title: Groups with fix-set quasi-order

authors: Stokes, Tim E.

abstract: If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of SX. Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.

text: Groups with fix-set quasi-order If X is a set, the fix-set quasiorder on a group of permutations of X is the quasiorder induced by containment of the fix-sets of elements of SX. Axioms for such quasiorders on groups have previously been given. We generalise these to allow non-faithful group actions, the resulting abstract quasiorders being called fix-orders. We characterise the possible fix-orders on a given group G in terms of certain families of subgroups of G. The special case in which the members of the defining family of subgroups are all normal is considered. Software is used to construct and analyse the lattices of fix-orders of many small finite groups.

year: 2015

title: Promoting pedagogical content knowledge development for early career secondary teachers in science and technology using content representations

authors: Williams, P. John

subjects: CoRE

abstract: Background: This research addressed the key area of early career teacher education and aimed to explore the use of a 'content representation' (CoRe) as a mediational tool to develop early career secondary teacher pedagogical content knowledge (PCK). This study was situated in the subject areas of science and technology, where sound teacher knowledge is particularly important to student engagement.Purpose: The study was designed to examine whether such a tool (a CoRe), co-designed by an early career secondary teacher with expert content and pedagogy specialists, can enhance the PCK of early career teachers. The research questions were: How can experts in content and pedagogy work together with early career teachers to develop one science topic CoRe and one technology topic CoRe to support the development of PCK for early career secondary teachers? How does the use of a collaboratively designed CoRe affect the planning of an early career secondary teacher in science or technology? How has engagement in the development and use of an expert-informed CoRe developed an early career teacher's PCK?Sample: The research design incorporated a unique partnership between two expert classroom teachers, two content experts, four early career teachers, and four researchers experienced in science and technology education.Design: This study employed an interpretivist-based methodology and an action research approach within a four-case study design. Data were gathered using qualitative research methods focused on semi-structured interviews, observations and document analysis.Results: The study indicated that CoRes, developed through this collaborative process, helped the early career teachers focus on the big picture of the topic, emphasize particularly relevant areas of content and consider alternative ways of planning for their teaching.Conclusions: This paper presents an analysis of the process of CoRe development by the teacher-expert partnerships and the effect that had on the early career teachers' PCK. In addition, as the same tools and methodology were applied to both a science and a technology teaching context, differences between the two learning areas are discussed.

text: Promoting pedagogical content knowledge development for early career secondary teachers in science and technology using content representations Background: This research addressed the key area of early career teacher education and aimed to explore the use of a 'content representation' (CoRe) as a mediational tool to develop early career secondary teacher pedagogical content knowledge (PCK). This study was situated in the subject areas of science and technology, where sound teacher knowledge is particularly important to student engagement.Purpose: The study was designed to examine whether such a tool (a CoRe), co-designed by an early career secondary teacher with expert content and pedagogy specialists, can enhance the PCK of early career teachers. The research questions were: How can experts in content and pedagogy work together with early career teachers to develop one science topic CoRe and one technology topic CoRe to support the development of PCK for early career secondary teachers? How does the use of a collaboratively designed CoRe affect the planning of an early career secondary teacher in science or technology? How has engagement in the development and use of an expert-informed CoRe developed an early career teacher's PCK?Sample: The research design incorporated a unique partnership between two expert classroom teachers, two content experts, four early career teachers, and four researchers experienced in science and technology education.Design: This study employed an interpretivist-based methodology and an action research approach within a four-case study design. Data were gathered using qualitative research methods focused on semi-structured interviews, observations and document analysis.Results: The study indicated that CoRes, developed through this collaborative process, helped the early career teachers focus on the big picture of the topic, emphasize particularly relevant areas of content and consider alternative ways of planning for their teaching.Conclusions: This paper presents an analysis of the process of CoRe development by the teacher-expert partnerships and the effect that had on the early career teachers' PCK. In addition, as the same tools and methodology were applied to both a science and a technology teaching context, differences between the two learning areas are discussed.

year: 2012

title: Does artificial intelligence modelling have anything to offer traditional management of freshwater food resources?

authors: Death, Russell G.

abstract: Management of freshwater systems and the ecosystem services they provide has become a multi-stakeholder activity. This requires information on resources and how to manage them to be disseminated to a wide range of users. While artificial intelligence modelling can provide a powerful tool in managing and understanding resources and their drivers, they can be confusing to many users. In this study, we explored the potential use of two alternative modelling approaches (Boosted Regression Trees (BRT) and Bayesian Belief Networks (BBN)) for managing three species of freshwater mahinga kai species-kākahi or kaeo (freshwater mussel), koura (freshwater crayfish) and tuna (freshwater eel). While the BBN model I sbetter for stakeholder communication, the BRT produced more accurate models for all species. However, variables identified as being important for predicting abundance and biomass of these species were often environmental parameters that cannot be managed to improve yield. The artificial intelligence modelling does provide some accurate linkages between the target species and their environmental drivers. Nevertheless, translating these relationships into management plans remains challenging. The models are clearly not a panacea for better resource management, but provide one more tool that might assist multi-stakeholder understanding of how best to manage freshwater resources.

text: Does artificial intelligence modelling have anything to offer traditional management of freshwater food resources? Management of freshwater systems and the ecosystem services they provide has become a multi-stakeholder activity. This requires information on resources and how to manage them to be disseminated to a wide range of users. While artificial intelligence modelling can provide a powerful tool in managing and understanding resources and their drivers, they can be confusing to many users. In this study, we explored the potential use of two alternative modelling approaches (Boosted Regression Trees (BRT) and Bayesian Belief Networks (BBN)) for managing three species of freshwater mahinga kai species-kākahi or kaeo (freshwater mussel), koura (freshwater crayfish) and tuna (freshwater eel). While the BBN model I sbetter for stakeholder communication, the BRT produced more accurate models for all species. However, variables identified as being important for predicting abundance and biomass of these species were often environmental parameters that cannot be managed to improve yield. The artificial intelligence modelling does provide some accurate linkages between the target species and their environmental drivers. Nevertheless, translating these relationships into management plans remains challenging. The models are clearly not a panacea for better resource management, but provide one more tool that might assist multi-stakeholder understanding of how best to manage freshwater resources.

year: 2017