title: αₙ-Designs

authors: Ruggiero, Katya

abstract: This thesis defines a broad class of resolvable incomplete block designs for multifactor experiments, called αₙ-designs. A general methodology for their construction is described and is shown to be a natural extension of the method used by Patterson and Williams (1976) in their construction of α-designs. In fact, the class of α-designs are a special case of αₙ-designs with n = 1. 

The family of αₙ-designs was primarily developed for their use in factorial experiments. While they are particularly suitable for this purpose, for some combinations of design parameters they also provide more efficient designs than the best available α-designs.

Algorithms for the generation of efficient designs require computationally expensive eigenvalue calculations. Therefore, considerable attention is devoted to the study of the structural properties of αₙ-designs and how these can be used to develop computationally fast algorithms. In this endeavour it is shown that the treatment concurrence and information matrices have an important property known as BⁿC-structure. This is used to derive a closed form mathematical expression for the average efficiency factor of any generalized interaction. It is further shown that this expression can be written recursively. These results, combined with the fact than an αₙ-design is completely specified by a small generating array, mean that computer search algorithms can be developed to quickly find highly efficient designs.

A desirable feature in a factorial design is the property of orthogonal factorial structure. The family of αₙ-designs do not, in general, admit this property. However, another class of n-dimensional cyclic designs, known as n-cyclic designs, suitable for non-resolvable designs for factorial experiments are also considered in this thesis. They possess orthogonal factorial structure and include a sizeable subset of designs which are resolvable. These resolvable n-cyclic designs are shown to be αₙ-designs.

The discovery and subsequent development of the family of αₙ-designs has stimulated a new set of interesting questions in relation to factorial experiments. These are discussed at the end of the thesis.

text: αₙ-Designs This thesis defines a broad class of resolvable incomplete block designs for multifactor experiments, called αₙ-designs. A general methodology for their construction is described and is shown to be a natural extension of the method used by Patterson and Williams (1976) in their construction of α-designs. In fact, the class of α-designs are a special case of αₙ-designs with n = 1. 

The family of αₙ-designs was primarily developed for their use in factorial experiments. While they are particularly suitable for this purpose, for some combinations of design parameters they also provide more efficient designs than the best available α-designs.

Algorithms for the generation of efficient designs require computationally expensive eigenvalue calculations. Therefore, considerable attention is devoted to the study of the structural properties of αₙ-designs and how these can be used to develop computationally fast algorithms. In this endeavour it is shown that the treatment concurrence and information matrices have an important property known as BⁿC-structure. This is used to derive a closed form mathematical expression for the average efficiency factor of any generalized interaction. It is further shown that this expression can be written recursively. These results, combined with the fact than an αₙ-design is completely specified by a small generating array, mean that computer search algorithms can be developed to quickly find highly efficient designs.

A desirable feature in a factorial design is the property of orthogonal factorial structure. The family of αₙ-designs do not, in general, admit this property. However, another class of n-dimensional cyclic designs, known as n-cyclic designs, suitable for non-resolvable designs for factorial experiments are also considered in this thesis. They possess orthogonal factorial structure and include a sizeable subset of designs which are resolvable. These resolvable n-cyclic designs are shown to be αₙ-designs.

The discovery and subsequent development of the family of αₙ-designs has stimulated a new set of interesting questions in relation to factorial experiments. These are discussed at the end of the thesis.

year: 2000

title: A literature review exploring a meaning for the term 'curriculum leadership'.

authors: Jefferies, Sherrin

subjects: curricula (courses of study)

abstract: Research on leadership in education often focuses on school management, educational change or curriculum development. There is little research however, in the area of curriculum leadership. With the introduction of seven new curriculum documents in the last eight years in New Zealand, I believe it has become increasingly important to consider who our curriculum leaders are, what it is they are leading, and the characteristics these people have that influence the practices and activities of others. In this article I have explored the roles of those people who might be considered to be curriculum leaders (Ministry of Education, School Support Services, Principals, Teachers, Consultants and Parents), in an attempt to define some of their leadership characteristics. I conclude the article with a summary of these characteristics.

text: A literature review exploring a meaning for the term 'curriculum leadership'. Research on leadership in education often focuses on school management, educational change or curriculum development. There is little research however, in the area of curriculum leadership. With the introduction of seven new curriculum documents in the last eight years in New Zealand, I believe it has become increasingly important to consider who our curriculum leaders are, what it is they are leading, and the characteristics these people have that influence the practices and activities of others. In this article I have explored the roles of those people who might be considered to be curriculum leaders (Ministry of Education, School Support Services, Principals, Teachers, Consultants and Parents), in an attempt to define some of their leadership characteristics. I conclude the article with a summary of these characteristics.

year: 2000

title: Te kura o Ruatoki 1896 - 1979

authors: Williams, Kim Reina Reremoana

subjects: Ruatoki Native School

abstract: Ko tēnei tuhinga roa e kōrero ana mō te Kura o Ruatoki i roto i te rohe o te iwi o Tūhoe. I whakatūria he kura i te tau 1896 i runga i te inoi a ngā Koroua ki te Kāwanatanga o taua wā.
Hai te Upoko tuatahi, ka whakatakotoria ngā kōrero mō te āhua o te whenua, ngā tāngata me ā rātau nekeneke. Tutū ana te puehu i runga i ngā whakatū waewae ki te iwi, ki te Pākehā hoki mō taua whenua.
Hai te Upoko tuarua ka takoto ngā kōrero mō te heke o ngā pānui o ngā inoi, ngā reta a ngā Koroua ki te Kāwanatanga mō te whakatū i tētahi Kura i Ruatoki. Te nuinga o ēnei rauemi i rangahaua, i kitea, i te Whare pukapuka o Pōneke. Ko ētahi i te Whare pukapuka o Tāmaki. Ka tau te tono, ka kitea te tūtukitanga o te ao Pākehā ki te ao Māori, otirā, kua puta te kaupapa i whakatūria ake ai te kura hei whakatangata whenua i ngā tāngata, i ngā aronga hinengaro Māori kia rite ki tō te Pākehā.
Hai te Upoko tuatoru ka tirohia ko ngā tuhinga a ngā Tumuaki mai i te tau 1896 ki te tau 1979 mō te Kura o Ruatoki. Ka kite i roto i ā rātau tirohanga te āhua o tā rātau kaihautū i te rerenga o te kaupapa nei. Ko ngā kaihautū i te waka nei, he tūmau noa nā te Kāwanatanga hai whakatō i te Pākehātanga ki roto i te whatumanawa Māori.
He tini o te whārua i hinga i roto i ēnei tau i runga i ngā mate urutī, mate tauhou i pā ki roto i te whārua. Ahakoa tērā ka tukuna tonu ngā tamariki ki te kura i runga i te whakapono he oranga ka puta mai i reira. I te tau 1946 ka tū he kura tuarua, he Māori District High School. Ko te nuinga o ngā tamariki o Tawera rāua ko Ruatoki i haere mai ki tēnei kura. Tokoiti ia tau i whiwhi karahipi mō te haere ki ngā kura hāhi o Tīpene rāua ko Wikitōria. Tērā pea he tango atu i ēnei tamariki mai i ngā āhuatanga Māori o te whārua.
Hai te upoko tuawhā, ka whakakorehia te kura tuarua. Ko ngā take mō te katinga ka āta whakamāramahia. He mahi nanakia nā te tari Mātauranga me āna āpiha i runga i ngā nekeneke mō tēnei kaupapa.
Hai te Upoko tuarima ka whakarerekēhia ngā marautanga ako kia tau ko te kaupapa ako i roto i ngā reo e rua ki roto i te kura. He whakautu tēnei i te kōrero a Richard Benton o te N.Z.C.E.R e kī ana, "Kāore e roa ka ngaro te reo Māori." Koinei te wā i whakapihihia ake ai te kaupapa ako i roto i ngā reo e rua, ā, ka tiritiria ko te kaupapa Rumaki Reo.
Hai te Upoko tuaono ko te kōhuretanga o te kaupapa Māori me te puāwaitanga o ngā hinengaro me ngā wairua o ngā tamariki ki te āhua o te ako i ā rātau mahi i roto i tō rātau ake reo. I tīmatahia te kaupapa i te tau 1977. Tae rawa atu ki ngā tau o muri mai kua kitea kē te huringa o ngā ngākau ki te ako.
Hai te Upoko tuawhitu ka whakaatahia mai ngā whakanekeneke i raro i tēnei kaupapa. He nui ngā tutukitanga ki ngā ture i te whakatūtanga o ngā Kura mō Āpōpō.
Hei whakarāpopototanga i ngā moemoeā me ngā tūmanako ka titiro ake ki ngā waru tekau tau kua pahemo. Kua turuki ki te pō, ki te ao. Kua noho te pukenga o te kupu kōrero, kua taipū ngā kaupapa. Ko taku mahi he whakarārangi i ngā pikinga i ngā hekenga i ngā āhuatanga katoa i mahia i roto i tēnei kura mai kore ka kitea atu he māramatanga he huarahi rānei e tiketike ake ai ngā mahi ako, ngā akoranga, ki ēnei o ā tātau mokopuna o Ngāi Tūhoe e tipu mai nei. Nō reira ka hoki rawa ngā kauhau ki ērā i whakatakotohia mai e ngā mātua tīpuna. Ka tīkina atu te kōrero i reira hai whakatinana i ngā tūmanako mō te wharekura o Ruatoki i tēnei wā.

text: Te kura o Ruatoki 1896 - 1979 Ko tēnei tuhinga roa e kōrero ana mō te Kura o Ruatoki i roto i te rohe o te iwi o Tūhoe. I whakatūria he kura i te tau 1896 i runga i te inoi a ngā Koroua ki te Kāwanatanga o taua wā.
Hai te Upoko tuatahi, ka whakatakotoria ngā kōrero mō te āhua o te whenua, ngā tāngata me ā rātau nekeneke. Tutū ana te puehu i runga i ngā whakatū waewae ki te iwi, ki te Pākehā hoki mō taua whenua.
Hai te Upoko tuarua ka takoto ngā kōrero mō te heke o ngā pānui o ngā inoi, ngā reta a ngā Koroua ki te Kāwanatanga mō te whakatū i tētahi Kura i Ruatoki. Te nuinga o ēnei rauemi i rangahaua, i kitea, i te Whare pukapuka o Pōneke. Ko ētahi i te Whare pukapuka o Tāmaki. Ka tau te tono, ka kitea te tūtukitanga o te ao Pākehā ki te ao Māori, otirā, kua puta te kaupapa i whakatūria ake ai te kura hei whakatangata whenua i ngā tāngata, i ngā aronga hinengaro Māori kia rite ki tō te Pākehā.
Hai te Upoko tuatoru ka tirohia ko ngā tuhinga a ngā Tumuaki mai i te tau 1896 ki te tau 1979 mō te Kura o Ruatoki. Ka kite i roto i ā rātau tirohanga te āhua o tā rātau kaihautū i te rerenga o te kaupapa nei. Ko ngā kaihautū i te waka nei, he tūmau noa nā te Kāwanatanga hai whakatō i te Pākehātanga ki roto i te whatumanawa Māori.
He tini o te whārua i hinga i roto i ēnei tau i runga i ngā mate urutī, mate tauhou i pā ki roto i te whārua. Ahakoa tērā ka tukuna tonu ngā tamariki ki te kura i runga i te whakapono he oranga ka puta mai i reira. I te tau 1946 ka tū he kura tuarua, he Māori District High School. Ko te nuinga o ngā tamariki o Tawera rāua ko Ruatoki i haere mai ki tēnei kura. Tokoiti ia tau i whiwhi karahipi mō te haere ki ngā kura hāhi o Tīpene rāua ko Wikitōria. Tērā pea he tango atu i ēnei tamariki mai i ngā āhuatanga Māori o te whārua.
Hai te upoko tuawhā, ka whakakorehia te kura tuarua. Ko ngā take mō te katinga ka āta whakamāramahia. He mahi nanakia nā te tari Mātauranga me āna āpiha i runga i ngā nekeneke mō tēnei kaupapa.
Hai te Upoko tuarima ka whakarerekēhia ngā marautanga ako kia tau ko te kaupapa ako i roto i ngā reo e rua ki roto i te kura. He whakautu tēnei i te kōrero a Richard Benton o te N.Z.C.E.R e kī ana, "Kāore e roa ka ngaro te reo Māori." Koinei te wā i whakapihihia ake ai te kaupapa ako i roto i ngā reo e rua, ā, ka tiritiria ko te kaupapa Rumaki Reo.
Hai te Upoko tuaono ko te kōhuretanga o te kaupapa Māori me te puāwaitanga o ngā hinengaro me ngā wairua o ngā tamariki ki te āhua o te ako i ā rātau mahi i roto i tō rātau ake reo. I tīmatahia te kaupapa i te tau 1977. Tae rawa atu ki ngā tau o muri mai kua kitea kē te huringa o ngā ngākau ki te ako.
Hai te Upoko tuawhitu ka whakaatahia mai ngā whakanekeneke i raro i tēnei kaupapa. He nui ngā tutukitanga ki ngā ture i te whakatūtanga o ngā Kura mō Āpōpō.
Hei whakarāpopototanga i ngā moemoeā me ngā tūmanako ka titiro ake ki ngā waru tekau tau kua pahemo. Kua turuki ki te pō, ki te ao. Kua noho te pukenga o te kupu kōrero, kua taipū ngā kaupapa. Ko taku mahi he whakarārangi i ngā pikinga i ngā hekenga i ngā āhuatanga katoa i mahia i roto i tēnei kura mai kore ka kitea atu he māramatanga he huarahi rānei e tiketike ake ai ngā mahi ako, ngā akoranga, ki ēnei o ā tātau mokopuna o Ngāi Tūhoe e tipu mai nei. Nō reira ka hoki rawa ngā kauhau ki ērā i whakatakotohia mai e ngā mātua tīpuna. Ka tīkina atu te kōrero i reira hai whakatinana i ngā tūmanako mō te wharekura o Ruatoki i tēnei wā.

year: 1998