Surveying theories and philosophies of mathematics education

Any theory of thinking or teaching or learning rests on an underlying philosophy of knowledge. Mathematics education is situated at the nexus of two fields of inquiry, namely mathematics and education. However, numerous other disciplines interact with these two fields which compound the complexity of developing theories that define mathematics education. We first address the issue of clarifying a philosophy of mathematics education before attempting to answer whether theories of mathematics education are constructible? In doing so we draw on the foundational writings of Lincoln and Guba (1994), in which they clearly posit that any discipline within education, in our case mathematics education, needs to clarify for itself the following questions: (1) What is reality? Or what is the nature of the world around us? (2) How do we go about knowing the world around us? [the methodological question, which presents possibilities to various disciplines to develop methodological paradigms] and, (3) How can we be certain in the “truth” of what we know? [the epistemological question]

Evolving Philosophies on Autonomous Obstacle/Collision Avoidance of Unmanned Aerial Vehicles

Much of the benefits of deploying unmanned aerial vehicles can be derived from autonomous missions. For such missions, however, sense-and-avoid capability (i.e., the ability to detect potential collisions and avoid them) is a critical requirement. Collision avoidance can be broadly classified into global and local path-planning algorithms, both of which need to be addressed in a successful mission. Whereas global path planning (which is mainly done offline) broadly lays out a path that reaches the goal point, local collision-avoidance algorithms, which are usually fast, reactive, and carried out online, ensure safety of the vehicle from unexpected and unforeseen obstacles/collisions. Even though many techniques for both global and local collision avoidance have been proposed in the recent literature, there is a great interest around the globe to solve this important problem comprehensively and efficiently and such techniques are still evolving. This paper presents a brief overview of a few promising and evolving ideas on collision avoidance for unmanned aerial vehicles, with a preferential bias toward local collision avoidance.

Explaining the Stunted Rise of Macroprudential Regulatory Philosophies

In the aftermath of the financial crash of 2008, policy makers operating in international financial regulatory networks discovered macroprudential regulation (MPR), but macroprudential regulation has had a stunted or arrested development that can be explained with reference to five factors that are recounted in this article

Philosophies, traditional pedagogy, and new technologies: a report on a case study of EAP teachers' integration of technology into traditional practice

This chapter reports on a study of teachers in transition, developing their practice and their cognitions regarding the integration of learning technologies with traditional approaches to the teaching of English for Academic Purposes (EAP). Taking a case study approach, it examines developments in the practice of three teachers during and after a teacher education programme on the use of technology in the EAP classroom. This is a study of cognition, teaching philosophy, and the relationship between pedagogy, technology, and content, and how teachers situate these within their own practice. The setting is the rapidly changing UK higher education environment, where the speed of change is such that today's latest fashions and gadgets may well be yesterday's news tomorrow. Thus, this is not a tale of individual technologies or tools to make teachers' lives better. This is a story of people, of pedagogy's traditional values intersecting with technology, and the issues arising from this, alongside the evolution of strategies for dealing with these issues.

Educators' attitudes to philosophies of music education

This study used Q methodology to measure the extent to which individuals with five educational roles (student teacher, elementary music teacher, principal, high school music teacher, and music consultant) held five proposed philosophies of music education (hedonic, utilitarian, aesthetic cognitivism, aesthetic formalist, and praxial). Twenty-seven sUbjects participated in the Q study. These subjects were a convenience sample based on their educational role, accessibility, and willingness to participate. Participants completed a background sheet which indicated their background in music, and their responsibility for teaching music. The sUbjects in this Q study rank-ordered a set of 60 Q sort items (each item representing a proposed philosophical position) twice: Sort P to reflect current practice, and Sort I to reflect the ideal situation. The results of the sorting procedures were recorded by the participant on the response page which organized the rankings according to an approximated normal distribution as required by Q methodology. The analysis of the data suggested that the comparison across philosophical positions was significant and that the results of the interaction between philosophical position and educational role were significant, although educational role alone was not significant. Post-hoc analysis of the data was used to determine the significant differences between the levels of the, independent variables used in the model: philosophical position, educational role, and music background. A model of the association of the five philosophical positions was presented and discussed in relation to the Q study results. Further research could refine the Q sort items to better reflect each philosophical position.

A study of face-to-face and online teaching philosophies in Canada and Australia

The perspectives of instructors who teach both online and face-to-face in a higher education context have been compared in this study. The differences and similarities between their approaches, and the influences each modality has on the other have been explored, as well as possible differences in organizational cultures between the groups who were based in Canada and Australia. The trend to blended learning in higher education was an important outcome of the study.

Performance evaluation and improved risk control philosophies for drinking water systems

World-wide, water is the single most used substance by humans every day. Water is also the major cause of illness and death in many countries including the affluent nations. Through this research, new risk control philosophies from catchment to consumers are highlighted. This thesis is about identifying the hazards, evaluating the risks and implementing controls to protect public health from drinking water.

Changing philosophies and tools for statistical inferences in behavioral ecology

Recent developments in ecological statistics have reached behavioral ecology, and an increasing number of studies now apply analytical tools that incorporate alternatives to the conventional null hypothesis testing based on significance levels. However, these approaches continue to receive mixed support in our field. Because our statistical choices can influence research design and the interpretation of data, there is a compelling case for reaching consensus on statistical philosophy and practice. Here, we provide a brief overview of the recently proposed approaches and open an online forum for future discussion (https://bestat.ecoinformatics.org/). From the perspective of practicing behavioral ecologists relying on either correlative or experimental data, we review the most relevant features of information theoretic approaches, Bayesian inference, and effect size statistics. We also discuss concerns about data quality, missing data, and repeatability. We emphasize the necessity of moving away from a heavy reliance on statistical significance while focusing attention on biological relevance and effect sizes, with the recognition that uncertainty is an inherent feature of biological data. Furthermore, we point to the importance of integrating previous knowledge in the current analysis, for which novel approaches offer a variety of tools. We note, however, that the drawbacks and benefits of these approaches have yet to be carefully examined in association with behavioral data. Therefore, we encourage a philosophical change in the interpretation of statistical outcomes, whereas we still retain a pluralistic perspective for making objective statistical choices given the uncertainties around different approaches in behavioral ecology. We provide recommendations on how these concepts could be made apparent in the presentation of statistical outputs in scientific papers.

A factor-analytic reinterpretation of the Clark-Trow "educational philosophies"

Each of four principal components analyses (n = 3,944) incorporated student self-ratings (Most accurate to Least accurate) on one of the four Clark-Trow educational philosophies: Vocational, Academic, Collegiate, Nonconformist. The analyses of these 25-variable correlation matrices yielded 2 factors differentially associated with educational philosophy: Sociability versus Independence (replacing Clark-Trow's "Identification with the College") and Liberalism versus Conservatism (replacing Clark-Trow's "Involvement with Ideas"). The Vocational philosophy was associated primarily with Conservatism, the Collegiate with Sociability, and the Nonconformist with Liberalism; the Academic was moderately associated with both Independence and Liberalism.