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.

Program Annotations: Feedback for Students Learning to Program

This paper presents a novel program annotation mechanism which enables students to obtain feedback from tutors on their programs in a far simpler and more efficient way than is possible with, for example, email. A common scenario with beginning students is to email tutors with copies of their malfunctioning programs. Unfortunately the emailed program often bears little resemblance to the program the student has been trying to make work; often it is incomplete, a different version and corrupted. We propose an annotation mechanism enabling students to simply and easily annotate their programs with comments asking for help. Similarly our mechanism enables tutors to view students’ programs and to reply to their comments in a simple and structured fashion. This means students can get frequent and timely feedback on their programs; tutors can provide such feedback efficiently, and hence students’ learning is greatly improved.