title: Te Reo Tātai: The Development of a Mathematics Register for Māori-Medium Schooling

authors: Trinick, Anthony

subjects: Indigenous Mathematics education

abstract: This thesis investigates the development of a lexicon and register to facilitate the teaching of mathematics in the medium of te reo Māori. This sociolinguistic development is situated within the wider Māori language revitalisation movement in Aotearoa/New Zealand, of which Māori-medium education is a central component. 
Lexication of a language is a subdomain of corpus planning. Corpus, status and language-in-education planning are considered the three major interconnected domains of language planning and policy (LPP). For decades, the primary focus of LPP research has been on the activities of states and their agencies at the macro (national) level. The significance of this study is that it addresses this gap in the research, by investigating the development of LPP at the meso/micro-level—in this case, with respect to the development of a mathematics register for an endangered indigenous language, te reo Māori.
The thesis draws on two major participant data sources. The first is the narratives of key individuals at the forefront of lexical development for Māori-medium mathematics who recounted their experiences. The second is interviews with principals and teachers from two Māori-medium case study schools to examine their own learning and usage of the standardised pāngarau lexicon.
Two complementary theoretical frameworks were used to investigate the topic. First, an LPP theoretical framework was applied to investigate the complex relationships between the various levels of LPP that have impacted on the evolution of te reo Māori and Māori-medium schooling. Second, a linguistic framework, systemic functional linguistics (SFL), was used to investigate the linguistic and pedagogical issues.
Thesis findings show that the status of te reo Māori was variously affected by linguistic ideologies such as assimilation, which in turn led to such policies as English only in schooling. As a consequence, at the micro-level of LPP, Māori-medium mathematics development went into a hiatus for over 100 years, and at the macro-level, considerable language shift occurred to English, causing te reo Maori to become endangered.
In response to language revitalisation efforts, the (re) vernacularisation of te reo Māori over the past 30 years has exhibited a complex combination of both bottom-up and top-down LPP. Within this, early pāngarau lexical developments were largely driven by local schools and their communities, which sometimes centred on the maintenance of their tribal dialects, often in conflict with later LPP agency language goals. 
Subsequently, lexication for pāngarau was influenced by macro-level sociolinguistic beliefs such as linguistic purism, which in turn have influenced the technical approach to creating terms and may have created particular pedagogical issues, such as a lack of intertranslatability between te reo Māori and English at the higher levels of mathematics study. 
While Māori-medium schooling has contributed significantly to language revitalisation in the past 30 years, its development has been very ad hoc. In the absence of a “formal” language plan for Māori-medium education, policy has been significantly driven by national education (English-medium) imperatives since the late 1970s to the present day. On the other hand, these policies have favoured mathematics education and directly supported the development of the Māori-medium specialised lexicon and register.

text: Te Reo Tātai: The Development of a Mathematics Register for Māori-Medium Schooling This thesis investigates the development of a lexicon and register to facilitate the teaching of mathematics in the medium of te reo Māori. This sociolinguistic development is situated within the wider Māori language revitalisation movement in Aotearoa/New Zealand, of which Māori-medium education is a central component. 
Lexication of a language is a subdomain of corpus planning. Corpus, status and language-in-education planning are considered the three major interconnected domains of language planning and policy (LPP). For decades, the primary focus of LPP research has been on the activities of states and their agencies at the macro (national) level. The significance of this study is that it addresses this gap in the research, by investigating the development of LPP at the meso/micro-level—in this case, with respect to the development of a mathematics register for an endangered indigenous language, te reo Māori.
The thesis draws on two major participant data sources. The first is the narratives of key individuals at the forefront of lexical development for Māori-medium mathematics who recounted their experiences. The second is interviews with principals and teachers from two Māori-medium case study schools to examine their own learning and usage of the standardised pāngarau lexicon.
Two complementary theoretical frameworks were used to investigate the topic. First, an LPP theoretical framework was applied to investigate the complex relationships between the various levels of LPP that have impacted on the evolution of te reo Māori and Māori-medium schooling. Second, a linguistic framework, systemic functional linguistics (SFL), was used to investigate the linguistic and pedagogical issues.
Thesis findings show that the status of te reo Māori was variously affected by linguistic ideologies such as assimilation, which in turn led to such policies as English only in schooling. As a consequence, at the micro-level of LPP, Māori-medium mathematics development went into a hiatus for over 100 years, and at the macro-level, considerable language shift occurred to English, causing te reo Maori to become endangered.
In response to language revitalisation efforts, the (re) vernacularisation of te reo Māori over the past 30 years has exhibited a complex combination of both bottom-up and top-down LPP. Within this, early pāngarau lexical developments were largely driven by local schools and their communities, which sometimes centred on the maintenance of their tribal dialects, often in conflict with later LPP agency language goals. 
Subsequently, lexication for pāngarau was influenced by macro-level sociolinguistic beliefs such as linguistic purism, which in turn have influenced the technical approach to creating terms and may have created particular pedagogical issues, such as a lack of intertranslatability between te reo Māori and English at the higher levels of mathematics study. 
While Māori-medium schooling has contributed significantly to language revitalisation in the past 30 years, its development has been very ad hoc. In the absence of a “formal” language plan for Māori-medium education, policy has been significantly driven by national education (English-medium) imperatives since the late 1970s to the present day. On the other hand, these policies have favoured mathematics education and directly supported the development of the Māori-medium specialised lexicon and register.

year: 2015

title: Restructuring and hospital care: Sub-national trends, differentials, and their impacts; New Zealand from 1981

authors: Pool, Ian

abstract: An analysis of the "nation's health" is the central concern of this study. Its genesis was a detailed, technical, time-series research on regional and ethnic differentials in health in New Zealand. But as this work progressed it became increasingly evident that the results of this more narrow analysis could make a wider contribution to the development of a knowledge-base on health trends and on the impacts of policy on these. In a sense, the analysis provides a demographic audit of health trends over the last two decades.
The focus here is different from that in most other studies on restructuring of the New Zealand health system as their concern was either to review in detail the rewriting of policy per se, and attendant structural and institutional changes (Fougere 2001), or to identify how these changes relate to changes in mortality (Blakely et al. 2008). The research question reported here was, instead, to analyse the most crucial of health outcomes, „how long we live and how often we end up in hospital‟, identified in the earlier quotation, to report patterns and trends in hospital use nationally and sub-nationally over the period under review, and to determine the degrees to which various sub-populations benefited, or did not benefit, from these changes. The analysis focuses on the hospital sector in the system, but it will also show relations between this and other sectors, formal (e.g. primary health) and less formal (notably the healthcare afforded sickness and invalid beneficiaries). Thus two questions are addressed:
1. whether or not the nation‟s population health improved over the period and;
2. whether or not there was a convergence in patterns of health gain across its constituent sub-populations defined geographically and ethnically.
This monograph deals with sub-national differences in health in New Zealand over a period of substantial socio-economic restructuring and associated radical changes in health policy, health systems and their related information systems (see also, Text Appendix A). It complements the recently published analysis of national ethnic trends in mortality (Blakely et al. 2004), but differs in several critical respects. That study reviewed health status by emphasising aetiologies and causes of death. In contrast, the present analysis focuses on actuarial dimensions of both mortality and morbidity and on health as measured by functional capacity rather than the disease orientated „burden of disease‟. It goes beyond health status issues to look at the system itself, to assess whether health policy outcomes were generated more through efficiency-gain (economic or service delivery, such as those resulting in a convergence sub-nationally of supply and demand effects), or through health gains, or ideally, by both.
To do this, and as a by-product to analyse changes in health status and the system in an era of restructuring, innovative methodologies and composite time-series indices combining the two dimensions of a „nation‟s health‟, needing hospital care and longevity, have had to be custom-designed. To achieve this objective, the ensuing analysis is often technical, and may introduce concepts that are unfamiliar to some readers. In order to look at possible inequalities of outcome, comparisons were made between regions and ethnic groups, as well as age-groups and genders, and as a result, in places the analysis becomes rather complex.

text: Restructuring and hospital care: Sub-national trends, differentials, and their impacts; New Zealand from 1981 An analysis of the "nation's health" is the central concern of this study. Its genesis was a detailed, technical, time-series research on regional and ethnic differentials in health in New Zealand. But as this work progressed it became increasingly evident that the results of this more narrow analysis could make a wider contribution to the development of a knowledge-base on health trends and on the impacts of policy on these. In a sense, the analysis provides a demographic audit of health trends over the last two decades.
The focus here is different from that in most other studies on restructuring of the New Zealand health system as their concern was either to review in detail the rewriting of policy per se, and attendant structural and institutional changes (Fougere 2001), or to identify how these changes relate to changes in mortality (Blakely et al. 2008). The research question reported here was, instead, to analyse the most crucial of health outcomes, „how long we live and how often we end up in hospital‟, identified in the earlier quotation, to report patterns and trends in hospital use nationally and sub-nationally over the period under review, and to determine the degrees to which various sub-populations benefited, or did not benefit, from these changes. The analysis focuses on the hospital sector in the system, but it will also show relations between this and other sectors, formal (e.g. primary health) and less formal (notably the healthcare afforded sickness and invalid beneficiaries). Thus two questions are addressed:
1. whether or not the nation‟s population health improved over the period and;
2. whether or not there was a convergence in patterns of health gain across its constituent sub-populations defined geographically and ethnically.
This monograph deals with sub-national differences in health in New Zealand over a period of substantial socio-economic restructuring and associated radical changes in health policy, health systems and their related information systems (see also, Text Appendix A). It complements the recently published analysis of national ethnic trends in mortality (Blakely et al. 2004), but differs in several critical respects. That study reviewed health status by emphasising aetiologies and causes of death. In contrast, the present analysis focuses on actuarial dimensions of both mortality and morbidity and on health as measured by functional capacity rather than the disease orientated „burden of disease‟. It goes beyond health status issues to look at the system itself, to assess whether health policy outcomes were generated more through efficiency-gain (economic or service delivery, such as those resulting in a convergence sub-nationally of supply and demand effects), or through health gains, or ideally, by both.
To do this, and as a by-product to analyse changes in health status and the system in an era of restructuring, innovative methodologies and composite time-series indices combining the two dimensions of a „nation‟s health‟, needing hospital care and longevity, have had to be custom-designed. To achieve this objective, the ensuing analysis is often technical, and may introduce concepts that are unfamiliar to some readers. In order to look at possible inequalities of outcome, comparisons were made between regions and ethnic groups, as well as age-groups and genders, and as a result, in places the analysis becomes rather complex.

year: 2009

title: Corrigendum to "The holomorphic flow of the Riemann Zeta function"

authors: Broughan, Kevin A.

subjects: mathematics

abstract: Theorem 4.5 of [2], describing the topological type of the zeros of the flow s˙ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gokcek for pointing out the error to us.

text: Corrigendum to "The holomorphic flow of the Riemann Zeta function" Theorem 4.5 of [2], describing the topological type of the zeros of the flow s˙ = ζ(s) at reflected points off the critical line, claiming they were the same, contains an error. We gratefully acknowledge Professor Cevat Gokcek for pointing out the error to us.

year: 2007