title: Considering pedagogical content knowledge in the context of research on teaching: An example from technology.

authors: Jones, Alister

subjects: teaching

abstract: When thinking about teaching, the pedagogical content knowledge of teachers cannot be ignored. We argue that pedagogical content knowledge is a major determiner of teaching practice and is central to teachers' curriculum decision-making at the classroom level. This paper takes a sociocultural perspective on the importance of developing teachers' pedagogical content knowledge. From our classroom-based research in technology education and the past research on pedagogical content knowledge we propose a model of pedagogical content knowledge with seven characteristics that we believe are important for effective teaching.

text: Considering pedagogical content knowledge in the context of research on teaching: An example from technology. When thinking about teaching, the pedagogical content knowledge of teachers cannot be ignored. We argue that pedagogical content knowledge is a major determiner of teaching practice and is central to teachers' curriculum decision-making at the classroom level. This paper takes a sociocultural perspective on the importance of developing teachers' pedagogical content knowledge. From our classroom-based research in technology education and the past research on pedagogical content knowledge we propose a model of pedagogical content knowledge with seven characteristics that we believe are important for effective teaching.

year: 2003

title: Override and restricted union for partial functions

authors: Stokes, Tim

abstract: The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

text: Override and restricted union for partial functions The override operation  is a natural one in computer science, and has connections with other areas of mathematics such as hyperplane arrangements. For arbitrary functions f and g, f  g is the function with
domain dom(f) ∪ dom(g) that agrees with f on dom(f) and with g on dom(g)\ dom(f). Jackson and the author have shown that there is no finite axiomatisation of algebras of functions of signature (). But adding operations (such as update) to this minimal signature can lead to finite axiomatisations. For the functional signature (, \) where \ is set-theoretic difference, Cirulis has given a finite equational axiomatisation as subtraction o-semilattices. Define f  g = (f g)∩(g f) for all functions f and g; this is the largest domain restriction of the binary relation f ∪ g that gives a partial function. Now f ∩g = f\(f\g) and f g = f  (f  g) for all functions f,g, so the signatures () and (, ∩) are both intermediate between () and (, \) in expressive power. We show that each is finitely axiomatised, with the former giving a proper quasivariety and the latter the variety of associative distributive o-semilattices in the sense of Cirulis.

year: 2024-08-12

title: George Lipsey: a Pakeha Maori who married Ema Mokena, daughter of mokena hou, and some of their children

authors: Hart, Philip

abstract: George Lipsey, an Irishman, went to the early Thames goldfield and became a publican. He soon acquired close links with Maori, notably with Ema Mokena, the younger daughter of Mokena Hou. After having two children, they married under Pakeha law just before the opening of the Te Aroha field, thereby ensuring that he was entitled to share in the goldfield’s revenue. From 1873 onwards he had been living at Te Aroha as a Pakeha Maori, erecting the first wooden house and the first Hot Springs Hotel. When gold was found, he encouraged Mokena Hou to open the field, and subsequently invested in the mines (as did Ema, to a much smaller extent). 
Ema and her two eldest children were granted land in a rapidly developing settlement, and the income received from leasing it enabled Lipsey to erect a substantial residence and to be a benefactor of the new settlement by donating land for churches and a school. A sympathetic landlord, he adjusted the rents to assist residents but opposed giving them the freehold because the land was held in trust for his two eldest children. Despite his steady income, his expenditure regularly exceeded it, and he ended up selling land, though not at first at Te Aroha. Initially opposed to his children selling their land, he came to accept this as being necessary, and spent years trying to obtain the highest prices possible from the government.
A leading figure in the local community, he held several local government positions. Sociable, with a fondness for drink that was usually under control, he was especially enthusiastic about horse-racing. As the spokesman for Ngati Rahiri, he advised the latter and was an interpreter.
All their children were educated, but some died tragically early deaths. After he died, the children sold their land because they needed money to develop their farms.

text: George Lipsey: a Pakeha Maori who married Ema Mokena, daughter of mokena hou, and some of their children George Lipsey, an Irishman, went to the early Thames goldfield and became a publican. He soon acquired close links with Maori, notably with Ema Mokena, the younger daughter of Mokena Hou. After having two children, they married under Pakeha law just before the opening of the Te Aroha field, thereby ensuring that he was entitled to share in the goldfield’s revenue. From 1873 onwards he had been living at Te Aroha as a Pakeha Maori, erecting the first wooden house and the first Hot Springs Hotel. When gold was found, he encouraged Mokena Hou to open the field, and subsequently invested in the mines (as did Ema, to a much smaller extent). 
Ema and her two eldest children were granted land in a rapidly developing settlement, and the income received from leasing it enabled Lipsey to erect a substantial residence and to be a benefactor of the new settlement by donating land for churches and a school. A sympathetic landlord, he adjusted the rents to assist residents but opposed giving them the freehold because the land was held in trust for his two eldest children. Despite his steady income, his expenditure regularly exceeded it, and he ended up selling land, though not at first at Te Aroha. Initially opposed to his children selling their land, he came to accept this as being necessary, and spent years trying to obtain the highest prices possible from the government.
A leading figure in the local community, he held several local government positions. Sociable, with a fondness for drink that was usually under control, he was especially enthusiastic about horse-racing. As the spokesman for Ngati Rahiri, he advised the latter and was an interpreter.
All their children were educated, but some died tragically early deaths. After he died, the children sold their land because they needed money to develop their farms.

year: 2016