Components of learning and assessment in linear algebra

Linear algebra provides theory and technology that are the cornerstones of a range of cutting edge mathematical applications, from designing computer games to complex industrial problems, as well as more traditional applications in statistics and mathematical modelling. Once past introductions to matrices and vectors, the challenges of balancing theory, applications and computational work across mathematical and statistical topics and problems are considerable, particularly given the diversity of abilities and interests in typical cohorts. This paper considers two such cohorts in a second level linear algebra course in different years. The course objectives and materials were almost the same, but some changes were made in the assessment package. In addition to considering effects of these changes, the links with achievement in first year courses are analysed, together with achievement in a following computational mathematics course. Some results that may initially appear surprising provide insight into the components of student learning in linear algebra.

The effects of habitat fragmentation on the demography and population genetic structure of Uromys Caudimaculatus

Habitat fragmentation can have an impact on a wide variety of biological processes including abundance, life history strategies, mating system, inbreeding and genetic diversity levels of individual species. Although fragmented populations have received much attention, ecological and genetic responses of species to fragmentation have still not been fully resolved. The current study investigated the ecological factors that may influence the demographic and genetic structure of the giant white-tailed rat (Uromys caudimaculatus) within fragmented tropical rainforests. It is the first study to examine relationships between food resources, vegetation attributes and Uromys demography in a quantitative manner. Giant white-tailed rat densities were strongly correlated with specific suites of food resources rather than forest structure or other factors linked to fragmentation (i.e. fragment size). Several demographic parameters including the density of resident adults and juvenile recruitment showed similar patterns. Although data were limited, high quality food resources appear to initiate breeding in female Uromys. Where data were sufficient, influx of juveniles was significantly related to the density of high quality food resources that had fallen in the previous three months. Thus, availability of high quality food resources appear to be more important than either vegetation structure or fragment size in influencing giant white-tailed rat demography. These results support the suggestion that a species’ response to fragmentation can be related to their specific habitat requirements and can vary in response to local ecological conditions. In contrast to demographic data, genetic data revealed a significant negative effect of habitat fragmentation on genetic diversity and effective population size in U. caudimaculatus. All three fragments showed lower levels of allelic richness, number of private alleles and expected heterozygosity compared with the unfragmented continuous rainforest site. Populations at all sites were significantly differentiated, suggesting restricted among population gene flow. The combined effects of reduced genetic diversity, lower effective population size and restricted gene flow suggest that long-term viability of small fragmented populations may be at risk, unless effective management is employed in the future. A diverse range of genetic reproductive behaviours and sex-biased dispersal patterns were evident within U. caudimaculatus populations. Genetic paternity analyses revealed that the major mating system in U. caudimaculatus appeared to be polygyny at sites P1, P3 and C1. Evidence of genetic monogamy, however, was also found in the three fragmented sites, and was the dominant mating system in the remaining low density, small fragment (P2). High variability in reproductive skew and reproductive success was also found but was less pronounced when only resident Uromys were considered. Male body condition predicted which males sired offspring, however, neither body condition nor heterozygosity levels were accurate predictors of the number of offspring assigned to individual males or females. Genetic spatial autocorrelation analyses provided evidence for increased philopatry among females at site P1, but increased philopatry among males at site P3. This suggests that male-biased dispersal occurs at site P1 and female-biased dispersal at site P3, implying that in addition to mating systems, Uromys may also be able to adjust their dispersal behaviour to suit local ecological conditions. This study highlights the importance of examining the mechanisms that underlie population-level responses to habitat fragmentation using a combined ecological and genetic approach. The ecological data suggested that habitat quality (i.e. high quality food resources) rather than habitat quantity (i.e. fragment size) was relatively more important in influencing giant white-tailed rat demographics, at least for the populations studied here . Conversely, genetic data showed strong evidence that Uromys populations were affected adversely by habitat fragmentation and that management of isolated populations may be required for long-term viability of populations within isolated rainforest fragments.

Discovering, applying and integrating: The process of learning in coaching

Professional coaching is a rapidly expanding field with interdisciplinary roots and broad application. However, despite abundant prescriptive literature, research into the process of coaching is minimal. Similarly, although learning is inherently recognised in the process of coaching, the process of learning in coaching is little understood and learning theory makes up only a small part of the evidence-based coaching literature. In this grounded theory study of coaches and their clients, the process of learning in coaching across a range of coaching models is examined and discussed. The findings demonstrate how learning in coaching emerged as a process of discovering, applying and integrating new knowledge, which culminated in a process of developing. This process occurred through eight key coaching processes shared between coaches and clients and combined a multitude of learning theories.

The influences of conceptions of learning and learner self-concept on high school students' approaches to learning

This study investigated the mediating effect of learner selfconcept between conceptions of learning and students' approaches to learning using structural equation modelling. Data were collected using a modified version of Biggs' Learning Process Questionnaire, together with the recently developed 'What is Learning Survey' and 'Learner Self-Concept Scale'. A sample of 355 high school students participated in the study. Results indicate that learner self-concept does mediate between conceptions of meaning and approaches to learning. Students who adopted a deep approach liked learning new things and indirectly viewed learning as experiential, involving social interaction and directly viewed learning as personal development. Implications for teachers are discussed, with consideration given to appropriate classroom practice.

An investigation into the use of a blended model of learning in a first year accounting subject

The weaknesses of ‗traditional‘ modes of instruction in accounting education have been widely discussed. Many contend that the traditional approach limits the ability to provide opportunities for students to raise their competency level and allow them to apply knowledge and skills in professional problem solving situations. However, the recent body of literature suggests that accounting educators are indeed actively experimenting with ‗non-traditional‘ and ‗innovative‘ instructional approaches, where some authors clearly favour one approach over another. But can one instructional approach alone meet the necessary conditions for different learning objectives? Taking into account the ever changing landscape of not only business environments, but also the higher education sector, the premise guiding the collaborators in this research is that it is perhaps counter productive to promote competing dichotomous views of ‗traditional‘ and ‗non-traditional‘ instructional approaches to accounting education, and that the notion of ‗blended learning‘ might provide a useful framework to enhance the learning and teaching of accounting. This paper reports on the first cycle of a longitudinal study, which explores the possibility of using blended learning in first year accounting at one campus of a large regional university. The critical elements of blended learning which emerged in the study are discussed and, consistent with the design-based research framework, the paper also identifies key design modifications for successive cycles of the research.