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 central role of communication in developing trust and its effect on employee involvement

Communication plays an important role in the development of trust within an organization. While a number of researchers have studied the relationship of trust and communication, little is known about the specific linkages among quality of information, quantity of information, openness, trust, and outcomes such as employee involvement. This study tests these relationships using communication audit data from 218 employees in the oil industry. Using mediation analysis and structural equation modeling, we found that quality of information predicted trust of one's coworkers and supervisors while adequacy of information predicted one's trust of top management. Trust of coworkers, supervisors, and top management influenced perceptions of organizational openness, which in turn influenced employees' ratings of their own level of involvement in the organization's goals. This study suggests that the relationship between communication and trust is complex, and that simple strategies focusing on either quality or quantity of information may be ineffective for dealing with all members in an organization.