Problems in physics and mathematics contexts with middle and high school classes: vertical and horizontal comparison

My thesis falls within the framework of physics education and teaching of mathematics. The objective of this report was made possible by using geometrical (in mathematics) and qualitative (in physics) problems. We have prepared four (resp. three) open answer exercises for mathematics (resp. physics). The test batch has been selected across two different school phases: end of the middle school (third year, 8\textsuperscript{th} grade) and beginning of high school (second and third year, 10\textsuperscript{th} and 11\textsuperscript{th} grades respectively). High school students achieved the best results in almost every problem, but 10\textsuperscript{th} grade students got the best overall results. Moreover, a clear tendency to not even try qualitative problems resolution has emerged from the first collection of graphs, regardless of subject and grade. In order to improve students' problem-solving skills, it is worth to invest on vertical learning and spiral curricula. It would make sense to establish a stronger and clearer connection between physics and mathematical knowledge through an interdisciplinary approach.

Spatial and temporal variation in settlement, growth and condition of the rockfish species Sebastes caurinus and Sebastes carnatus in the Channel Islands region, Santa Barbara, CA

Survival during the early life stages of marine species, including nearshore temperate reef fishes, is typically very low, and small changes in mortality rates, due to physiological and environmental conditions, can have marked effects on survival of a cohort and, on a larger scale, on the success of a recruitment season. Moreover, trade offs between larval growth and accumulation of energetic resources prior to settlement are likely to influence growth and survival until this critical period and afterwards. Rockfish recruitment rates are notoriously variable between years and across geographic locations. Monitoring of rates of onshore delivery of pelagic juveniles (defined here as settlement) of two species of nearshore rockfishes, Sebastes caurinus and Sebastes carnatus, was done between 2003-2009 years using artificial collectors placed at San Miguel and Santa Cruz Island, off Southern California coast. I investigated spatiotemporal variation in settlement rate, lipid content, pelagic larval duration and larval growth of the newly settled fishes; I assessed relationships between birth date, larval growth, early life-history characteristics and lipid content at settlement, considering also interspecific differences; finally, I attempt to relate interannual patterns of settlement and of early life history traits to easily accessible, local and regional indices of ocean conditions including in situ ocean temperature and regional upwelling, sea surface temperature (SST) and Chlorophyll-a (Chl-a) concentration. Spatial variations appeared to be of low relevance, while significant interannual differences were detected in settlement rate, pelagic larval duration and larval growth. The amount of lipid content of the newly settled fishes was highly variable in space and time, but did not differ between the two species and did not show any relationships with early life history traits, indicating that no trade off involved these physiological processes or they were masked by high individual variability in different periods of larval life. Significant interspecific differences were found in the timing of parturition and settlement and in larval growth rates, with S. carnatus growing faster and breeding and settling later than S. caurinus. The two species exhibited also different patterns of correlations between larval growth rates and larval duration. S. carnatus larval duration was longer when the growth in the first two weeks post-hatch was faster, while S. caurinus had a shorter larval duration when grew fast in the middle and in the end of larval life, suggesting different larval strategies. Fishes with longer larval durations were longer in size at settlement and exhibited longer planktonic phase in periods of favourable environmental conditions. Ocean conditions had a low explanatory power for interannual variation in early life history traits, but a very high explanatory power for settlement fluctuations, with regional upwelling strength being the principal indicator. Nonetheless, interannual variability in larval duration and growth were related to great phenological changes in upwelling happened during the period of this study and that caused negative consequences at all trophic levels along the California coast. Despite the low explanatory power of the environmental variables used in this study on the variation of larval biological traits, environmental processes were differently related with early life history characteristics analyzed to species, indicating possible species-specific susceptibility to ocean conditions and local environmental adaptation, which should be further investigated. These results have implications for understanding the processes influencing larval and juvenile survival, and consequently recruitment variability, which may be dependent on biological characteristics and environmental conditions.