title: Body fractions: A physical approach to fraction learning

authors: Mills, Judith Patricia

subjects: primary school

abstract: Many students experience great difficulty understanding the meaning of fractions (Anthony & Walshaw, 2007; Behr, Lesh, Post & Silver, 1983; Davis, Hunting & Pearn, 1993; Lamon, 2007; Verschaffel, Greer & Torbeyns, 2006; Young-Loveridge, Taylor, Hawera & Sharma, 2007). For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is the idea that they are parts of a whole. The fact that one whole object can be divided into many equal parts, with each part having a name relative to the original whole, opens up a whole new realm of number understanding for the students.

text: Body fractions: A physical approach to fraction learning Many students experience great difficulty understanding the meaning of fractions (Anthony & Walshaw, 2007; Behr, Lesh, Post & Silver, 1983; Davis, Hunting & Pearn, 1993; Lamon, 2007; Verschaffel, Greer & Torbeyns, 2006; Young-Loveridge, Taylor, Hawera & Sharma, 2007). For many students who have spent their early mathematics lessons focusing on counting (whole) numbers, recognising that there are many numbers between those whole numbers called fractional numbers, is quite revolutionary. The foundation of understanding fractions is the idea that they are parts of a whole. The fact that one whole object can be divided into many equal parts, with each part having a name relative to the original whole, opens up a whole new realm of number understanding for the students.

year: 2011

title: Superintegrability on the two-dimensional hyperboloid. II

authors: Kalnins, Ernie G.

subjects: Mathematics

abstract: This work is devoted to the investigation of the quantum mechanical systems on the two-dimensional hyperboloid which admits separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C. P. Boyer, E. G. Kalnins, and P. Winternitz [J. Math. Phys. 24, 2022 (1983)], which have not yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.

text: Superintegrability on the two-dimensional hyperboloid. II This work is devoted to the investigation of the quantum mechanical systems on the two-dimensional hyperboloid which admits separation of variables in at least two coordinate systems. Here we consider two potentials introduced in a paper of C. P. Boyer, E. G. Kalnins, and P. Winternitz [J. Math. Phys. 24, 2022 (1983)], which have not yet been studied. We give an example of an interbasis expansion and work out the structure of the quadratic algebra generated by the integrals of motion.

year: 1999-05

title: Akuhata Mokena: Eldest son of Mokena Hou

authors: Hart, Philip

abstract: Akuhata Mokena was recorded as being the first child of Mokena Hou and Rina. By the early 1860s he was living at the northern boundary of the Aroha Block as well as at Puriri, where he dug kauri gum. From 1857 to 1868 he also cultivated close to the southern edge of the future Thames township. Having run cattle on the Aroha block from 1867 onwards, he settled there in 1878, operating the first hotel to be erected at the hot springs. 
In the land court he tried to obtain interests in as many land blocks as possible, and obtained income by selling some of these. After a brief involvement in Te Aroha mining, when he was the only member of his family to delay ceding their land for mining, he returned to live at Puriri. He also invested, very modestly, in mining at Thames and Puriri. 
A rangatira who was steadfastly loyal to the Crownt, when he died without issue his estate became a cause of conflict between Maori and Pakeha perceptions of how it should be shared amongst his wife and his family.

text: Akuhata Mokena: Eldest son of Mokena Hou Akuhata Mokena was recorded as being the first child of Mokena Hou and Rina. By the early 1860s he was living at the northern boundary of the Aroha Block as well as at Puriri, where he dug kauri gum. From 1857 to 1868 he also cultivated close to the southern edge of the future Thames township. Having run cattle on the Aroha block from 1867 onwards, he settled there in 1878, operating the first hotel to be erected at the hot springs. 
In the land court he tried to obtain interests in as many land blocks as possible, and obtained income by selling some of these. After a brief involvement in Te Aroha mining, when he was the only member of his family to delay ceding their land for mining, he returned to live at Puriri. He also invested, very modestly, in mining at Thames and Puriri. 
A rangatira who was steadfastly loyal to the Crownt, when he died without issue his estate became a cause of conflict between Maori and Pakeha perceptions of how it should be shared amongst his wife and his family.

year: 2016