The project of comparative cognition benefits from common measures across species. We report here on five experiments using the violation of expectancy looking time measure with free-ranging rhesus macaques ("Macaca mulatta"), each designed to build on current knowledge concerning spontaneous representations of number. Each subject, tested in only…

The present study aims to investigate the relationship between the rhythmical and the kinetic parts of the Hasapikos dance--both slow and fast--so that, after their relation is determined and recorded, the authentic form of the dance can be formally expressed with rhythmical numeration for teaching purposes. The collection of the data was based on…

This note gives geometrical/graphical methods of finding solutions of the quadratic equation ax[squared] + bx + c = 0, a [not equal to] 0, with non-real roots. Three different cases which give rise to non-real roots of the quadratic equation have been discussed. In case I a geometrical construction and its proof for finding the solutions of the…

In this note, using the method of undetermined coefficients, we obtain the power series for exp ( f ( x )) and ln ( f ( x )) by means of a simple recursion. As applications, we show how those power series can be used to reproduce and improve some well-known results in analysis. These results may be used as enrichment material in an advanced…

This note generalizes the well-known Leibnitz rule of successive differentiation for the product of two functions to a similar result for the product of three functions.

In this paper, the author gives a further simple generalization of a power series evaluation of an integral using Taylor series to derive the result. The author encourages readers to consider numerical methods to evaluate the integrals and sums. Such methods are suitable for use in courses in advanced calculus and numerical analysis.

Some useful approaches to assist students with the uncertainty of measurement and the necessity of significant figures through age conversion exercise and activity are presented. It showed that while two people might be born on the same date, they are not born at the same instant once, it considers the birth time to an appropriate number of…

This article explores the origins and potential benefits of the empty number line for the development of mental computation. It also provides a learner's perspective of its use through the reflections of nine-year-old Emily. (Contains 3 figures.)

This article describes how the story of Alice in Wonderland helps students understand the operation of multiplying by a rational number less than 1 and related aspects of ratio and proportion. Included with this article is a "How Tall Is Alice?" Worksheet. (Contains 1 table and 6 figures.)

This article explores how counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. It is suggested that the teacher's role is one of noticing, questioning,…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

Children's literature can play a significant role in integrating math and science concepts into real-world applications. One particularly delightful selection is "Cucumber Soup" (Krudwig, 1998). This book can create a context--making cucumber soup--for weighing and for a real-life on adding fractions. This kind of learning context takes children…

Although many studies have examined the alignment of state standards with large-scale assessment and instruction, fewer have attended to alignment concerning alternate assessments for students with significant disabilities. This study was designed to (1) compare expectations in one state's alternate assessment (AA) with curricular priorities…

The aim of this series of four articles is to look critically, and in some detail, at the primary strategy approach to written calculation, as set out on pages 5 to 16 of the "Guidance paper" "Calculation." The underlying principle of that approach is that children should use mental methods whenever they are appropriate, whereas for calculations…

This article describes a recent and successful initiative on teaching place value and the decomposition method of subtraction to pupils having difficulty with this technique in the 9-12-year age range. The aim of the research was to explore whether using the metaphor of selling chews (i.e., sweets) in a tuck shop and developing this into an iconic…