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.

Urban and peri-urban agricultural production along railway tracks: a case study from the Mumbai Metropolitan Region

Urban and peri-urban agriculture (UPA) contributes to food security, serves as an opportunity for income generation, and provides recreational services to urban citizens. With a population of 21 Million people, of which 60 % live in slums, UPA activities can play a crucial role in supporting people’s livelihoods in Mumbai Metropolitan Region (MMR). This study was conducted to characterize the railway gardens, determine their role in UPA production, and assess potential risks. It comprises a baseline survey among 38 railway gardeners across MMR characterized by different demographic, socio-economic, migratory, and labour characteristics. Soil, irrigation water, and plant samples were analyzed for nutrients, heavy metals, and microbial load. All the railway gardeners practiced agriculture as a primary source of income and cultivated seasonal vegetables such as lady’s finger (Abelmoschus esculentus L. Moench), spinach (Spinacia oleracea L.), red amaranth (Amaranthus cruentus L.), and white radish (Raphanus sativus var. longipinnatus) which were irrigated with waste water. This irrigation water was loaded with 7–28 mg N l^(−1), 0.3–7 mg P l^(−1), and 8–32 mg K l^(−1), but also contained heavy metals such as lead (0.02–0.06 mg Pb l^(−1)), cadmium (0.03–0.17 mg Cd l^(−1)), mercury (0.001–0.005 mg Hg l^(−1)), and pathogens such as Escherichia coli (1,100 most probable number per 100 ml). Levels of heavy metals exceeded the critical thresholds in surface soils (Cr, Ni, and Sr) and produce (Pb, Cd, and Sr). The railway garden production systems can substantially foster employment and reduce economic deprivation of urban poor particularly slum dwellers and migrant people. However this production system may also cause possible health risks to producers and consumers.