Future teachers’ professional knowledge on argumentation and proof: a case study from universities in three countries

In this paper, qualitative results of a case study about the professional knowledge in the area of argumentation and proof of future teachers from universities in three countries are described. Based on results of open questionnaires, data about the competencies these future teachers have in the areas of mathematical knowledge and knowledge of mathematics pedagogy are presented. The study shows that the majority of the future teachers at the participating universities situated in Germany, Hong Kong and Australia, were not able to execute formal proofs, requiring only lower secondary mathematical content, in an adequate and mathematically correct way. In contrast, in all samples there was evidence of at least average competencies of pedagogical content reflection about formal and pre-formal proving in mathematics teaching. However, it appears that possessing a mathematical background as mandated for teaching and having a high affinity with proving in mathematics teaching at the lower secondary level are not a sufficient preparation for teaching proof.     

Electrochemical Kinetic Characterization of Redox Mediated Glucose Oxidase Reactions: A Simplified Approach

One of the main drawbacks affecting first‐generation electrochemical biosensors in the analysis of real matrices is the interference of electroactive species present in the sample under investigation. Several approaches have been attempted to overcome this problem in the past ten years but the best results were achieved by using mediated based electrochemical biosensors. Despite this, the kinetic of the redox mediators‐enzymatic proteins interaction has not been studied deeply enough. In this work we have developed a theoretical‐methodological approach for the characterization of the kinetic of interaction between redox enzymes and substrates and/or redox mediators. Particularly, the interaction of glucose oxidase (GOx) with several commercially available redox mediators has been studied by means of amperometry and cyclic voltammetry. The main kinetic parameters for different mediators were exploited and discussed with the aim of finding the best mediator for a glucose biosensor to be used on real samples.     

Increasing engineering students' awareness to environment through innovative teaching of mathematical modelling

This article presents the results of two studies on using aninnovative pedagogical strategy in teaching mathematical modellingand applications to engineering students. Both studies are dealingwith introducing non-traditional contexts for engineering studentsin teaching/learning of mathematical modelling and applications:environment and ecology. The aims of using these contexts were:to introduce students to some of the techniques, methodologiesand principles of mathematical modelling for ecological andenvironmental systems; to involve the students in solving real-lifeproblems adjusted to their region emphasizing the aspects ofboth survival (short term) and sustainability (long term); toencourage students to pay attention to environmental issues.On one hand, the contexts are not directly related to engineering.On the other hand, the chances are that many graduates of engineeringwill deal with mathematical modelling of environmental systemsin one way or another in their future work because nearly everyengineering activity has an impact on the environment. The firststudy is a parallel study conducted in New Zealand and Germanysimultaneously with first-year students studying engineeringmathematics. The second study is a case study of the experimentalcourse Mathematical Modelling of Survival and Sustainabilitytaught to a mixture of year 2–5 engineering students inGermany by a visiting lecturer from New Zealand. The modelsused with the students from both studies had several specialfeatures. Analysis of students’ responses to questionnaires,their comments and attitudes towards the innovative approachin teaching are presented in the article.     

Synthesis of 5-trichloromethyl-Δ-1,2,4-oxadiazolines and their rearrangement into formamidine derivatives

A series of 5-trichloro-Δ⁴-1,2,4-oxadiazolines have been synthesised by 1,3-dipolar cycloaddition of nitrones to trichloroacetonitrile. These oxadiazolines rearrange into formamidine derivatives, via ring opening and a 1,2-aryl shift from carbon to the adjacent amino nitrogen. Both cycloaddition and rearrangement are facilitated when electron deficient nitriles and electron rich nitrones are used.     

A novel and efficient method for the catalytic direct oxidative carbonylation of 1,2- and 1,3-diols to 5-membered and 6-membered cyclic carbonates

In the presence of a PdI₂-based catalytic system, 1,2-diols undergo an oxidative carbonylation process to afford 5-membered cyclic carbonates in good to excellent yields (84-94%) and with unprecedented catalytic efficiencies for this kind of reaction (up to ca. 190 mol of product per mol of PdI₂). Under similar conditions, 6-membered cyclic carbonates are obtained for the first time through a direct catalytic oxidative carbonylation of 1,3-diols (66-74% yields).     

pePC-SAFT: Modeling of polyelectrolyte systems: 1. Vapor–liquid equilibria

A molecular thermodynamic model for polyelectrolyte systems—called pePC-SAFT—is proposed. The effect of charged monomers within the polyelectrolyte chain is explicitly taken into account in the reference term by replacing the hard-chain contribution of the PC-SAFT model by a charged-hard-chain contribution. Moreover, counterion condensation is accounted for to determine the effective number of charges along the polyion as well as of free counterions. The electrostatic contribution of the free counterions is described by a Debye–Hückel term.     

Preparation of imine complexes of ruthenium and osmium stabilised by [MCl(η -p-cymene)(PR3)] fragments

Imine complexes [MCl(η ⁶-p-cymene){η¹-NHC(H)Ar}(PR₃)]BPh₄ (1-3) [M = Ru, Os; PR₃ = PPh(OEt)₂, PPh₂OEt; Ar = Ph, p-tolyl] were prepared by reacting MCl₂(η ⁶-p-cymene)(PR₃) precursors with benzyl azide ArCH₂N₃ in the presence of NaBPh₄. Benzophenone-imine complexes [MCl(η ⁶-p-cymene){η¹-NHCPh₂}(PR₃)]BPh₄ (4-6) [M = Ru, Os; PR₃ = PPh(OEt)₂, PPh₂OEt] were also prepared by allowing MCl₂(η ⁶-p-cymene)(PR₃) to react with Ph₂CNH in the presence of NaBPh₄. The complexes were characterised spectroscopically (IR, ¹H, ¹³C, ³¹P, ¹⁵N NMR) and by X-ray crystal structure determination of [RuCl(η ⁶-p-cymene){η¹-NHC(H)-p-tolyl}{PPh(OEt)₂}]BPh₄ (1b).     

Laccase–polyazetidine prepolymer–MWCNT integrated system: Biochemical properties and application to analytical determinations in real samples

Bioelectrochemical properties of Trametes versicolor Laccase (TvL) and Trametes hirsuta Laccase (ThL) immobilized by using polyazetidine prepolymer (PAP) onto multi-walled carbon nanotubes (MWCNTs) screen printed electrode (SPE) surface, have been studied with several redox mediators by cyclic voltammetry (CV). The efficient entrapment of laccase in the PAP layer was confirmed by determination of both kinetic parameters (maximum current and Michaelis–Menten apparent constant) and analytical performances by chronoamperometry. The Laccase-modified MWCNTs electrode provides an effective biosensor for determination of polyphenols and catecholamines in real matrices; performances of the considered biosensors for real samples analysis are also compared and discussed.