Many institutions have adopted a variety of Learning Management Systems (LMS) as platforms for e-learning implementation. However, the design and nature of LMS technologies present challenges to design of LMS based activities that engage students in learning to do mathematics. There are no clear guidelines or strategies for the design of LMS based activities that engage students in complex mathematical processes. Hence the use of LMS technologies in mathematics education often results in instructivist practices. Conversely, the use of constructivist principles (C), modes of mathematical engagement (E) and e-learning tools (T) to mediate learning provides an integrated, CEM, framework to transform not only the use of LMS as platform for e-learning implementation but also promote engaged mathematical learning. The objective of this study was to explore ways that CEM based strategies could be useful for conceiving activities to support the learning of Mathematics using a LMS hosted tutorial. The design, redesign and evaluation of a LMS hosted tutorial is reported upon. In preparation for the study, an LMS based tutorial was designed and developed to be used as a test-bed to investigate how these e-learning tools could be to support learning to do mathematics. A Trigonometry module, consisting of course content in the form of resources and tasks to help the students to explore, practice and apply right triangle concepts, was used to investigate and to derive design strategies. A qualitative research approach with a reflexive self-study research design was used. A group of first year university student volunteers, studying mathematics for mechanical engineering department were used to test the tutorial. The students were asked to do a series of tasks using the e-learning environment during the Mathematics tutorial period. Data was collected using screen capture software and the LMS. All students were encouraged to complete a learning journal detailing their experiences during the tutorial, using an LMS based tool. The students were given no training but a tutor (researcher) was available to answer any questions they may have had. Contradiction analysis was used to evaluate the data, to compare purpose and practice and to judge whether the activity or tool was fit for the intended purpose. The results of the first phase indicated a number of challenges encountered by the students. In order to adapt and further develop design strategies for the second phase, design objectives were derived from the challenges encountered in the first phase. These design strategies and objectives were then used to adapt the tutorial for the second phase of the research The results emerging from both phases suggest the efficacy of the following design principles: The LMS hosted tutorial should be exploratory in nature and not instructive. Activities should be used to create a demand for knowledge and multimedia resources should provide corresponding reference content. Activities should incorporate quizlets (built using quiz software) that yield immediate and elaborated feedback that provides guidance as the student answers the questions. Activities should allow multiple attempts to enable students to review resources and try again. The provision of partial credit for activities should be made possible by using fill in multiple blanks question types. A number of students did struggle with using the e-learning tools and a number of strategies were implemented in order to address this problem: The tutor provided assistance (blending) especially in how to get started. Also, extensive troubleshooting help was provided to help them along the way. Students were also allowed to work through the assigned activities in pairs. In addition, the design strategy of including examples of model answers to the questions (format) at the start of tasks seemed to improve the accessibility of the e-learning tool.
