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.

Settlement history of a mountain oasis in Northern Oman

To unravel the settlement history of oases in northern Oman, data on topography, the agricultural setting, water and soil parameters and archaeological findings were collected in the Wadi Bani Awf with its head oasis Balad Seet. Data collection lasted from April 2000 to April 2003 and was based on the establishment of a 3D-georeferenced map of the oasis comprising all its major infrastructural and agronomic features. At today's Balad Seet, a total of 8.8 ha are planted to 2,800 date palms and 4.6 ha are divided into 385 small fields dedicated to wheat, barley, sorghum, oats, alfalfa, garlic, onion, lime and banana. Radiocarbon dating of charcoal in the lower part of the main terrace system determined its age to 911 ± 43 years. Monthly flow measurements of four major aflaj systems showed a total maximum flow of 32 m^3 h^-1 with the largest falaj contributing 78% of the total flow. During drought periods, average water flow decreased by 3% per month, however, with significant differences between the spring systems. The analysis of the tritium/^3helium ratio in the water led to an estimated water age of up to 10 years. In combination with the flow data, this provided insights into the elasticity of the spring flow over time. The use of the natural resources of the Wadi Bani Awf by a pastoral population started probably in the early 3rd millennium BC. The first permanent settlement might have been established at Balad Seet during the first part of the 1st millennium BC. Presumably it was initiated by settlers from al-Hamra, a village at the southern foot of the Hajar mountains. Given an abundant und stable flow of springs, even in periods of drought, the construction of Balad Seet's first irrigation systems may have occurred at this early time. The combination of topographic, agricultural, hydro-pedological and archaeological data allowed assessment of the carrying capacity of this oasis over the three millennia of its likely existence. The changing scarcity of land and water and the eventual optimisation of their use by different aflaj constructions have been major driving forces for the development and apparent relativeley stable existence of this oasis.

Competencies of Higher Education Graduates: A Case of Universitas Kristen Indonesia

This dissertation investigated higher education graduate competencies, acquired during their study period and required at work as perceived by the graduates themselves. This study also investigated whether graduates of professional, semiprofessional, and non-professional study programs acquired different levels of competencies during their studies and compared the gaps among the three groups of graduates. The case study is Universitas Kristen Indonesia graduates of graduation years 2001, 2003, and 2005, from the Faculties of Engineering, Economics and English, representing professional, semi-professional and nonprofessional study programs respectively.