Audit of mathematics learning support in Ireland in 2015 – the key findings

In 2015 the Irish Mathematics Learning Support Network (IMLSN) commissioned a comprehensive audit of the extent and nature of mathematics learning support (MLS) provision on the island of Ireland. An online survey was sent to 32 institutions, including universities, institutes of technology, further education and teacher training colleges, and a 97% response rate was achieved. While the headline figure – 84% of institutions that responded to the survey provide MLS – sounds good, deeper analysis reveals that the true state of MLS is not so solid. For example, in 25% of institutions offering MLS, only five hours per week (at most) of physical MLS are available, while in 20% of institutions the service is provided by only one or two staff members. Furthermore, training of tutors is minimal or non-existent in at least half of the institutions offering MLS. The results provide an illuminating picture, however, identifying the true state of MLS in Ireland is beneficial only if it informs developments in the years ahead. This talk will present some of the findings of the survey in more depth along with conclusions and recommendations. Key among these is the need for institutions to recognise MLS as a vital element of mathematics teaching and learning strategy at third level and devote the necessary resources to facilitate the provision of a service which can grow and adapt to meet student requirements.

Mathematics background of engineering students in Northern Ireland and Finland

The Organisation for Economic Co-operation and Development investigated numeracy proficiency among adults of working age in 23 countries across the world. Finland had the highest mean numeracy proficiency for people in the 16 – 24 age group while Northern Ireland’s score was below the mean for all the countries. An international collaboration has been undertaken to investigate the prevalence of mathematics within the secondary education systems in Northern Ireland and Finland, to highlight particular issues associated with transition into university and consider whether aspects of the Finnish experience are applicable elsewhere. In both Northern Ireland and Finland, at age 16, about half of school students continue into upper secondary level following their compulsory education. The upper secondary curriculum in Northern Ireland involves a focus on three subjects while Finnish students study a very wide range of subjects with about two-thirds of the courses being compulsory. The number of compulsory courses in maths is proportionally large; this means that all upper secondary pupils in Finland (about 55% of the population) follow a curriculum which has a formal maths content of 8%, at the very minimum. In contrast, recent data have indicated that only about 13% of Northern Ireland school leavers studied mathematics in upper secondary school. The compulsory courses of the advanced maths syllabus in Finland are largely composed of pure maths with a small amount of statistics but no mechanics. They lack some topics (for example, in advanced calculus and numerical methods for integration) which are core in Northern Ireland. This is not surprising given the much broader curriculum within upper secondary education in Finland. In both countries, there is a wide variation in the mathematical skills of school leavers. However, given the prevalence of maths within upper secondary education in Finland, it is to be expected that young adults in that country demonstrate high numeracy proficiency.

Maximal C*-algebras of quotients and injective envelopes of C*-algebras

A new C*-enlargement of a C*-algebra A nested between the local multiplier algebra of A and its injective envelope is introduced. Various aspects of this maximal C*-algebra of quotients are studied, notably in the setting of AW*-algebras. As a by-product we obtain a new example of a type I C*-algebra such that its second iterated local multiplier algebra is strictly larger than its local multiplier algebra.

Jordan isomorphism of purely infinite C*-algebras

We prove that every unital bounded linear mapping from a unital purely infinite C*-algebra of real rank zero into a unital Banach algebra which preserves elements of square zero is a Jordan homomorphism. This entails a description of unital surjective spectral isometries as the Jordan isomorphisms in this setting.