In a future that is likely to be increasingly dominated by new technology, it is important to consider what mathematics is and how it might be taught. This article discusses these and related issues in the context of both universities and schools.

The efficiency and modes of usage of computerized tools (DGE and some other types of tools) were studied in relation to: students' abilities; the routineness of a problem; and the type of course (all three parameters defined in the paper). It was found that there was no significant difference in modes of computer usage for routine problems; a…

Undergraduate and graduate mathematics teacher education frameworks must ensure professional development of two groups of practitioners within the community of mathematics educators, namely pre-service and in-service mathematics teachers. The relationship between them serves as an example of connection theory and practice in mathematics teacher…

This article analyses mathematical modelling from several different perspectives and contrasts modelling with problem solving. Then it describes the ways in which modelling, applications, and problem solving are approached in several Latin American countries. It further describes workshops for secondary schools and for university teachers in which…

The purpose of this research is to investigate students' cognitive behaviour in the subjects of function, limit, and derivative according to gender. The research was conducted with the participation of 67 female and 58 male 11th grade students of Gazi High School in Eskisehir in the academic year 2000/2001. The data were obtained through a test…

The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

In rare cases, the use of advanced mathematical calculators can give incorrect results. One such error occurs with graphing calculators because the screen is not continuous, but a rectangular array of pixels. On some frequently used calculators, the graph of sin80x looks like sin x. We also study other related examples.

This note discusses some of the shortcomings of multiple choice tests in Mathematics given to undergraduate engineering students. Examples are presented, where the disadvantages of a multiple choice test are pointed out and suggestions how to overcome the difficulties are given.

The Kolmogorov?Smirnov (K-S) test for goodness of fit was developed by Kolmogorov in 1933 [1] and Smirnov in 1939 [2]. Its procedures are suitable for testing the goodness of fit of a data set for most probability distributions regardless of sample size [3-5]. These procedures, modified for the exponential distribution by Lilliefors [5] and…

The problem of comparison of answers in trigonometric equations arises frequently when different solution strategies are encouraged in the classroom. This paper shows how such a problem can be put in context structured by classic and contemporary perspectives on teaching problem solving, including the use of technology.

Catalan numbers are defined by combinatorial properties, in numerous situations. Here, an integral representation for these Catalan numbers is computed.

It is well known that e-squared is irrational: this note presents a simple proof of it. The arguments stay within the realms of a first proof course in mathematical analysis offered for undergraduates.

This paper presents a critical analysis of data analysis requirements in physics tertiary entrance examinations. The setting is Western Australia. Common aspects of the questions asked over 14 years and changes in the questions since a major syllabus reform are identified. Similar changes in other jurisdictions are referenced. The data analysis…

A regular problem in regression analysis is estimating the comparative importance of the predictors in the model. This work considers the 'net effects', or shares of the predictors in the coefficient of the multiple determination, which is a widely used characteristic of the quality of a regression model. Estimation of the net effects can be a…

This paper presents a context lead approach to rotational dynamics. By using nothing more than two cans of cola the basic notions of linear velocity, angular velocity, moments of inertia and conservation of energy can be explored. The approach can be used equally well as both a demonstration or an investigative assignment. The same starting point…