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.

Evaluation of the agricultural vocational training programmes conducted by the Krishi Vigyan Kendras (Farm Science Centres) in Indian Punjab

Krishin Vigyan Kendras-KVKs (Farm Science Centres) have been established by the Indian Council of Agricultural Research in 569 districts. The trust areas of KVKs are refinement and demonstration of technologies, and training of farmers and extension functionaries. Imparting vocational trainings in agriculture and allied fields for the rural youth is one of its mandates. The study was undertaken to do a formative and summative (outcome and impact) evaluation of the beekeeping and mushroom growing vocational training programmes in the Indian state of Punjab. One-group pre and post evaluation design was employed for conducting a formative and outcome evaluation. The knowledge tests were administered to 35 beekeeping and 25 mushroom cultivation trainees, before and after the training programmes organized in 2004. The trainees significantly gained in knowledge. A separate sample of 640 trainees, trained prior to 2004, was selected for finding the adoption status. Out of 640, a sample of 200 was selected by proportionate sampling technique out of three categories, namely: non-adopters, discontinued-adopters and continued-adopters for evaluating the long-term impact of these training programmes. Ex-post-facto one-shot case study design was applied for this impact analysis. The vocational training programmes have resulted in continued-adoption of beekeeping and mushroom cultivation enterprises by 20% and 51% trained farmers, respectively. Age and trainee occupation had significant influence on the adoption decision of beekeeping vocation, whereas education and family income significantly affected the adoption decision of mushroom cultivation. The continued adopters of beekeeping and mushroom growing had increased their family income by 49% and 24%, respectively. These training programmes are augmenting the dwindling farm income of the farmers in Indian Punjab.

Ethnomethodologie als handlungstheoretische Grundlage einer Didaktik der Kommunikation

Our focus is the question as to how communication in school and instruction can be organized in an open-ended yet methodical fashion. Accordingly we proceed from the thesis that teaching methodology must be in accordance with the methodology od everyday activities so that school instruction can build on the structure of reflexive communication. We therefore adopt ethnomethodology as a theory of everyday activities in order to establish a repertoire of teaching methodologies. Taking an ethnomethodological perspective we analyze two examples of pupil aggression from the aspect of the reflexivity of accounts and develop suggestions for openended teaching methodologies.