Twenty classes in ten schools with 627 sixth-grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One-way ANOVA analysis indicate that significant difference…

This paper investigates some aspects of number patterns that have been a subject of interest and engaged students of mathematics for many years. It is left for the teacher to select and fashion any aspects they feel suit their own students.

Five-year-old children categorized as skilled versus unskilled counters were given verbal estimation and number word comprehension tasks with numerosities 20-120. Skilled counters showed a linear relation between number words and nonsymbolic numerosities. Unskilled counters showed the same linear relation for smaller numbers to which they could…

Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those…

In 4 experiments, the authors investigated the reversal of spatial congruency effects when participants concurrently practiced incompatible mapping rules (J. G. Marble & R. W. Proctor, 2000). The authors observed an effect of an explicit spatially incompatible mapping rule on the way numerical information was associated with spatial responses. The…

It is much debated whether translation is semantically mediated or based on word-word associations at the lexical level. In 2 experiments with Dutch (L1)-French (L2) bilinguals, the authors showed that there is a semantic number magnitude effect in both forward and backward translation of number words: It takes longer to translate number words…

A semigroup G is a group if it has a left identity and every element has a left inverse. The purpose of this note is to weaken this condition further in two different ways. A semigroup G with an identity e is a group if every element x in G has an inverse. It is well known that this statement can be weakened. A semigroup G with a left identity e…

Recently, [Kunde, W., Kiesel, A., & Hoffmann, J. (2003). Conscious control over the content of unconscious cognition. "Cognition," 88, 223-242] used a masked priming paradigm to argue that neither the "elaborate processing" or the "evolving automaticity" view can account for the processing of unconscious numerical stimuli. In our Experiment 1 we…

Six proofs are given for the fact that for each integer n [greater than or equal to] 2, the nth root function, viewed as a function from the set of non-negative real numbers to itself, is not linear. If p is a prime number, then [Zeta]/p[Zeta] is characterized, up to isomorphism, as the only integral domain D of characteristic p such that D admits…

This article describes how to determine your return on investment when deposits of varying amounts are made over irregular time intervals.

This paper aims to explore some properties of certain third-order linear sequences which have some properties analogous to the better known second-order sequences of Fibonacci and Lucas. Historical background issues are outlined. These, together with the number and combinatorial theoretical results, provide plenty of pedagogical opportunities for…

Responsiveness to Intervention (RtI) is recommended both as an essential step before identifying learning disabilities (LD) and as a mechanism for preventing learning difficulties. The use of evidence-based multi-tiered interventions is of critical importance when implementing RtI. This article presents the results of a study that examined the…

The mathematical performance of 182 third and fourth graders in 8 different areas of mathematics was examined. The children belonged to 4 achievement groups: children with mathematic difficulties (MD only), children with both mathematic and reading difficulties (MD-RD), children with reading difficulties (RD only), and normally achieving children…

"Math is language, too," Phyllis and David Whitin (2000) remind everyone in their informative book about reading and writing in the mathematics classroom. This means that students in elementary school math classes are learning two distinct, yet related languages--one of numbers, the other of words. These languages of numbers and words…

The "General Mathematics" series is intended to introduce students to basic mathematic principles and concepts as well as to the opportunity to apply those principles and concepts. This color coded module, one of six in the series, will allow students to build or increase their level of understanding of whole numbers and will help…