Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

Using Mathematical Modelling has become a useful tool in teaching-learning mathematics at all levels. This is so because mathematical objects are seen from their very applications, giving them meaning from the beginning. In this paper we present some details on the development of a teacher's training course called Modelling in the Teaching of…

In this paper we describe a teaching approach focusing on modelling in physics, emphasizing scientific reasoning based on empirical data and using the notion of multiple representations of physical phenomena as a framework. We describe modelling activities from a project (PHYS 21) and relate some experiences from implementation of the modelling…

Introduces a model of differential equations for students--a very real overpopulation problem is occurring in the Ndumu Game Reserve in KwaZulu-Natal, South Africa, where one species of antelope, the Nyala, is crowding out another species, the Bushbuck. Constructs a competing species model to mathematically describe what is occurring in Ndumu.…

Adds a cropping or harvesting term to the animal overpopulation model developed in Part I of this article. Investigates various harvesting strategies that might suggest a solution to the overpopulation problem without actually culling any animals. (ASK)

This document consists of seven chapters. The first chapter analyzes the modeling process and gives reasons for introducing a modeling approach in classrooms, arguing that students will develop more confident and positive attitudes toward mathematics. The next five chapters contain case studies, which focus, respectively on: whether it is more…

Discusses three types of bridges to determine how best to model each one: (1) drawbridge; (2) balance bridge; and (3) bascule bridge. Describes four experiments with assumptions, analyses, interpretations, and validations. Provides several diagrams and pictures of the bridges, and typical data. (YP)

Presents a methodology of mathematical and technological principles as integrated components of the Design and Technology syllabus of the National Curriculum in the United Kingdom. The methodology is based on the syllabus area of product analysis and employs a structured problem-solving approach. (ASK)

Geometric axioms are discussed in terms of philosophy, history, refinements, and basic concepts. The triumphs and limitations of the formalism theory are included. Described is the status of high school geometry internationally. (KR)

Discusses some of the aspects of problem solving that teachers can observe for assessment purposes in a student's practical and written work. Suggests that these observations can be incorporated into a student's assessment traditionally or using alternative assessment devices. (PK)