Theories of mathematics education: European perspectives, commentaries and viable research directions

We briefly comment on different perspectives on (1) the role of mathematics education theories, (2) the issue of plurality and healthy heterogeneity versus consolidation; (3) underlying inquiry systems or the implicit role of philosophy in theories of mathematics education. This paper also outlines developments within the European research scene on theory usage in mathematics education research, which complement the discussion at the 29th PME research forum in Melbourne.     

Theory usage and theoretical trends in Europe: a survey and preliminary analysis of CERME4 research reports

The 29th PME research forum on theories included only one European perspective on mathematics education. In order to convey trends in theory usage in Europe we compile, survey and analyze a large subset of the research papers from the 4^th European Congress on Mathematics Education (CERME4). That is, this paper includes a discussion of trends seen within CERME4 reports¹ on theory usage by European researchers inseven of the fourteen working groups and (a) Outlines similarities and differences in theory usage and (b) takes a futuristic stance on ways in which researchers from different traditions could understand each other. Such an enterprise would further Hans-Georg Steiner's vision of bridging theoretical traditions which are independently formulated in different regions of the world.     

Coarse master equation from Bayesian analysis of replica molecular dynamics simulations

We use Bayesian inference to derive the rate coefficients of a coarse master equation from molecular dynamics simulations. Results from multiple short simulation trajectories are used to estimate propagators. A likelihood function constructed as a product of the propagators provides a posterior distribution of the free coefficients in the rate matrix determining the Markovian master equation. Extensions to non-Markovian dynamics are discussed, using the trajectory "paths" as observations. The Markovian approach is illustrated for the filling and emptying transitions of short carbon nanotubes dissolved in water. We show that accurate thermodynamic and kinetic properties, such as free energy surfaces and kinetic rate coefficients, can be computed from coarse master equations obtained through Bayesian inference.     

Characterization of cores of assignment games

We consider the assignment game of Shapley and Shubik (1972). We prove that the class of possible cores of such games (expressed in terms of payoffs for players on one side of the market) is exactly the same as a special class of polytopes, called 45-lattices. These results parallel similar work done by Conway (in Knuth, 1976) and Blair (1984) for marriage markets.Research supported by the Office of Naval Technology.     

Mediated action in teachers’ discussions about mathematics tasks

This paper presents analyses of teachers?? discussions within mathematics teaching developmental research projects, taking mediation as the central construct. The relations in the so-called ??didactic triangle?? form the basic framework for the analysis of two episodes in which upper secondary school teachers discuss and prepare tasks for classroom use. The analysis leads to the suggestion that the focus on tasks places an emphasis on the task as object and its resolution as goal; mathematics has the role of a mediating artefact. Subject content in the didactic triangle is thus displaced by the task and learning mathematics may be relegated to a subordinate position.     

Characterization of the Reaction of Chloroacetaldehyde with Single and Double Stranded DNA

Chloroacetaldehyde reacts with viral M13mp18 single and double stranded DNA to form the highly fluorescent adducts, etheno-AMP and etheno-CMP.

Absorbance and fluorescence spectroscopy can be used to monitor and characterize these reactions. Both single and double stranded DNA showed increases in the absorbance following reaction with the aldehyde. The fluorescence also increased in these two groups and continued to rise with increasing time of incubation until a point of saturation was reached. The fluorescence of the double stranded moiety was considerably enhanced following reaction with the aldehyde while that of the single stranded population was not, making this method appropriate for the separation of small quantities of the two populations of DNA.     

NaOH/Et3N-Promoted Stereoselective One-Pot Synthesis of α-Diazo Oxime Ethers via Diazo Transfer Reaction

For the first time, we have observed a combined effect of two bases NaOH/Et₃N to promote the diazo transfer reaction of β-oximino esters. This unusual synergistic effect has been employed to obtain α-diazo oxime ethers directly from β-keto esters by one-pot process. This method is simple and cost-effective and the reagents are readily available.