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.

Egyptian wheat

Wheat as the major cereal crop in Egypt is the core of the government's food security policy. But there are rapid losses of the genetic resources of the country as a result of ongoing modernization and development. Thus we compiled the largest possible number of Egyptian accessions preserved in the world gene banks. In the present study we collected nearly 1000 Egyptian wheat accessions. A part from the Triticum species of the Egyptian flora four species have been found, which were recorded for the first time T. turanicum, T. compactum, T. polonicum and T. aethiopicum. To classify the Egyptian wheat species using morphological studies, 108 accessions were selected. Thereafter, these accessions were cultivated and evaluated morphologically to confirm the validity of the classified species. During the morphological evaluation study, a new case was noticed for the number of glumes in one of the Egyptian wheat accessions. Three glumes per spikelet were observed in a branched spike. This led us to assess the phenomenon in all varieties with branching spikes within the genus Triticum. All varieties which have branching spikes at least in some spikletes have three glumes. We considered the case of the third glume as indicator for the domestication syndrome. Also, a new case of other forms of branching in the genus Triticum was investigated, which was a compromise between true and false-branching. We called it true-false branching. Comparative anatomical studies were carried out between Egyptian Triticum species to investigate the possibility of using anatomical features to classify the Egyptian wheat species. It was concluded that it is difficult to use anatomical features alone to differentiate between two Triticum species, especially when they belong to the same ploidy level. A key for the identification of Egyptian Triticum taxa was established.

Optical Characterization of Organic Gain Materials for UV-emitting Hybrid Complex Coupled VCSELs

In this thesis, optical gain measurement setup based on variable stripe length method is designed, implemented and improved. The setup is characterized using inorganic and organic samples. The optical gain of spiro-quaterphenyl is calculated and compared with measurements from the setup. Films with various thicknesses of spiro-quaterphenyl, methoxy-spiro-quaterphenyl and phenoxy-spiro-quaterphenyl are deposited by a vacuum vapor deposition technique forming asymmetric slab waveguides. The optical properties, laser emission threshold, optical gain and loss coefficient for these films are measured. Additionally, the photodegradation during pumping process is investigated.