of NCTM's "Curriculum Focal Points." The release of "Curriculum Focal Points"--particularly the suggestion that number sense and computation be focal areas in the second-grade mathematics curriculum--resulted in positive changes in this…

The purpose of this study was to investigate children's construction of 10s out of the 1s they have already constructed. It was found that, for many younger children, a dime was something different from 10 pennies even though they could say with confidence that a dime was worth 10 cents. As the children grew older, their performance improved.…

Worksheets for the lower grades involve locating numbers on the number line; the activities for the upper levels focus on the estimation of sums and products. (DT)

The addition and subtraction of integers is the first major avenue, and roadblock, to student success in learning algebra. This article describes a hands-on activity using a regular deck of playing cards that facilitates class discussion and helps students overcome this initial roadblock. (Contains 14 figures.)

A discussion of early Egyptian hieroglyphic numeration and calculation is presented. (SD)

Activities are presented that focus on attributes of numbers. The activities highlight such attributes as more than, equal to, greater than, less than, LCM, prime and factor. The activities provide practice in motivational game-oriented situations. (RH)

The number charts described in this article have been used successfully with elementary students as young as first graders to teach the concepts of even and odd numbers. Students construct charts and then answer a series of questions about the patterns that they observe. (RH)

This dissertation explores the robust confluence of syntactic and cultural factors involved in the structure and content of chengyu. It unpacks a number of structural tendencies in the data sample, and illuminates selected underlying cultural themes. The presence of syntactic and semantic parallelism within chengyu, as an expression of the…

Arithmetic tests for divisibility of an integer by another integer are well known. This article states and proves conditions for divisibility in binary form.