title: Tools for verifying classical and quantum superintegrability

authors: Kalnins, Ernie G.

subjects: superintegrability

abstract: Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, so that they are in fact superintegrable. These newly discovered systems are all separable in some coordinate system and, typically, they depend on one or more parameters in such a way that the system is superintegrable exactly when some of the parameters are rational numbers. Most of the constructions to date are for n=2 but cases where n>2 are multiplying rapidly. In this article we organize a large class of such systems, many new, and emphasize the underlying mechanisms which enable this phenomena to occur and to prove superintegrability. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stäckel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k in the potential.

text: Tools for verifying classical and quantum superintegrability Recently many new classes of integrable systems in n dimensions occurring in classical and quantum mechanics have been shown to admit a functionally independent set of 2n−1 symmetries polynomial in the canonical momenta, so that they are in fact superintegrable. These newly discovered systems are all separable in some coordinate system and, typically, they depend on one or more parameters in such a way that the system is superintegrable exactly when some of the parameters are rational numbers. Most of the constructions to date are for n=2 but cases where n>2 are multiplying rapidly. In this article we organize a large class of such systems, many new, and emphasize the underlying mechanisms which enable this phenomena to occur and to prove superintegrability. In addition to proofs of classical superintegrability we show that the 2D caged anisotropic oscillator and a Stäckel transformed version on the 2-sheet hyperboloid are quantum superintegrable for all rational relative frequencies, and that a deformed 2D Kepler-Coulomb system is quantum superintegrable for all rational values of a parameter k in the potential.

year: 2010

title: Building computational thinking through programming in K-6 education: A New Zealand experience

authors: Falloon, Garry

subjects: computational

abstract: The recent inclusion of computational skills in core curriculum by governments in the UK and Australia, has been linked to industry calls for schools to better equip young people with capabilities and dispositions aligned with needs of future high-tech industries and rapidly changing workplaces. This move has stimulated much interest in New Zealand, and while lacking any compulsory curriculum mandate, many teachers in K-12 classrooms are exploring the potential of coding tasks for developing computational skills as part of their mathematics, science and technology curricula. 
This paper reports findings from a study that used a unique data capture app embedded in iPads to record 9&10 year old students while they used two apps of very different designs for coding tasks. Using Studiocode video analysis software, data were analysed using a framework developed from Brennan and Resnick’s [1] three dimensions of computational thinking, to learn more about how these apps constituted useful environments for developing computational thinking. Results suggest that coding apps of a ‘teaching’ design complement apps where computational concepts and practices are applied to project creation, and indeed may be more efficient if the desired outcome specifically targets the learning of concepts. Implications for teachers exploring coding apps for computational thinking development are drawn.

text: Building computational thinking through programming in K-6 education: A New Zealand experience The recent inclusion of computational skills in core curriculum by governments in the UK and Australia, has been linked to industry calls for schools to better equip young people with capabilities and dispositions aligned with needs of future high-tech industries and rapidly changing workplaces. This move has stimulated much interest in New Zealand, and while lacking any compulsory curriculum mandate, many teachers in K-12 classrooms are exploring the potential of coding tasks for developing computational skills as part of their mathematics, science and technology curricula. 
This paper reports findings from a study that used a unique data capture app embedded in iPads to record 9&10 year old students while they used two apps of very different designs for coding tasks. Using Studiocode video analysis software, data were analysed using a framework developed from Brennan and Resnick’s [1] three dimensions of computational thinking, to learn more about how these apps constituted useful environments for developing computational thinking. Results suggest that coding apps of a ‘teaching’ design complement apps where computational concepts and practices are applied to project creation, and indeed may be more efficient if the desired outcome specifically targets the learning of concepts. Implications for teachers exploring coding apps for computational thinking development are drawn.

year: 2015

title: Travel writing and the first Marists in New Zealand

authors: Jennings, William

subjects: travel writing

abstract: French Marist missionaries arrived in New Zealand in 1838 and travelled extensively throughout the country during the next two decades. The letters they sent to France, now published in Girard's Lettres recues d'Ocanie (2009), include accounts of journeys that reveal the Marists' different perspectives of New Zealand's landscape and inhabitants. French romanticism and their religious vows emphasised a spiritual connection with the landscape, in sharp contrast with prevailing utilitarian European views. The Marists' status as Frenchmen in a British colony meant they encountered two alterities: British and Maori. Influenced by the noble savage of the French Romantics and by anti-Protestant bias, the Marists portrayed Maori favourably, reserving their more hostile comments for the British missionaries.

text: Travel writing and the first Marists in New Zealand French Marist missionaries arrived in New Zealand in 1838 and travelled extensively throughout the country during the next two decades. The letters they sent to France, now published in Girard's Lettres recues d'Ocanie (2009), include accounts of journeys that reveal the Marists' different perspectives of New Zealand's landscape and inhabitants. French romanticism and their religious vows emphasised a spiritual connection with the landscape, in sharp contrast with prevailing utilitarian European views. The Marists' status as Frenchmen in a British colony meant they encountered two alterities: British and Maori. Influenced by the noble savage of the French Romantics and by anti-Protestant bias, the Marists portrayed Maori favourably, reserving their more hostile comments for the British missionaries.

year: 2010-12