Applications and modelling in mathematics teaching

The aim of this paper is a comprehensive presentation of some important basic and general aspects of the topic applications and modelling, with emphasis on the secondary school level. Owing to the review character of this paper, some overlap with the survey paper Blum and Niss (1989) for ICME-6 in Budapest is inevitable. The paper will consist of three parts. In part 1, I shall try to clarify some basic concepts and remind the reader of a few application and modelling examples suitable for teaching. In part 2, I shall formulate some general aims for mathematics instruction and, on that basis, summarise the most important arguments for and against applications and modelling in mathematics teaching. Finally, in part 3, I shall discuss some relevant instructional aspects resulting from the considerations in part 2.

Mathematical modelling in mathematics education and instruction

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

Analysis of applications and of conceptions for an application-oriented mathematics instruction

In connection with the (revived) demand for considering applications in the teaching of mathematics, various schemata or lists of criteria have been developed since the end of the sixties, which set up requirements about closeness to the real world or about the type of mathematics being used, and which have made it possible to analyze the available applications in their light. After having stated the problem (in section 1), we present (in section 2) a sketch of some of the best known of these and of some earlier schemata, although we are not aiming for a complete picture. Then (in section 3) we distinguish among different dimensions.in the analysis of applications. With this as a basis, we develop (in section 4) our own suggestion for categorizing types of applications and conceptions for an application-oriented mathematics instruction. Then (in section 5) we illustrate our schemata by some examples of performed evaluations. Finally (in section 6), we present some preliminary first results of the analysis of teaching conceptions.

Wild food trees in Eastern Nuba Mountains, Sudan: Use diversity and threatening factors

This study was conducted in 2010 in Eastern Nuba Mountains, Sudan to investigate ethnobotanical food and non-food uses of 16 wild edible fruit producing trees. Quantitative and qualitative information was collected from 105 individuals distributed in 7 villages using a semi-structured questionnaire. Also gathering of data was done using a number of rapid rural appraisal techniques, including key informant interviews, group discussion, secondary data sources and direct observations. Data was analysed using fidelity level and informant consensus factor methods to reveal the cultural importance of species and use category. Utilizations for timber products were found of most community importance than food usages, especially during cultivated food abundance. Balanites aegyptiaca, Ziziphus spina-christi and Tamarindus indica fruits were asserted as most preferable over the others and of high marketability in most of the study sites. Harvesting for timber-based utilizations in addition to agricultural expansion and overgrazing were the principal threats to wild edible food producing trees in the area. The on and off prevailing armed conflict in the area make it crucial to conserve wild food trees which usually play a more significant role in securing food supply during emergency times, especially in times of famine and wars. Increasing the awareness of population on importance of wild food trees and securing alternative income sources, other than wood products, is necessary in any rural development programme aiming at securing food and sustaining its resources in the area.