In order to deliver high-quality learning and teaching, the Open University (OU) has adopted an approach to developing its curriculum called OU Learning Design, which supports a consistent and structured design, specification and review process. It provides a simple set of tools and resources to assist teams in choosing and integrating an effective range of media and technologies, defining their pedagogic approach, and sharing good practice across the institution (Subotzky and Prinsloo 2011). The objective of this study was to apply OU Learning Design tools in the context of the largest distance education university in Africa (Unisa) to identify areas that could be changed in order to improve student outcomes and retention. Two Unisa first-level mathematics modules were evaluated and mapped using OU Learning Design approaches and tools to identify areas for improvement. Qualitative and quantitative data on students' educational experience in these modules and longitudinal academic progress data were used to better understand the challenges students are facing on those courses. The process uncovered areas where improvements need to be made and among the core recommendations were improvement of workload distribution across both modules, the timing of the examination period, and a greater variety of learning activities. These reflections will be used Greyling, Huntley, Reedy and Rotagen Improving distance learning mathematics modules 90 to inform the next "Plan" stage of the Action Research spiral.

Curriculum mapping is a common practice amongst test designers but not amongst teachers. As part of the Data Informed Practice Improvement Project’s (DIPIP) attempt to de-fetishise accountability assessment, teachers were tasked to investigate the alignment of a large-scale assessment with the South African mathematics curriculum. About 50 mathematics teachers from Grade 3–9 worked in groups together with subject facilitators from the Gauteng Department of Education and a university postgraduate student or lecturer who acted as group leader. The first project activity, curriculum mapping, provided a professional development opportunity in which groups mapped mathematical assessment items to the assessment standards of the curriculum. The items were taken from three sources: the 2006 and 2007 International Competitions and Assessments for Schools tests and from ‘own tests’ developed by the groups in the last term of the project. Groups were required to analyse the knowledge base underlying test items and to reflect on what they teach in relation to what the curriculum intends them to teach. They used a protocol (mapping template) to record their responses. This article deals with the question of how to transform data collected from large- scale learner assessments into structured learning opportunities for teachers. The findings were that through the curriculum mapping activity, groups became more aware of what is intended by the curriculum and how this differs from what is enacted in their classes. The findings were also that the capacity of groups to align content was better when they worked with leaders and that with more experience they gained confidence in mapping test items against the curriculum and made better judgments in relation to curriculum alignment. Involving teachers in the interpretation of both public assessment data and data from their own classroom activities can build their own understanding of the knowledge base of test items and of the curriculum.

In this study we propose a taxonomy for assessment in mathematics, which we call the assessment component taxonomy, to identify those components of mathematics that can be successfully assessed using alternative assessment formats. Based on the literature on assessment models and taxonomies in mathematics, this taxonomy consists of seven mathematics assessment components, hierarchically ordered by cognitive level, as well as the nature of the mathematical tasks associated with each component. Using a model that we developed earlier for measuring the quality of mathematics test items, we investigate which of the assessment components can be successfully assessed in the provided response question (PRQ) format, in particular multiple choice questions (MCQs), and which can be better assessed in the constructed response question (CRQ) format. The results of this study show that MCQs can be constructed to evaluate higher order levels of thinking and learning. The conclusion is that MCQs can be successfully used as an assessment format in undergraduate mathematics, more so in some assessment components than in others. The inclusion of the PRQ assessment format in all seven assessment components can reduce the large marking loads, associated with continuous assessment practices in undergraduate mathematics, without compromising the validity of the assessment.

This paper explores and promotes the notion of ‘procept’ in an undergraduate mathematics course in Linear Algebra for first year pure and engineering students. On the basis of students’ preference for procedural to conceptual solutions to mathematical problems, this paper augments the role of certain concepts in pure and applied mathematics, particularly in the problem‐solving approaches at the undergraduate level by providing novel solutions to problems solved in the usual traditional manner. The development of the concept of ‘procept’ and its applicability to mathematics teaching and learning is important to mathematics education research and tertiary pure and applied mathematics didactics in South Africa, welcoming the amalgamation of the theories developed at pre‐tertiary level mathematics with theorems and proof at the undergraduate level