To what extent does the use of computational tools offer teachers the possibility of constructing dynamic models to identify and explore diverse mathematical relations? What ways of reasoning or thinking about the problems emerge during the model construction process that involves the use of the tools? These research questions guided the…

Student activities focused on discovering mathematics play an important role in the teaching and learning process. WebMathematics Interactive (WMI2) was developed to offer a fast and user-friendly on-line web interface to enhance the quality of both theoretical and applied mathematics courses. For the teacher, in the classroom, it provides…

Many familiar household objects (such as sausages) involve the maximization of a volume under geometric constraints. A flexible but inextensible membrane bounds a volume which is to be filled to capacity. In the case of the sausage, a full analytic solution is here provided. Other related but more difficult problems seem to demand approximate…

Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that…

Many classes of differential equations are shown to be open to solution through a method involving a combination of a direct integration approach with suitably modified Picard iterative procedures. The classes of differential equations considered include typical initial value, boundary value and eigenvalue problems arising in physics and…

A number of schools have recently introduced new courses dealing with various aspects of iteration theory or at least have found ways of including topics such as chaos and fractals in existing courses. In this note, we will consider a family of functions whose members are especially well suited to illustrate many of the concepts involved in these…

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

This article presents a study in which applications were integrated in the Multivariable Calculus course at the Technion in the framework of supplementary tutorials. The purpose of the study was to test the opportunity of extending the conventional curriculum by optional applied problem-solving activities and get initial evidence on the possible…

This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…

This paper uses a partial differential equation which occurs in a reduced model of large scale circulation in an ocean basin as an educational vehicle through which to demonstrate the usefulness of a set of mathematical techniques in analysing the equation. A parameter occurring in the equation does in reality vary from very small through…

This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

Simple examples are really encouraging in the understanding of rearrangements of infinite series, since many texts and teachers provide only existence theorems. In the absence of examples, an existence theorem is just a statement and lends little confidence to understanding. Iterated sums of double series seem to have a similar spirit of…

The paper describes the use of a spreadsheet in a mathematics teacher education course. It shows how the tool can serve as a link between seemingly disconnected mathematical concepts. The didactical triad of using a spreadsheet as an agent, consumer, and amplifier of mathematical activities allows for an extended investigation of simple yet…

Time delays are an important aspect of mathematical modelling, but often result in highly complicated equations which are difficult to treat analytically. In this paper it is shown how careful application of certain undergraduate tools such as the Method of Steps and the Principle of the Argument can yield significant results. Certain delay…