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.     

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.     

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.     

The development of platinum-rhodium alloy coatings on SS304 using a pulse/direct electrodeposition technique and their application to antibacterial activity

The current research focused on the development of Platinum–Rhodium alloy coating (Pt– Rh) on SS304 and its applications in antibacterial studies. Electrodeposition is considered to be one of the most suitable methods because it enhances the therapeutic effects of noble metals (Pt–Rh alloy). The electrodeposited coating is an economical and time-saving alternative to existing coating methods. The newly developed Pt–Rh coating was investigated using a scanning electron microscope (SEM) and an atomic force microscope (AFM). Using the agar Petri plate and broth culture method, the antibacterial effect of the platinum-rhodium alloy was investigated against Gram-negative Escherichia coli and Gram-positive bacteria such as Staphylococcus saprophytes, Bacillus Subtilis, and Enterococcus faecalis. The Pt–Rh alloy coated samples obtained by Direct current (DC) and Pulse coating (PC 50% and PC 75%) were examined for antibacterial study. The PC 75% Pt–Rh alloy coating exhibits significant antibacterial activity, demonstrating a maximum zone of inhibition while leaving the rest of the coated samples by DC and PC 50% duty cycles. The study also found that when the concentration of Pt–Rh solution rises from 5 μL to 15 μL, so does the antibacterial activity. The findings of the study showed that electrodeposited platinum-rhodium alloy metal ions may be handy bacteriostatic in the coming years.     

Coarse nonlinear dynamics and metastability of filling-emptying transitions: water in carbon nanotubes

Using a coarse-grained molecular dynamics (CMD) approach we study the apparent nonlinear dynamics of water molecules filling or emptying carbon nanotubes as a function of system parameters. Different levels of the pore hydrophobicity give rise to tubes that are empty, water-filled, or fluctuate between these two long-lived metastable states. The corresponding coarse-grained free-energy surfaces and their hysteretic parameter dependence are explored by linking MD to continuum fixed point and bifurcation algorithms. The results are validated through equilibrium MD simulations.