Chebyshev Action on Finite Fields

Given a polynomial f and a finite field F one can construct a directed graph where the vertices are the values in the finite field, and emanating from each vertex is an edge joining the vertex to its image under f. When f is a Chebyshev polynomial of prime degree, the graphs display an unusual degree of symmetry. In this paper we provide a complete description of these graphs, and also provide some examples of how these graphs can be used to determine the decomposition of primes in certain field extensions

Unearthing learners’ conceptions of reflection to innovate business education for the 21st century

The development of learners’ capacities for critical reflection is an important learning outcome for 21st century business education. Theories suggest that a learner holds a particular orientation to reflection, and that this perspective will be influenced by his or her underlying beliefs. This, coupled with an increased focus on the student experience, personal development, and self-regulation in higher education, offers scope for considering instructional design from a second-order perspective, or in other words, from the student’s point of view. This study sought to understand: 1) the ways that business students orientate to reflection, 2) the different conceptions they hold of reflection, and 3) whether there is a relationship between the two. Reflective learning questionnaires were completed by 112 business students studying at the University of Northampton. Survey results showed that while the research instrument was a good fit for investigating orientations to and conceptions of reflection, there did not appear to be a correlation between the two. Learning analytics such as these will be useful for considering how the University can design more meaningful business curricula. However, the disconnect between conceptions of and orientations to reflection needs to be explored through further research

Promoting reflection in asynchronous virtual learning spaces: tertiary distance tutors' conceptions

Increasingly, universities are embedding reflective activities into the curriculum. With the growth in online tertiary education, how effectively is reflection being promoted or used in online learning spaces? Based on the notion that teachers’ beliefs will influence their approaches to teaching, this research sought to understand how a group of distance tutors at the UK Open University conceptualised reflection. It was hoped that these findings would illuminate their approaches to promoting reflection as part of their online pedagogies. Phenomenographic analysis indicated that these tutors conceptualised reflection in four qualitatively different ways. Furthermore, the data suggested that these educators held a combination of two conceptions: one that understood the origin of being reflective and one that understood the purpose of reflection. Analysis of structural aspects of these conceptions offered insight into tutors’ own perspectives for what is needed to make online learning environments fertile territory for reflective learning

Using student experience as a model for designing an automatic feedback system for short essays

The SAFeSEA project (Supportive Automated Feedback for Short Essay Answers) aims to develop an automated feedback system to support university students as they write summative essays. Empirical studies carried out in the initial phase of the system’s development illuminated students’ approaches to and understandings of the essay-writing process. Findings from these studies suggested that, regardless of their experience of higher education, students consider essay-writing as: 1) a sequential set of activities, 2) a process that is enhanced through particular sources of support and 3) a skill that requires the development of personal strategies. Further data collected from tutors offered insight into the feedback and reflection stages of essay-writing. These perspectives offered a fundamental model of essay-writing and feedback to inform the ongoing, iterative development of this automated feedback system and indeed, for any institution developing tools to support students’ writing