title: Constructive Mathematics in Theory and Programming Practice

authors: Bridges, Douglas

subjects: computer science

abstract: The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics(BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focuses on the relation between constructive mathematics and programming, with emphasis on Martin-Lof’s theory of types as a formal system for BISH.

text: Constructive Mathematics in Theory and Programming Practice The first part of the paper introduces the varieties of modern constructive mathematics, concentrating on Bishop’s constructive mathematics(BISH). It gives a sketch of both Myhill’s axiomatic system for BISH and a constructive axiomatic development of the real line R. The second part of the paper focuses on the relation between constructive mathematics and programming, with emphasis on Martin-Lof’s theory of types as a formal system for BISH.

year: 1999

title: Sounds of Waitakere: Using practitioner research to explore how Year 6 recorder players compose responses to visual representations of a natural environment

authors: Locke, Linda

subjects: New Zealand

abstract: How might primary students utilise the stimulus of a painting in a collaborative composition drawing on a non-conventional sound palette of their own making? This practitioner research features 17 recorder players from a Year 6 class (10–11-year-olds) who attend a West Auckland primary school in New Zealand. These children were invited to experiment with the instrument to produce collectively an expanded ‘repertoire’ or ‘palette’ of sounds. In small groups, they then discussed a painting by an established New Zealand painter set in the Waitakere Ranges and attempted to formulate an interpretation in musical terms. On the basis of their interpretation, drawing on sounds from the collective palette (complemented with other sounds), they worked collaboratively to develop, refine and perform a structured composition named for their chosen painting. This case study is primarily descriptive (providing narrative accounts and rich vignettes of practice) and, secondarily, exploratory (description and analysis leading to the development of hypotheses). It has implications for a range of current educational issues, including curriculum integration and the place of composition and notation in the primary-school music programme.

text: Sounds of Waitakere: Using practitioner research to explore how Year 6 recorder players compose responses to visual representations of a natural environment How might primary students utilise the stimulus of a painting in a collaborative composition drawing on a non-conventional sound palette of their own making? This practitioner research features 17 recorder players from a Year 6 class (10–11-year-olds) who attend a West Auckland primary school in New Zealand. These children were invited to experiment with the instrument to produce collectively an expanded ‘repertoire’ or ‘palette’ of sounds. In small groups, they then discussed a painting by an established New Zealand painter set in the Waitakere Ranges and attempted to formulate an interpretation in musical terms. On the basis of their interpretation, drawing on sounds from the collective palette (complemented with other sounds), they worked collaboratively to develop, refine and perform a structured composition named for their chosen painting. This case study is primarily descriptive (providing narrative accounts and rich vignettes of practice) and, secondarily, exploratory (description and analysis leading to the development of hypotheses). It has implications for a range of current educational issues, including curriculum integration and the place of composition and notation in the primary-school music programme.

year: 2011

title: Whānau mentoring, Māori youth and crime

authors: Joseph, Robert

abstract: This article will discuss how the whänau was the traditional institution for teaching and nurturing children through (among other things) effective mentoring, and how children were taught tikanga, or the ‘right way’ to think, speak, act and become. Traditional leadership development, whänau dysfunction and whänau renewal are also discussed, followed by my conclusions. This article will not be discussing the place of colonisation, high unemployment, lower education rates and other socio-economic disparities among Mäori that play a part in the causes and perpetuation of Mäori youth and crime. A discussion on the Treaty of Waitangi, indigenous rights, and Mäori development is also omitted although the importance of each of these areas is acknowledged. As the theme of this issue of Childrenz Issues is ‘seeking pathways beyond colonisation’, the focus of this article is on Mäori dealing appropriately with the problems of Mäori youth and crime through effective mentoring within the institution of the whänau.

text: Whānau mentoring, Māori youth and crime This article will discuss how the whänau was the traditional institution for teaching and nurturing children through (among other things) effective mentoring, and how children were taught tikanga, or the ‘right way’ to think, speak, act and become. Traditional leadership development, whänau dysfunction and whänau renewal are also discussed, followed by my conclusions. This article will not be discussing the place of colonisation, high unemployment, lower education rates and other socio-economic disparities among Mäori that play a part in the causes and perpetuation of Mäori youth and crime. A discussion on the Treaty of Waitangi, indigenous rights, and Mäori development is also omitted although the importance of each of these areas is acknowledged. As the theme of this issue of Childrenz Issues is ‘seeking pathways beyond colonisation’, the focus of this article is on Mäori dealing appropriately with the problems of Mäori youth and crime through effective mentoring within the institution of the whänau.

year: 2007-01