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 impact of organisational culture on ERP systems implementation : lessons from Jordan

Jordan is adopting Enterprise Resource Planning (ERP) systems in both its public and private sectors. Jordan's emerging private sector has historically close ties to the public sector; though a global market orientation requires a shift in its organisational culture. ERPs however embed business processes which do not necessarily fit with traditional cultural practices, and implementation success is not assured. This study looks at the perceptions of both public and private sector ERP implementations in Jordan and assesses these on various measures of success. There were few differences between public and private sectors, but the benefits actually realised in Jordanian ERPs fell short of claims made for the technology in other cultures.

A hiccup or a rift? ERP implementation success in Jordan

Like many other developing countries, Jordan is adopting Enterprise Resource Planning (ERP) systems in both its public and private sectors. Jordan's emerging private sector has historically close ties to the public sector, though a global market orientation requires a shift in its organisational culture. ERPs however embed business processes which do not necessarily fit with traditional cultural practices, and implementation success is not assured.. This study looks at the perceptions of both public and private sector ERP implementations in Jordan and assesses these on various measures of success. There were few differences between public and private sectors, but the benefits actually realized in Jordanian ERPs fell short of claims made for the technology in other cultures. Considerable customisation was required in both sectors, and the traditional style of management in Jordan did not fit well with the requirements for successful implementation. This is consistent with recent studies from various countries that show cultural fit is a particularly neglected factor in assessing ERP success.

ERP systems implementation and organizational culture : the case of Jordan

Jordan is adopting Enterprise Resource Planning (ERP) systems in both its public and private sectors. Jordan's emerging private sector has historically close ties to the public sector; though a global market orientation requires a shift in its organizational culture. ERPs however embed business processes which do not necessarily fit with traditional cultural practices, and implementation success is not assured. This study looks at the perceptions of both public and private sector ERP implementations in Jordan and assesses these on various measures of success. There were few differences between public and private sectors, but the benefits actually realized in Jordanian ERPs fell short of claims made for the technology in other cultures.

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.

Learning the kernel matrix with semidefinite programming

Kernel-based learning algorithms work by embedding the data into a Euclidean space, and then searching for linear relations among the embedded data points. The embedding is performed implicitly, by specifying the inner products between each pair of points in the embedding space. This information is contained in the so-called kernel matrix, a symmetric and positive semidefinite matrix that encodes the relative positions of all points. Specifying this matrix amounts to specifying the geometry of the embedding space and inducing a notion of similarity in the input space - classical model selection problems in machine learning. In this paper we show how the kernel matrix can be learned from data via semidefinite programming (SDP) techniques. When applied to a kernel matrix associated with both training and test data this gives a powerful transductive algorithm -using the labeled part of the data one can learn an embedding also for the unlabeled part. The similarity between test points is inferred from training points and their labels. Importantly, these learning problems are convex, so we obtain a method for learning both the model class and the function without local minima. Furthermore, this approach leads directly to a convex method for learning the 2-norm soft margin parameter in support vector machines, solving an important open problem.