Mindfulness: An Ancient Wisdom for the Reconceptualisation of Modern Education in the Complex World

Exploring the new science of emergence allows us to create a very different classroom than how the modern classroom has been conceptualised under the mentality of efficiency and output. Working on the whole person, and not just the mind, we see a shift from the epistemic pillars of truth to more ontological concerns as regards student achievement in our post-Modern and critical discourses. It is important to understand these shifts and how we are to transition our own perception and mentality not only in our research methodologies but also our approach to conceptualisations of issues in education and sustainability. We can no longer think linearly to approach complex problems or advocate for education and disregard our interconnectedness insofar as it enhances our children’s education. We must, therefore, contemplate and transition to a world that is ecological and not mechanical, complex and not complicated—in essence, we must work to link mind-body with self-environment and transcend these in order to bring about an integration toward a sustainable future. A fundamental shift in consciousness and perception may implicate our nature of creating dichotomous entities in our own microcosms, yet postmodern theorists assume, a priori, that these dualities can be bridged in naturalism alone. I, on the other hand, embrace metaphysics to understand the implicated modern classroom in a hierarchical context and ask: is not the very omission of metaphysics in postmodern discourse a symptom from an education whose foundation was built in its absence? The very dereliction of ancient wisdom in education is very peculiar indeed. Western mindfulness may play a vital component in consummating pragmatic idealism, but only under circumstances admitting metaphysics can we truly transcend our limitations, thereby placing Eastern Mindfulness not as an ecological component, but as an ecological and metaphysical foundation.

RelMDD-A Library for Manipulating Relations Based on MDDs

Relation algebras is one of the state-of-the-art means used by mathematicians and computer scientists for solving very complex problems. As a result, a computer algebra system for relation algebras called RelView has been developed at Kiel University. RelView works within the standard model of relation algebras. On the other hand, relation algebras do have other models which may have different properties. For example, in the standard model we always have L;L=L (the composition of two (heterogeneous) universal relations yields a universal relation). This is not true in some non-standard models. Therefore, any example in RelView will always satisfy this property even though it is not true in general. On the other hand, it has been shown that every relation algebra with relational sums and subobjects can be seen as matrix algebra similar to the correspondence of binary relations between sets and Boolean matrices. The aim of my research is to develop a new system that works with both standard and non-standard models for arbitrary relations using multiple-valued decision diagrams (MDDs). This system will implement relations as matrix algebras. The proposed structure is a library written in C which can be imported by other languages such as Java or Haskell.

The Search for Scholarly Teaching in Elementary Education

Elementary teachers are expected to prepare students to work efficiently with others, solve complex problems and self-regulate their own learning. Considering the importance of a solid educational foundation in the early years, students would benefit if elementary teachers engaged in scholarly teaching. The purpose of this study was to investigate Boyer’s (1990) four dimensions of scholarship, application, integration, teaching and discovery, to better understand if there is scholarly teaching in elementary education. Four professional teaching documents were analyzed using a hermeneutic orientation. A deductive analysis suggests that we do have scholarly teaching in elementary education, with strong evidence that elementary teachers are scholars of application and integration. An inductive analysis of latent and manifest content suggests that underlying humanistic values run deeply through elementary education driving current curricular, instructional and pedagogical practices.

Heuristics for the Critical Node Detection Problem in Large Complex Networks

Complex networks have recently attracted a significant amount of research attention due to their ability to model real world phenomena. One important problem often encountered is to limit diffusive processes spread over the network, for example mitigating pandemic disease or computer virus spread. A number of problem formulations have been proposed that aim to solve such problems based on desired network characteristics, such as maintaining the largest network component after node removal. The recently formulated critical node detection problem aims to remove a small subset of vertices from the network such that the residual network has minimum pairwise connectivity. Unfortunately, the problem is NP-hard and also the number of constraints is cubic in number of vertices, making very large scale problems impossible to solve with traditional mathematical programming techniques. Even many approximation algorithm strategies such as dynamic programming, evolutionary algorithms, etc. all are unusable for networks that contain thousands to millions of vertices. A computationally efficient and simple approach is required in such circumstances, but none currently exist. In this thesis, such an algorithm is proposed. The methodology is based on a depth-first search traversal of the network, and a specially designed ranking function that considers information local to each vertex. Due to the variety of network structures, a number of characteristics must be taken into consideration and combined into a single rank that measures the utility of removing each vertex. Since removing a vertex in sequential fashion impacts the network structure, an efficient post-processing algorithm is also proposed to quickly re-rank vertices. Experiments on a range of common complex network models with varying number of vertices are considered, in addition to real world networks. The proposed algorithm, DFSH, is shown to be highly competitive and often outperforms existing strategies such as Google PageRank for minimizing pairwise connectivity.