Decomposition of variance in terms of conditional means

We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing techniques to study the interdependence of the variables involved. According to our method the variance is expressed as a sum of orthogonal components, obtained as differences of conditional means, with respect to the qualitative characters. The resulting expression for the variance depends on the ordering in which the characters are considered. We suggest an algorithm which leads to an ordering which is deemed natural. The first set of data concerns the score achieved by a population of students, on an entrance examination, based on a multiple choice test with 30 questions. In this case the qualitative characters are dyadic and correspond to correct or incorrect answer to each question. The second set of data concerns the delay in obtaining the degree for a population of graduates of Italian universities. The variance in this case is analyzed with respect to a set of seven specific qualitative characters of the population studied (gender, previous education, working condition, parent's educational level, field of study, etc.)Comment: 3 figure

Trends in the chemistry of atmospheric deposition and surface waters in the Lake Maggiore catchment

The Lake Maggiore catchment is the area of Italy most affected by acid deposition. Trend analysis was performed on long-term (15-30 years) series of chemical analyses of atmospheric deposition, four small rivers draining forested catchments and four high mountain lakes. An improvement in the quality of atmospheric deposition was detected, due to decreasing sulphate concentration and increasing pH. Similar trends were also found in high mountain lakes and in small rivers. Atmospheric deposition, however, is still providing a large and steady flux of nitrogen compounds (nitrate and ammonium) which is causing increasing nitrogen saturation in forest ecosystems and increasing nitrate levels in rivers. Besides atmospheric deposition, an important factor controlling water acidification and recovery is the weathering of rocks and soils which may be influenced by climate warming. A further factor is the episodic deposition of Saharan calcareous dust which contributes significantly to base cation deposition.</p> <p style='line-height: 20px;'><b>Keywords: </b>trend, atmospheric deposition, nitrogen, stream water chemistry

Interdisciplinarity for learning and teaching mathematics

Complex problems need interdisciplinary approaches. Thinking in an interdisciplinary way asks for changes in learning and teaching and hence in our views on pedagogical problems. An interdisciplinary approach could provide a new framework also for dealing with disciplinary didactical problems. In this paper, we propose a methodology which we call globally interdisciplinary laboratories as an effective way to practice interdisciplinary teaching at the high school level. We discuss the possibility of applying this methodology to the learning and teaching of mathematics. Globally interdisciplinary laboratories are designed by a pool of researchers in collaboration with high school teachers of several disciplines and they are delivered in the classroom by a pool of teachers in co-presence. This has been experimented in Italy in many classes which are part of a national educational project called Liceo matematico. In this paper, we discuss the general design principle of a GIL and exemplify the methodology by considering the one we have called educate the sight, which aims at stimulating, within an interdisciplinary framework, intellectual curiosity, the ability to spot the prominent features of a problem and, in mathematics, the ability of conjecturing, which should be one of the fundamental concerns of mathematical teaching, according to Polya’s decalogue for mathematics teachers (POLYA, 1981)

Trends in the chemistry of atmospheric deposition and surface waters in the Lake Maggiore catchment

International audienceThe Lake Maggiore catchment is the area of Italy most affected by acid deposition. Trend analysis was performed on long-term (15-30 years) series of chemical analyses of atmospheric deposition, four small rivers draining forested catchments and four high mountain lakes. An improvement in the quality of atmospheric deposition was detected, due to decreasing sulphate concentration and increasing pH. Similar trends were also found in high mountain lakes and in small rivers. Atmospheric deposition, however, is still providing a large and steady flux of nitrogen compounds (nitrate and ammonium) which is causing increasing nitrogen saturation in forest ecosystems and increasing nitrate levels in rivers. Besides atmospheric deposition, an important factor controlling water acidification and recovery is the weathering of rocks and soils which may be influenced by climate warming. A further factor is the episodic deposition of Saharan calcareous dust which contributes significantly to base cation deposition. Keywords: trend, atmospheric deposition, nitrogen, stream water chemistry

Modelling the effects of atmospheric sulphur and nitrogen deposition on selected lakes and streams of the Central Alps (Italy)

International audienceThe dynamic model MAGIC was calibrated and applied to selected sites in north-western Italy (3 rivers, 10 alpine lakes) to predict the future response of surface water to different scenarios of atmospheric deposition of S and N compounds. Results at the study sites suggest that several factors other than atmospheric deposition may influence the long-term changes in surface water chemistry. At present the lumped approach of dynamic models such as MAGIC cannot represent all the processes occurring at the catchment scale. Climate warming in particular and its effects on surface water chemistry proved to be important in the study area. Furthermore the river catchments considered here showed clear signs of N saturation. This condition and the increasing concentrations of NO3 in river water were simulated using N dynamics recently included in MAGIC. The modelling performed in this study represents the first application of MAGIC to Italian sites. The results show that inclusion of other factors specific to the Mediterranean area, such as dust deposition and climate change, may improve the fit to observed data and the reliability of the model forecast. Despite these limitations, the model captured well the main trends in chemical data in both rivers and lakes. The outputs clearly demonstrate the benefits of achieving the emission reductions in both S and N compounds as agreed under the Gothenburg Protocol rather than making no further emission reductions. It was also clear that, besides the substantial reduction of SO4 deposition from the peak levels of the 1980s, N deposition must also be reduced in the near future to protect freshwaters from further acidification. Keywords: MAGIC, northern Italy, acidification, recovery, nitrogen saturatio