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.

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.

Assessing the structure of learning outcomes from counselling using the SOLO taxonomy: an exploratory study

Thirty-five clients who had received counselling completed a letter to a friend describing in as much detail as possible what they had learned from counselling. The participants' written responses were analysed and classified using the Structure of Learning Outcomes (SOLO) taxonomy. The results suggested that an expanded SOLO offers a promising and exciting way to view the outcomes of counselling within a learning framework. If the SOLO taxonomy is found to be stable in subsequent research, and clients are easily able to be classified using the taxonomy, then this approach may have implications for the process of counselling. To maximise the learning outcomes, counsellors could use strategies and techniques to enhance their clients' learning.

Transfer of learning across the globe : pre-service teachers taking the initiative

A continuing challenge for pre-service teacher education is the learning transfer between the university based components and the practical school based components of their training. It is not clear how easily pre-service teachers can transfer university learnings into ‘in school’ practice. Similarly, it is not clear how easily knowledge learned in the school context can be disembedded from this particular context and understood more generally by the pre-service teacher. This paper examines the effect of a community of practice formed specifically to explore learning transfer via collaboration and professional enquiry, in ‘real time’, across the globe. “Activity Theory” (Engestrom, 1999) provided the theoretical framework through which the cognitive, physical and social processes involved could be understood. For the study, three activity systems formed community of practice network. The first activity system involved pre-service teachers at a large university in Queensland, Australia. The second activity system was introduced by the pre-service teachers and involved Year 12 students and teachers at a private secondary school also in Queensland, Australia. The third activity system involved university staff engineers at a large university in Pennsylvania, USA. The common object among the three activity systems was to explore the principles and applications of nanotechnology. The participants in the two Queensland activity systems, controlled laboratory equipment (a high powered Atomic Force Microscope – CPII) in Pennsylvania, USA, with the aim of investigating surface topography and the properties of nano particles. The pre-service teachers were to develop their remote ‘real time’ experience into school classroom tasks, implement these tasks, and later report their findings to other pre-service teachers in the university activity system. As an extension to the project, the pre-service teachers were invited to co-author papers relating to the project. Data were collected from (a) reflective journals; (b) participant field notes – a pre-service teacher initiative; (c) surveys – a pre-service teacher initiative; (d) lesson reflections and digital recordings – a pre-service teacher initiative; and (e) interviews with participants. The findings are reported in terms of the major themes: boundary crossing, the philosophy of teaching, and professional relationships The findings have implications for teacher education. The researchers feel that deliberate planning for networking between activity systems may well be a solution to the apparent theory/practice gap. Proximity of activity systems need not be a hindering issue.