title: On the Fürstenberg closure of a class of binary recurrences

authors: Broughan, Kevin A.

subjects: full topology

abstract: In this paper, we determine the closure in the full topology over Z of the set {un: n≥0}, where (un)n≥0 is a nondegenerate binary recurrent sequence with integer coefficients whose characteristic roots are quadratic units. This generalizes the result for the case when un=Fn was the nth Fibonacci number.

text: On the Fürstenberg closure of a class of binary recurrences In this paper, we determine the closure in the full topology over Z of the set {un: n≥0}, where (un)n≥0 is a nondegenerate binary recurrent sequence with integer coefficients whose characteristic roots are quadratic units. This generalizes the result for the case when un=Fn was the nth Fibonacci number.

year: 2010

title: The provision of European languages in Anglophone contexts: Aotearoa/New Zealand in focus

authors: Johnson, Diane

subjects: European languages

abstract: The provision of European languages within the New Zealand education system is discussed here in the context of the origins and evolution of language education in the country and the various problems that have been associated with it. These problems include the fact that any discussion of languages inevitably raises issues concerning the endangered status of Māori, the indigenous language of the country, issues which have the potential to highlight deep divisions within society. Hence, there is an unwillingness on the part of successive governments to engage seriously in debate about language needs and aspirations. Only a very small percentage of students at any level of the education system study languages other than English and Māori. Although European languages are studied by over half of those who do study languages, there is very little choice in terms of the European languages on offer. Furthermore, public opinion favours the teaching and learning of Asian and Pacific languages. In fact, two of the languages on offer that originated in Europe, French and Spanish, may have retained their position, in part, because they are, for many New Zealanders, at least as strongly associated with the Pacific and Pacific Rim countries where they are spoken as they are with their countries of origin.

text: The provision of European languages in Anglophone contexts: Aotearoa/New Zealand in focus The provision of European languages within the New Zealand education system is discussed here in the context of the origins and evolution of language education in the country and the various problems that have been associated with it. These problems include the fact that any discussion of languages inevitably raises issues concerning the endangered status of Māori, the indigenous language of the country, issues which have the potential to highlight deep divisions within society. Hence, there is an unwillingness on the part of successive governments to engage seriously in debate about language needs and aspirations. Only a very small percentage of students at any level of the education system study languages other than English and Māori. Although European languages are studied by over half of those who do study languages, there is very little choice in terms of the European languages on offer. Furthermore, public opinion favours the teaching and learning of Asian and Pacific languages. In fact, two of the languages on offer that originated in Europe, French and Spanish, may have retained their position, in part, because they are, for many New Zealanders, at least as strongly associated with the Pacific and Pacific Rim countries where they are spoken as they are with their countries of origin.

year: 2015

title: Young Maori males experiences in a secondary school context as sporting, academic and cultural identities.

authors: Porteous, Erin

subjects: Male Maori

abstract: This research focused on the journey of male Māori through secondary school and the effect on their identities in terms of sport, culture and academia. The two key areas of focus were how the culture of the school, including cultural stereotypes, impacts on male Māori learner self-concept, and whether the effect of creating an all Māori boys form class has resulted in an increased sense of belonging and engagement. 
The research was conducted as a case study underpinned by an interpretive methodology, using a focus group interview. The group was made up of five boys, chosen from a newly formed all boys’ Year 11 Māori form class. The boys were selected in conjunction with their form teacher and the schools Kaitiaki, in order to reflect a range of sporting, academic and cultural levels. 
The research findings found that although the boys view of their experiences in school seemed positive overall, they described common incidences and reactions to racial discrimination. The exposure to embedded racial stereotypes and behaviours caused them to create their own solutions, often through threatening violence or aggressive reactions. It appears that when young male Māori are more closely connected to Māori culture, they are more likely they are to create these responses. 
Teachers remain integral to the engagement and belonging of a young male Māori in secondary school. In support of the findings from Kia Eke Panuku (2013), this study found that male Māori require positive relationships with their teachers to engage in the subject and school in a general sense. Relationships based on ako and manaakitanga are key to these students viewing their experiences in school as successful.
Another finding showed the importance of sport and physical activity to young male Māori, though success in this area has been a limiting factor in contributing to overall success in secondary school. The placing of male Māori as a ‘physical being’ (Hokowhitu, 2003a; Hokowhitu, 2003b; Hokowhitu, 2004) creates spaces where Māori can be successful, such as practical based subjects like physical education. This success is perceived as acceptable yet often isolates them away from success in other areas (Erueti & Palmer, 2014), feeding into the stereotype itself.
The success of the all boys’ Māori form class was scrutinised by this study, and found the intended outcomes had not necessarily been met. The overall impact was that the boys had been grouped with a Māori form teacher and the intentions of additional support had been overlooked due to time pressures and deficit thinking in terms of capabilities of the class members.  For the Māori boys in this study, the challenges of overcome historical cultural stereotypes added to the challenge of succeeding at secondary school. The expectation that they walk successfully between the realms of Māori and pākehā to achieve in the current education system coupled with the feeling they needed to act ‘pākehā’ in order to achieve is particularly disturbing. The inequity for them in denying part of their identity seems a hefty price to pay for educational success.
This study highlights the need for schools, communities and individual teachers to recognise these racial and systemic inequities and work tirelessly to develop strategies to eliminate them, in order to create to take a giant step towards equity for all New Zealanders within education.

text: Young Maori males experiences in a secondary school context as sporting, academic and cultural identities. This research focused on the journey of male Māori through secondary school and the effect on their identities in terms of sport, culture and academia. The two key areas of focus were how the culture of the school, including cultural stereotypes, impacts on male Māori learner self-concept, and whether the effect of creating an all Māori boys form class has resulted in an increased sense of belonging and engagement. 
The research was conducted as a case study underpinned by an interpretive methodology, using a focus group interview. The group was made up of five boys, chosen from a newly formed all boys’ Year 11 Māori form class. The boys were selected in conjunction with their form teacher and the schools Kaitiaki, in order to reflect a range of sporting, academic and cultural levels. 
The research findings found that although the boys view of their experiences in school seemed positive overall, they described common incidences and reactions to racial discrimination. The exposure to embedded racial stereotypes and behaviours caused them to create their own solutions, often through threatening violence or aggressive reactions. It appears that when young male Māori are more closely connected to Māori culture, they are more likely they are to create these responses. 
Teachers remain integral to the engagement and belonging of a young male Māori in secondary school. In support of the findings from Kia Eke Panuku (2013), this study found that male Māori require positive relationships with their teachers to engage in the subject and school in a general sense. Relationships based on ako and manaakitanga are key to these students viewing their experiences in school as successful.
Another finding showed the importance of sport and physical activity to young male Māori, though success in this area has been a limiting factor in contributing to overall success in secondary school. The placing of male Māori as a ‘physical being’ (Hokowhitu, 2003a; Hokowhitu, 2003b; Hokowhitu, 2004) creates spaces where Māori can be successful, such as practical based subjects like physical education. This success is perceived as acceptable yet often isolates them away from success in other areas (Erueti & Palmer, 2014), feeding into the stereotype itself.
The success of the all boys’ Māori form class was scrutinised by this study, and found the intended outcomes had not necessarily been met. The overall impact was that the boys had been grouped with a Māori form teacher and the intentions of additional support had been overlooked due to time pressures and deficit thinking in terms of capabilities of the class members.  For the Māori boys in this study, the challenges of overcome historical cultural stereotypes added to the challenge of succeeding at secondary school. The expectation that they walk successfully between the realms of Māori and pākehā to achieve in the current education system coupled with the feeling they needed to act ‘pākehā’ in order to achieve is particularly disturbing. The inequity for them in denying part of their identity seems a hefty price to pay for educational success.
This study highlights the need for schools, communities and individual teachers to recognise these racial and systemic inequities and work tirelessly to develop strategies to eliminate them, in order to create to take a giant step towards equity for all New Zealanders within education.

year: 2016