A philosophical exploration of some unstated educational presuppositions concerning Polynesian education in New Zealand : a thesis presented in partial fulfilment of the requirements for the degree of Master of Arts in Education at Massey University

A PHILOSOPHICAL EXPLORATION OF SOME UNSTATED EDUCATIONAL PRESUPPOSITIONS CONCERNING POLYNESIAN EDUCATION IN NEW ZEALAND. The prime concern in a multi-racial society should. be to encourage harmonious race relations in a system which aims at 'equality'. The Education system is one way of achieving this objective. Historically New Zealand educational policy has emphasised assimilation or its later more euphemistic derivative integration. This policy effectively increased the rate of acculturation but only at the expense of Polynesian culture and 'Maoritanga'. Subsequent academic failure, coupled with a steady decline in enthusiasm for formal education has resulted in the Polynesian devaluing education for other more tangible rewards. Innovation in educational policy aimed. at providing the Polynesian with an education which is intrinsically valuable to him, has been slow. This despite the immediate urgency and despite the findings and recommendations of the various commissions and committees set up by Government. Specifically, what is needed is the type of innovation which will encourage a greater degree of involvement by both pupil and parent; innovation that will effectively close the gap in attainment level between Polynesian and European. In examining this problem it becomes obvious that the assumptions which may be widely held, either consciously on partly or wholly unconsciously, concerning education must also be explored so that the various types of innovation can be analysed in terms of their effect in the system and on the community. An examination of these presuppositions is necessary to allow for, and to counteract, possible bias which may interfere with any recommendations which may ensue. Also, it allows for critical thought and reflection on that assumption so that the universal tendency to make no systematic attempt to explain and justify the principles on which the education system is based can be avoided. These presuppositions can be found within existing or implemented policies and have largely determined the various policy statements: educational, racial, social, recreational, penal. Any one of these presuppositionse, once exposed and found to be an immediate influence, can be examined to determine just what extent they have influenced, or are influencing, the Polynesian educational structure. A variety of alternatives and possible solutions could instead be implemented. The principle objective then is: to explore these presuppositions and possible alternatives in order that the resultant recommendations might be implemented in an attempt to raise the level of Polynesian under-achievement. The four main steps in this process are: 1. To show that any one educational presupposition 'may' be held or that it is widely held, consciously or unconsciously. 2. To show what effect this presupposition has had, or is having, upon the Polynesian educational system. 3. To examine this effect and to explore the possible variations and solutions of diverse alternative policies. 4. To arrive at and to recommend what action might be taken to alleviate the discrepancies and inequalities that are found to be important determinants of Polynesian under-achievement. The solutions and recommendations that are advanced in this thesis have been the result of careful analysis and examination of the unstated presuppositions, the principal factors affecting them and the principles in which they are embedded. These recommendations are not intended to be prescriptive. They are not the only possible recommendations but are perhaps the most appropriate. They are the end product of an inductive logical inquiry utilizing the findings of empirical research where available and appropriate. Some of them have already been implemented since this thesis was begun. However, it is not desirable, nor necessary, to remove them simply because they have been implemented and therefore rendered obsolete. The argumentation for them, in fact, is given greater credence in a world that views philosophical inquiry as merely a priori. These recommendations must be retained to allow for the continuity of argument and the facts which support them

Saturation numbers in tripartite graphs

Given graphs $H$ and $F$, a subgraph $G\subseteq H$ is an $F$-saturated subgraph of $H$ if $F\nsubseteq G$, but $F\subseteq G+e$ for all $e\in E(H)\setminus E(G)$. The saturation number of $F$ in $H$, denoted $\text{sat}(H,F)$, is the minimum number of edges in an $F$-saturated subgraph of $H$. In this paper we study saturation numbers of tripartite graphs in tripartite graphs. For $\ell\ge 1$ and $n_1$, $n_2$, and $n_3$ sufficiently large, we determine $\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell})$ and $\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell-1})$ exactly and $\text{sat}(K_{n_1,n_2,n_3},K_{\ell,\ell,\ell-2})$ within an additive constant. We also include general constructions of $K_{\ell,m,p}$-saturated subgraphs of $K_{n_1,n_2,n_3}$ with few edges for $\ell\ge m\ge p>0$.Comment: 18 pages, 6 figure

Strong existence and uniqueness for stochastic differential equation with H{\"o}lder drift and degenerate noise

In this paper, we prove pathwise uniqueness for stochastic degenerate systems with a H{\"o}lder drift, for a H{\"o}lder exponent larger than the critical value 2/3. This work extends to the degenerate setting the earlier results obtained by Zvonkin, Veretennikov, Krylov and R{\"o}ckner from non-degenerate to degenerate cases. The existence of a threshold for the H{\"o}lder exponent in the degenerate case may be understood as the price to pay to balance the degeneracy of the noise. Our proof relies on regularization properties of the associated PDE, which is degenerate in the current framework and is based on a parametrix method

A characterization of Dynkin elements

We give a characterization of the Dynkin elements of a simple Lie algebra. Namely, we prove that one-half of a Dynkin element is the unique point of minimal length in its N-region. In type A_n this translates into a statement about the regions determined by the canonical left Kazhdan-Lusztig cells. Some possible generalizations are explored in the last section.Comment: 9 page

Product Differentiation in Successive Vertical Oligopolies

This is a successive oligopoly model with two brands. Each downstream firm chooses one brand to sell on a final market. The upstream firms specialize in the production of one input specifically designed for the production of one brand, but they also produce the input for the other brand at an extra cost. We show that when more downstream firms choose one brand, more upstream firms will specialize in the input specific to that brand, and vice versa. Hence, multiple equilibria are possible and the softening effect of brand differentiation on competition might not be strong enough to induce maximal differentiation. The existence of equilibria and their welfare performance are also examined.Product differentiation, Vertical relationships, Oligopoly

An Assessment of Health Disparities among a Community Sample of LGBQ College Students

Lesbian, gay, bisexual, and queer (LGBQ) individuals are a marginalized population in the United States, and this status places them at a greater risk for adverse health outcomes, such as tobacco and substance use, obesity, cancer, sexually-transmitted infections, violence, mental health issues, and suicide. The present study used individual- and microsystem-level data from the American College Health Association (ACHA)-National College Health Assessment (NCHA) to compose a risk assessment for LGBQ students at a mid-Atlantic university. The study incorporated various levels of the ecological social model in an analysis of potentially influential factors on the development of LGBQ health disparities. 856 participants completed a self-administered anonymous survey that included questions assessing a broad variety of health indicators, such as alcohol, tobacco, and other substance use, sexual health, mental health, nutrition, and personal safety and violence. A significant minority of the sample identified with a sexual orientation other than heterosexual (n=184, 21.6%). Sexual minority students reported significantly higher rates of various types of substance use [e.g., sedatives x2 (1,N=856)=3.543,