title: Symmetries of the Hamilton–Jacobi equation

authors: Boyer, C.P.

subjects: Mathematics

abstract: We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local Lie group of point transformations locally isomorphie to O(3,2). We show that the separation of variables of the corresponding Hamilton-Jacobi equation n the form of a sum is related to orbits in the Schrödinger subalgebra of c(3,2). The remaining orbits of o(3,2) yield symmetry related solutions which separate in more complicated product forms. Finally some connections with the primordial equation of hydrodynamics (without force terms) are made.

text: Symmetries of the Hamilton–Jacobi equation We present a detailed discussion of the infinit esimal symmetries of the Hamilton-Jacobi equation (an arbitrary first order partial equation) Our presentation clucidates the role played by the characteristic system in determining the symmetries. We then specialize to the case of a free particle in one space and one time dimension, and study of local Lie group of point transformations locally isomorphie to O(3,2). We show that the separation of variables of the corresponding Hamilton-Jacobi equation n the form of a sum is related to orbits in the Schrödinger subalgebra of c(3,2). The remaining orbits of o(3,2) yield symmetry related solutions which separate in more complicated product forms. Finally some connections with the primordial equation of hydrodynamics (without force terms) are made.

year: 1977-05

title: Our journey to school: A collaboratively constructed, digitally facilitated transition to school

authors: Woodhouse, Hazel Maxine

subjects: transition to school

abstract: A parent’s role in supporting their child’s transition to school has been well researched and the importance of educational settings developing a partnership with parents has been identified as a key factor in a child’s effective transition to school. However, this idea is based on the belief that it is the child who is experiencing the transition, while the parents have only a supporting role to play. A smaller body of research and literature focuses on a family’s transition to school and acknowledges that the parents as well as the child are undergoing their own processes of change, and may need support in this process.
Taking a new approach to the transition to school process, this thesis explores the use of Facebook by a New Entrant teacher to develop a Community of Practice (CoP) to collaborate with families in making decisions about their own transition to school process. Applying a qualitative, case study approach involving 20 families who had children transitioning from three early childhood centres to the same primary school, online questionnaires were used to generate data from families and teachers at the start of the process to support the purpose and design and of each of the two separate Facebook group (families and teachers) sites. van Gennep’s three phases of transition provided a framework to perceive transition as a process where families’ needs changed over the period of their transition. Reflecting the onging process of transition, the two groups’ online data generated through the Facebook page over the period of seven months were used formatively to provide for the families’ immediate needs, and summatively to view activity and the evolving CoP.
The research found that Facebook was an accessible and flexible tool, and allowed families to participate and collaborate as much as they wanted or needed. This study shows that the functions available through Facebook provided opportunities to share children’s learning with all stakeholders, and so develop transition practices in both ECE and NE environments through sharing and discussing examples of practices. The CoP framework provided a network that enabled those families who needed advice or support about their child’s transition to seek this from experienced members of the group. Facebook facilitated the development of a range of resources for families and teachers to return to at their leisure. It also provided a space to ask questions, have anxieties alleviated and success celebrated. Using the digital space in Facebook, traditionally not the place for more formal orientation meetings, allowed the subsequent face-to-face meetings to become social events. These face-to-face opportunities to meet supported the connections that the families and teachers had initially made online. This thesis advocates for the use of social media platforms, such as Facebook, to enhance a blended approach of both digital and face-to-face opportunities to give families greater agency during their child’s transition to school.

text: Our journey to school: A collaboratively constructed, digitally facilitated transition to school A parent’s role in supporting their child’s transition to school has been well researched and the importance of educational settings developing a partnership with parents has been identified as a key factor in a child’s effective transition to school. However, this idea is based on the belief that it is the child who is experiencing the transition, while the parents have only a supporting role to play. A smaller body of research and literature focuses on a family’s transition to school and acknowledges that the parents as well as the child are undergoing their own processes of change, and may need support in this process.
Taking a new approach to the transition to school process, this thesis explores the use of Facebook by a New Entrant teacher to develop a Community of Practice (CoP) to collaborate with families in making decisions about their own transition to school process. Applying a qualitative, case study approach involving 20 families who had children transitioning from three early childhood centres to the same primary school, online questionnaires were used to generate data from families and teachers at the start of the process to support the purpose and design and of each of the two separate Facebook group (families and teachers) sites. van Gennep’s three phases of transition provided a framework to perceive transition as a process where families’ needs changed over the period of their transition. Reflecting the onging process of transition, the two groups’ online data generated through the Facebook page over the period of seven months were used formatively to provide for the families’ immediate needs, and summatively to view activity and the evolving CoP.
The research found that Facebook was an accessible and flexible tool, and allowed families to participate and collaborate as much as they wanted or needed. This study shows that the functions available through Facebook provided opportunities to share children’s learning with all stakeholders, and so develop transition practices in both ECE and NE environments through sharing and discussing examples of practices. The CoP framework provided a network that enabled those families who needed advice or support about their child’s transition to seek this from experienced members of the group. Facebook facilitated the development of a range of resources for families and teachers to return to at their leisure. It also provided a space to ask questions, have anxieties alleviated and success celebrated. Using the digital space in Facebook, traditionally not the place for more formal orientation meetings, allowed the subsequent face-to-face meetings to become social events. These face-to-face opportunities to meet supported the connections that the families and teachers had initially made online. This thesis advocates for the use of social media platforms, such as Facebook, to enhance a blended approach of both digital and face-to-face opportunities to give families greater agency during their child’s transition to school.

year: 2024-06-11

title: Investigating commentary on the fifth labour-led government’s third way approach

authors: Piercy, Gemma Louise

abstract: After the 1999 election of a Labour-led coalition government in Aotearoa New Zealand, a raft of policy reforms adopted characteristics of the ‘Third Way’ ideology promoted by Anthony Giddens. We argue, however, that Third Way characteristics were not implemented in Aotearoa New Zealand without attracting criticism. This article reviews academic analysis and wider commentary on the Third Way in Aotearoa New Zealand, much of which particularly focused on social policy reforms made by the Labour-led coalition government (1999-2008). We have used this literature to identify the varied ways in which the Third Way was defined and the extent to which Third Way ideology was considered to have influenced policy and practice the Aotearoa New Zealand context. Our semi-systematic literature review shows that many commentators argued that New Zealand did indeed implement a policy platform consistent with Third Way ideological characteristics but these were also adapted to the unique context of Aotearoa New Zealand. We explore in detail two key examples of adaptation di scussed in the literature: the Labour-led government’s early focus on reducing inequalities between Māori and non-Māori and on renewing civil society through subsidiarity and a partnership approach.

text: Investigating commentary on the fifth labour-led government’s third way approach After the 1999 election of a Labour-led coalition government in Aotearoa New Zealand, a raft of policy reforms adopted characteristics of the ‘Third Way’ ideology promoted by Anthony Giddens. We argue, however, that Third Way characteristics were not implemented in Aotearoa New Zealand without attracting criticism. This article reviews academic analysis and wider commentary on the Third Way in Aotearoa New Zealand, much of which particularly focused on social policy reforms made by the Labour-led coalition government (1999-2008). We have used this literature to identify the varied ways in which the Third Way was defined and the extent to which Third Way ideology was considered to have influenced policy and practice the Aotearoa New Zealand context. Our semi-systematic literature review shows that many commentators argued that New Zealand did indeed implement a policy platform consistent with Third Way ideological characteristics but these were also adapted to the unique context of Aotearoa New Zealand. We explore in detail two key examples of adaptation di scussed in the literature: the Labour-led government’s early focus on reducing inequalities between Māori and non-Māori and on renewing civil society through subsidiarity and a partnership approach.

year: 2017