In this paper, we consider some combinatorial and statistical aspects of the popular "Powerball" lottery game. It is not difficult for students in an introductory statistics course to compute the probabilities of winning various prizes, including the "jackpot" in the Powerball game. Assuming a unique jackpot winner, it is not difficult to find the…

This article focuses on the specific skills and abilities of young children in oral counting and enumeration. Responses to an oral counting task and an enumeration task by a sample (n=93) of 3- and 4-year old children attending a range of pre-five establishments in an urban district of northern England are described. The findings, whilst providing…

Given three points in the plane, interest is in the locus of all points for which the sum of the distances to the given points is a prescribed constant. These curves turn out to be sixth degree polynominals in x and y , and thus are complicated. However, it turns out that often there is a point, within the triangle formed by the three given…

This note could find use as enrichment material in a course on the classical geometries; its preliminary results could also be used in an advanced calculus course. It is proved that if a , b and c are positive real numbers such that a[squared] + b[squared] = c[squared] , then cosh ( a ) cosh ( b ) greater than cosh ( c ). The proof of this result…

Given two circles C 1 and C 2 in a plane such that neither one of the two circles is contained in the other, there are either four common tangents when the circles do not intersect at all or the circles have three common tangents when they touch each other externally or only two common tangents when the circles intersect exactly at two points. The…

Multilevel analysis is a useful technique for analyzing longitudinal data. To describe a person's development across time, the quality of the estimates of the random coefficients, which relate time to individual changes in a relevant dependent variable, is of importance. The present study compares three estimators of the random coefficients: the…

In a recent edition of "Mathematics Teaching" Midge Pasternack argued the case for the use of the 0-99 square with young children rather than the ubiquitous 1-100 square. In this article, the author would like to take the opportunity to mount a defence in favour of the much maligned 1-100 square. His main criticism of the 0-99 square (apart from…

An integral, either definite or improper, cannot always be computed by elementary methods, such as reversed usage of differentiation formulae. Graphical properties, in particular symmetries, can be useful to compute the integral, via an auxiliary computation. We present graded examples, then prove a general result. (Contains 4 figures.)

The method of least squares enables the determination of an estimate of the slope and intercept of a straight line relationship between two quantities or variables X and Y. Although a theoretical relationship may exist between X and Y of the form Y = mX + c, in practice experimental or measurement errors will occur, and the observed or measured…

Digital cameras are a piece of technology routinely used by students. To demonstrate the camera's use as a scientific instrument, the author developed an exercise to challenge students' scientific creativity and provide an experience in the scientific research process. Students designed and carried out experiments to determine the distance from…

In this article a new approach to calculate the return-on-investment (ROI) when introducing technology in education or training is introduced. After an identification of major aspects that are of significance when talking about traditional ROI an alternative method called Simplified ROI is introduced. The main function of Simplified ROI is less to…

Are salary and wage trends in public education keeping up or falling behind in the race with inflation? Are salary increases for central-office administrators and school building administrators keeping pace with increases received by classroom teachers and support personnel? How do overall salary and wage changes in one school system compare with…

In this article, we review the empirical evidence on the impact of education vouchers on student achievement, and briefly discuss the evidence from other forms of school choice. The best research to date finds relatively small achievement gains for students offered education vouchers, most of which are not statistically different from zero.…

Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…