Continues the theme developed in the first paper on this topic which was published in volume 10 of this journal. Carries the historical tale of pi from the late 16th century to the present. (ASK)

Mathematics has had a spiritual aspect throughout its history. Discusses the nature of the interplay between mathematics and spirituality in some traditional and modern contexts. (Contains 29 references.) (ASK)

One minor but irritating problem that most composition teachers face--especially those who handle masses of papers at the high school level--involves coming up with a method of grading that is demonstrably objective but not so rigid that it allows no room for judgment. The author proposes a hybrid grading system: combining numbers and letters. The…

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…

We used a numerical bisection procedure to examine preschool children's sensitivity to the numerical attributes of stimuli. In Experiment 1 children performed two tasks. In the Cups Task they earned coins for choosing a green cup after two drumbeats and a blue cup after eight drumbeats. In the Gloves Task they earned coins for raising a red glove…