Three methods for using four-function, counting calculators for developing understanding of the meaning of square roots and operations on whole and rational numbers are described. (MP)

The purpose of this report is to make a tentative contribution to the knowledge of students' understanding of the significance of numerical information. The article relates to a study made by the author. (Author/MK)

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)

Extensive studies have documented various difficulties with, and misconceptions about, decimal numeration across different levels of education. This paper reports on pre-service teachers' misconceptions about the density of decimals. Written test data from 140 Indonesian pre-service teachers, observation of group and classroom discussions provided…

One of the best known numbers in mathematics is the number denoted by the symbol [pi]. This column describes activities that teachers can utilize to encourage students to explore the use of [pi] in one of the simplest of geometric figures: the circle.

A key area of weakness in individuals with fetal alcohol spectrum disorder (FASD) is working memory, thus the goal of this study was to determine whether teaching children (aged 4-11) with FASD verbal rehearsal would increase their memory. Rehearsal training has been effective in other populations with working memory difficulties, so we…

We review recently published papers that have contributed to our understanding of how the preverbal infant represents number, area and time. We review evidence that infants rely on two distinct systems to represent number nonverbally and highlight the similarities in the ratio-dependent discrimination of number, time and area. Contrary to earlier…

This article looks at how the activity of decomposing number--having students write numerical expressions equivalent to the number of days in school--can help students develop understanding of place value. (Contains 3 figures.)

The balance between the preservation of early cognitive functions and serious transformations on these functions shifts across time. Piaget's writings, which favored transformations, are being replaced by writings that emphasize continuities between select cognitive functions of infants and older children. The claim that young infants possess…

Technology and mathematics. manipulatives have been brought together in a new format. This joining has resulted in virtual manipulatives that are available on the Internet for students. Virtual manipulatives have been defined as computer based renditions of common mathematics manipulatives and tools. Just as a physical object can be flipped,…

A theoretical analysis of the development of numerical representations indicated that playing linear number board games should enhance preschoolers' numerical knowledge and ability to acquire new numerical knowledge. The effect on knowledge of numerical magnitudes was predicted to be larger when the game was played with a linear board than with a…

The purpose of this study was to determine whether children's recall of tones, numbers, and words was supported by a common temporal sequencing mechanism; whether children's patterns of memory for tones, numbers, and nonsense words were the same despite differences in symbol systems; and whether children's recall of tones, numbers, and nonsense…

This article reports results of a four-year longitudinal study that investigated the impact of specific and non-specific precursors on mathematical school achievement. Preschool quantity-number competencies (QNC) predicted mathematical achievement in primary school. Furthermore, basic arithmetic fact retrieval in Grade 1 had an impact on early…

The underlying neural mechanisms of developmental dyscalculia (DD) are still far from being clearly understood. Even the behavioral processes that generate or influence this heterogeneous disorder are a matter of controversy. To date, the few studies examining functional brain activation in children with DD mainly focus on number and counting…

Appropriate concrete and pictorial models allow students to construct meaning for rational numbers and operations with the numbers. To develop deep understanding of rational number, sixth through eighth graders must experience a variety of models (NCTM 2000). Since 1979, personnel from the Rational Number Project (RNP), a cooperative research and…