As geometry involves lot of graphics, it acts as a link between mathematical model and real-world phenomena. An effective tool like geometry software can help students to explore the ellipse.

Discusses a real-world problem-solving lesson that emerged when a high school math teacher used a motion detector with a CBL and graphing calculator to obtain the bounce data of a ping-pong ball. Describes the lesson in which students collect bad data then fill in the missing parabolas that result using critical components of parabolas and…

In the paper the results of an empirical study, which has evaluated the development of mathematical literacy in an innovative teaching programme, are presented. The theoretical approach of mathematical literacy relies strongly on applications and modelling and the study follows the approach of R. Bybee, who develops a theoretical concept of…

Categories can be counted, rated, or ranked, but they cannot be measured. Likewise, persons or individuals can be counted, rated, or ranked, but they cannot be measured either. Nevertheless, psychology has realized early on that it can take an indirect road to measurement: What can be measured is the strength of association between categories in…

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 the use of a Dutch pyramid model that may help teachers design assessment problems that go beyond reproduction and need mathematization, generalization, and insight. (Contains 4 figures.)

"Chemical Engineering Modeling" is a first-semester graduate course traditionally taught in a lecture format at Oklahoma State University. The course as taught by the author for the past seven years focuses on numerical and mathematical methods as necessary skills for incoming graduate students. Recent changes to the course have included Visual…

This article analyses the modeling approach used by one student in a business problem. It is argued that if we use previous frameworks we are not able to classify the students' approach to modeling as purely theoretical or empirical. Instead the student used a theoretical approach when constructing a real model, but abandoned it when she had to…

We focus on the problem of ignoring statistical independence. A binomial experiment is used to determine whether judges could match, based on looks alone, dogs to their owners. The experimental design introduces dependencies such that the probability of a given judge correctly matching a dog and an owner changes from trial to trial. We show how…

The paper reports on studies of the impact of harvesting on a prey-predator system with non-monotonic functional response and intra-specific competition in the predator growth dynamics. The existence of its steady states and their stability are studied using eigenvalue analysis. The possibility of the existence of bionomic equilibria has been…

This article proposes a mathematical model of Intelligent Tutoring Systems (ITS), based on observations of the behaviour of these systems. One of the most important problems of pedagogical software is to establish a common language between the knowledge areas involved in their development, basically pedagogical, computing and domain areas. A…

We report on a small scale study with six experienced teachers of mathematics in which we have applied a general theoretical model of expert practice (developed by the second author) to explore the nature of the knowledge base that enables teachers to operate effectively in the complexity of a class of 30 pupils. This model uses the notion of…

The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…

The idea of using mathematical research in the classroom to collect real data has been spoken about within education for many years. The question is, why should teachers bother with real data from their students' worlds and how do they actually put it into practice in the classroom? When using the mathematical research strategy for collecting,…

The purpose of this study is to determine the latent structure of the California Verbal Learning Test-Second Edition (CVLT-II; Delis, Kramer, Kaplan, & Ober, 2000) at three different age levels, using the standardization sample. Maximum likelihood confirmatory factor analyses are performed to test four competing hypothetical models for fit and…