title: Laying the tracks: Investigating the potential benefits for autistic children of a model railway initiative

authors: Gedye, Jacob

abstract: This study described a model railway programme in terms of its benefits for autistic children and their families/communities. A non-experimental mixed-method design was conducted, in which an observation schedule was designed to determine whether behaviours which are associated with language development were facilitated by the programme. Interviews with parents/caregivers were conducted to collect qualitative data about the programme, to better understand how it is perceived by visitors and what draws them to attend. Individual case studies with children and their parents/caregivers were done to build a clearer picture of what can be seen at an individual level. Finally, a focus group was arranged with members of the railway modeller’s club to find out their point of view and broaden the qualitative scope of the data. Findings suggest potential utility in this programme for autistic children and future research implications are discussed.

text: Laying the tracks: Investigating the potential benefits for autistic children of a model railway initiative This study described a model railway programme in terms of its benefits for autistic children and their families/communities. A non-experimental mixed-method design was conducted, in which an observation schedule was designed to determine whether behaviours which are associated with language development were facilitated by the programme. Interviews with parents/caregivers were conducted to collect qualitative data about the programme, to better understand how it is perceived by visitors and what draws them to attend. Individual case studies with children and their parents/caregivers were done to build a clearer picture of what can be seen at an individual level. Finally, a focus group was arranged with members of the railway modeller’s club to find out their point of view and broaden the qualitative scope of the data. Findings suggest potential utility in this programme for autistic children and future research implications are discussed.

year: 2025

title: Biembeddings of cycle systems using integer Heffter arrays

authors: Cavenagh, Nicholas J.

subjects: mathematics

abstract: In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and when n ≡ 0(mod 3) then k ≡ 7(mod 12), there exist face 2-colorable embeddings of the complete graph K₂ₙₖ₊₁ onto an orientable surface where each face is a cycle of a fixed length k. In these embeddings the vertices of K₂ₙₖ₊₁ will be labeled with the elements of Z₂ₙₖ₊₁ in such a way that the group, (Z₂ₙₖ₊₁, +) acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays, H (n ; k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo 2nk + 1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays H (n ; k) that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, for k ⩾ 11, that there are at least (n − 2)[((k − 11)/4)!/ ]² such nonequivalent H (n ; k) that satisfy both conditions (1) and (2).

text: Biembeddings of cycle systems using integer Heffter arrays In this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and when n ≡ 0(mod 3) then k ≡ 7(mod 12), there exist face 2-colorable embeddings of the complete graph K₂ₙₖ₊₁ onto an orientable surface where each face is a cycle of a fixed length k. In these embeddings the vertices of K₂ₙₖ₊₁ will be labeled with the elements of Z₂ₙₖ₊₁ in such a way that the group, (Z₂ₙₖ₊₁, +) acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays, H (n ; k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo 2nk + 1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays H (n ; k) that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, for k ⩾ 11, that there are at least (n − 2)[((k − 11)/4)!/ ]² such nonequivalent H (n ; k) that satisfy both conditions (1) and (2).

year: 2020

title: Restorative Practices in Schools: Far-Reaching Implications

authors: Drewery, Wendy

subjects: New Zealand

abstract: In 1999, the New Zealand Ministry of Education contracted a team from the University of Waikato to develop a process for conferencing in schools. The brief was to utilise restorative justice principles to develop a conferencing process for use in schools. The purpose was to test whether such an approach to wrongdoing could reduce the exponential increase of suspensions, particularly of Maori boys, who were, and still are, disproportionately represented in reported numbers of suspensions, stand-downs and exclusions.

text: Restorative Practices in Schools: Far-Reaching Implications In 1999, the New Zealand Ministry of Education contracted a team from the University of Waikato to develop a process for conferencing in schools. The brief was to utilise restorative justice principles to develop a conferencing process for use in schools. The purpose was to test whether such an approach to wrongdoing could reduce the exponential increase of suspensions, particularly of Maori boys, who were, and still are, disproportionately represented in reported numbers of suspensions, stand-downs and exclusions.

year: 2007