Gender bias in the Trends in Mathematics and Science Study 2003 (TIMMS) for Canadian students /

This study is a secondary data analysis of the Trends in Mathematics and Science Study 2003 (TIMSS) to determine if there is a gender bias, unbalanced number of items suited to the cognitive skill of one gender, and to compare performance by location. Results of the Grade 8, math portion of the test were examined. Items were coded as verbal, spatial, verbal /spatial or neither and as conventional or unconventional. A Kruskal- Wallis was completed for each category, comparing performance of students from Ontario, Quebec, and Singapore. A Factor Analysis was completed to determine if there were item categories with similar characteristics. Gender differences favouring males were found in the verbal conventional category for Canadian students and in the spatial conventional category for students in Quebec. The greatest differences were by location, as students in Singapore outperformed students from Canada in all areas except for the spatial unconventional category. Finally, whether an item is conventional or unconventional is more important than whether the item is verbal or spatial. Results show the importance of fair assessment for the genders in both the classroom and on standardized tests.

A geochemical and petrological study of volcanic rocks in the Beardmore-Geraldton Archaean Greenstone Belt, Northwestern Ontario

Three repetitive sequences of northward youngIng, east striking, linear, volcano-sedimentary units are found in the late Archaean BeardmoreGeraldton greenstone belt, situated within the Wabigoon subprovince of the Superior Province of northwestern Ontario. The volcanic components are characterised by basaltic flows that are pillowed at the top and underlain by variably deformed massive flows which may In part be intrusive. Petrographic examination of the volcanic units indicates regional metamorphism up to greenschist facies (T=3250 C - 4500 C, P=2kbars) overprinted by a lower amphibolite facies thermal event (T=5750 C, P=2kbars) confined to the south-eastern portion of the belt. Chemical element results suggest olivine, plagioclase and pyroxene are the main fractionating mineral phases. Mobility studies on the varIOUS chemical elements indicate that K, Ca, Na and Sr are relatively mobile, while P, Zr, Ti, Fet (total iron = Fe203) and Mg are relatively immobile. Discriminant diagrams employing immobile element suggests that the majority of the samples are of oceanic affinity with a minor proportion displaying an island arc affinity. Such a transitional tectonic setting IS also refle.cted in REE data where two groups of volcanic samples are recognised. Oceanic tholeiites are LREE depleted with [La/Sm] N = 0.65 and a relatively flat HREE profile with [Sm/Yb] N = 1.2. Island arc type basalts (calc-alkaline) are LREE enriched, with a [La/Sm] N = 1.6, and a relatively higher fractionated HREE profile with [Sm/Yb] N = 1.9. Petrogenetic modelling performed on oceanIC tholeiites suggests derivation from a depleted spinel lherzolite source which undergoes 20% partial melting. Island arc type basalts can be derived by 10% partial melting of a hypothetical amphibolitised oceanic tholeiite source. The majority of the volcanic rocks in the Beardmore-Geraldton Belt are interpreted to represent fragments of oceanic crust trapped at a consuming plate margin. Subsequent post accretionary intrusion of gabbroic rocks (sensu lato) with calc-alkaline affinity is considered to result in the apparent hybrid tectonic setting recognized for the BGB.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.