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Teaching Mathematics and its Applications: An International Journal of the IMA Advance Access

Published: Thu, 26 Oct 2017 00:00:00 GMT

Last Build Date: Thu, 26 Oct 2017 06:50:50 GMT


The emergent models in linear algebra: an example with spanning set and span


A continuing challenge in mathematics education at the university level is how to create learning environments that give students the opportunity to progress from their informal ways of reasoning to more formal ways of reasoning. This article shows how the emergent models heuristic (Gravemeijer, 1999, Math. Think. Learn, 1, 155–177) provides this opportunity to first-year university students, specifically for them to construct the Linear Algebra concepts of spanning set and span. For this, a design-based research methodology was used. A hypothetical learning trajectory (HLT) was applied, created within the framework of this heuristic. The results provide evidence that the emergent models heuristic support the construction of these concepts of Linear Algebra. Moreover, useful tips are given for using this heuristic to construct mathematical concepts.

Community perspectives of mathematics and statistics support in higher education: building the infrastructure


Over the last two decades, mathematics support has, increasingly, been seen by higher education institutions as a vital mechanism for helping students enhance their mathematical and statistical skills, particularly as they make the transition to university study. Several studies have shown the growth of mathematics support across the higher education sector within the UK, Ireland and beyond. Others have demonstrated its impact upon learners. However, few have explored the extent to which mathematics support is embedded within institutions or the extent to which it is likely to be sustainable. Such analyses are important for both the institutions themselves and the many colleagues who are working to develop mathematics support into an area of study in its own right. Here, we report on a survey of 47 institutions offering mathematics and statistics support within the UK. Findings show that, within many institutions, mathematics support is now embedded as part of student-focused institutional support provision. Further, its impacts are increasingly extending beyond those students who access the support: there is evidence that mechanisms are in place for feeding findings from mathematics and statistics support into mainstream teaching and learning and curriculum development. Significantly, the analysis shows that mathematics support offers good potential for sustainability such that the legacy of national endeavours to establish it more widely will continue to exist into the future.