Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Professional modellers’ conceptions of the notion of mathematical modelling : Ideas for education

The notion of mathematical modelling has multiple interpretations in research literature and has been included in curriculum documents in various ways. This study presents a thematic analysis of nine professional modellers’ conceptions of the notion of mathematical modelling, representing scholarly knowledge. The result is organised according to four main aspects of modelling, that is description, understanding, abstraction and negotiation, representing key features of mathematical models and how people are affected by, or engage in, modelling work. The paper concludes with a discussion of some potential benefits for mathematics education that might be drawn from the study from the perspective of the ‘gap’ between mathematical modelling in educational and non-educational contexts, in terms of curriculum design and teaching practice

Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art

The teaching and learning of mathematical modelling is an important research field all over the world. In this paper we present a survey of the state-of-the-art on empirical studies in this field. We analyse the development of studies focusing on cognitive aspects of the promotion of modelling, i.e. the promotion of modelling abilities resp. skills, or in newer terminology, modelling competencies. Furthermore, we provide a literature search on the role of empirical research in important mathematics education journals and point out that this topic is only seldom treated in these journals. In addition, Proceedings of the conference series on the teaching and learning of mathematical modelling and applications were analysed in order to identify the role of empirical research in this important series and the kind of topics which are examined. The literature research points out the dominance of case study approaches and cognitively oriented studies compared to studies which used quantitative research methods or focused on affect-related issues. Finally, the papers in this special issue are described and developments and future prospects are identified

Reaction and strain engineering for improved stereo-selective whole-cell reduction of a bicyclic diketone

Reduction of bicyclo[2.2.2]octane-2,6-dione to (1R, 4S, 6S)-6-hydroxy-bicyclo[2.2.2]octane-2-one by whole cells of Saccharomyces cerevisiae was improved using an engineered recombinant strain and process design. The substrate inhibition followed a Han-Levenspiel model showing an effective concentration window between 12 and 22 g/l, in which the activity was kept above 95%. Yeast growth stage, substrate concentration and a stable pH were shown to be important parameters for effective conversion. The over-expression of the reductase gene YDR368w significantly improved diastereoselectivity compared to previously reported results. Using strain TMB4110 expressing YDR368w in batch reduction with pH control, complete conversion of 40 g/l (290 mM) substrate was achieved with 97% diastereomeric excess (de) and >99 enantiomeric excess (ee), allowing isolation of the optically pure ketoalcohol in 84% yield