In this paper, the author demonstrates a case study of undergraduate mathematics research in trigonometric sums. Involving undergraduates in research has been a long standing practice in the experimental sciences. However, it has only been recently that undergraduates have been involved in research in mathematics in significant numbers. Obviously,…

The standard derivative tests for extrema and inflection points from Calculus I can be revisited subsequently from the perspective of Taylor polynomial approximations to provide additional insights into those tests, as well as to extend them to additional criteria. (Contains 3 figures.)

Stimulated by a picture of a Sierpinski-pyramid and an article by Stewart, students were asked about a connection between this pyramid and the well-known trinomial formula. The results of all the work done with students are presented in this note. (Contains 8 figures.)

This paper develops a mathematical model for the nonselective harvesting of a prey-predator system in which both the prey and the predator obey the Gompertz law of growth and some prey avoid predation by hiding. The steady states of the system are determined, and the dynamical behaviour of both species is examined. The possibility of existence of…

This paper deals with a prey-predator model incorporating a prey refuge and harvesting of the predator species. A mathematical analysis shows that prey refuge plays a crucial role for the survival of the species and that the harvesting effort on the predator may be used as a control to prevent the cyclic behaviour of the system. The optimal…

This report is designed to assist school administrators and school boards to prepare for negotiating issues relating to class size. It includes a brief summary of the research on class size, adapted from ERS's report Class Size: A Summary of Research. Viewpoints of both school management leaders and teacher organization leaders on negotiating the…

In the "Sydney Morning Herald" of 23 March 2005, Ross Gittins argued that the funding arrangements for private schools positively encourage parents to move their children from the state system. The then Federal Minister for Education, Dr Brendan Nelson, in a letter to the "Herald" of 25-27 March, responded by saying that 68% of…

This paper suggests that mathematics teacher educators should listen carefully to what their students are saying. More specifically, it demonstrates how from one pre-teacher's non-traditional geometric representation of a unit fraction, a variety of learning environments that lead to the enrichment of mathematics for teaching can be developed. The…

Formulas for estimating cross-validated hit-rates, the number of correct classifications into an a priori grouping structure, were examined. The following mathematical formulas were compared: McLachlan's formula estimator, two Snappin and Knoke smoothed formula estimators, and the analytic leave-one-out estimator. The R method was included as a…

A formula is derived for the asymptotic standard error of a true-score equating by item response theory (IRT). The equating method is applicable when the two tests to be equated are administered to different groups along with an "anchor test." Numerical standard errors are shown for an actual equating 1) comparing the standard errors of…

Learnability theory involves the construction of formal mathematical proofs whose goal is to demonstrate how the child can successfully induce a mature grammar. An empirically adequate learnability proof constitutes a detailed hypothesis concerning the boundary conditions within which acquisition proceeds and can provide a general framework for…

An interpretation of the transformation formulas for rotations in a plane in terms of the exponential function is given. Addition of two rotations is shown to correspond to the multiplication of the two corresponding matrices. (Author/LS)

This material was prepared to help students understand the algebraic process involved in solving mixture problems. The paper copy is designed to be used with a 25-minute audiotape. Students are given a problem which is solved step by step; then they are to answer questions about each step. (MNS)