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 effect of brand extensions on parent-brand relationship quality

A recognized brand name that provides a competitive advantage is considered one of a firm’s most valuable assets. Many firms have benefitted from their well-established brand name by adopting the strategy of brand extension (Aaker and Keller, 1990). Many academic studies have examined the methods used to introduce successful brand extensions, and analysed how consumers evaluate the brand extensions (Aaker and Keller, 1990; Barone, 2005; Bath, 1997; Bottomley and Holden, 2001; Edelman, 2003; Fedorikhin, Park and Thomson, 2008; Kwun, 2004; Lockhart and Ford, 2005). Some researchers have suggested that brand extension strategies may carry the risk of diluting important consumer trust in the parent brand (Martinez and Pina, 2003; C. W. Park, Milberg and Lawson, 1991). Furthermore, some studies have focused on the role of the parent brand in brand extensions (Apostolopoulou, 2002; Bath, 1997; Bhat and Reddy, 2001; Yeung and Wyer Jr, 2005). Brand extensions may have a positive or a negative influence on the parent brand, so it is important to understand the specific impact on dimensions such as brand image, brand awareness, and customer-brand relationships. This study will carry investigate the effects of brand extensions on the relationships customers have with the parent brand.

Sequential development of algebra knowledge : a cognitive analysis

Learning to operate algebraically is a complex process that is dependent upon extending arithmetic knowledge to the more complex concepts of algebra. Current research has shown a gap between arithmetic and algebraic knowledge and suggests a pre-algebraic level as a step between the two knowledge types. This paper examines arithmetic and algebraic knowledge from a cognitive perspective in an effort to determine what constitutes a pre-algebraic level of understanding. Results of a longitudinal study designed to investigate students' readiness for algebra are presented. Thirty-three students in Grades 7, 8, and 9 participated. A model for the transition from arithmetic to pre-algebra to algebra is proposed and students' understanding of relevant knowledge is discussed.

The Kinaesthetic Fusion Effect : mechanisms and extensions

This study investigated the Kinaesthetic Fusion Effect (KFE) that was first described by Craske and Kenny in 1981. It was reported that when, without vision, participants pressed a button that resulted in a probe simultaneously touching the contralateral limb at a displaced location, they perceived an apparent change in limb length. The current study did not fully replicate these earlier findings. Participants did not perceive any reduction in the sagittal separation of the button and probe following repeated exposure to the tactile stimuli that was present on both arms. However, a localised and partial medio-lateral fusion was observed, with the touched positions seeming closer together. In addition, tactile acuity was found to decrease progressively for distal positions of the upper limb and a foreshortening effect was found which may result from a line-of-sight judgment and represent a feature of the reporting method used. A number of years have elapsed since the description of the original KFE. Although frequently cited in the literature, there has been no further investigation into the mechanisms of action. The results of the current study are considered in light of more recent literature concerning intersensory integration. Future research should focus on further clarification for the specific conditions that must be present for a fusion effect to occur. Finally, this thesis will benefit future studies that require participants to report the perceived locations of the unseen limbs.