Beliefs and beyond: hows and whys in the teaching of proof

In this paper, we report on a study aimed at describing the way secondary school teachers treat proof and at understanding which factors may influence such a treatment. This study is part of a wider project on proof carried out for many years. In our theoretical framework, we combine references from research on proof with those from research on teachers in relation to their beliefs. The study was carried out through interviews with secondary school teachers aimed at learning how they describe their work with proof in the classroom, and to elicit beliefs and other factors that shape this work. Through the interviews we were able to detect reasons behind teachers’ choices in planning their work in the classroom. In the present paper, we concentrate on four cases that, among other factors, offer elements suitable to unravel the problem of inconsistencies using the construct of leading beliefs, i.e., beliefs (whose nature may vary from teacher to teacher) that seem to drive the way each teacher treats proof.     

New chiral P-N ligands for the regio- and stereoselective Pd-catalyzed dimerization of styrene

Two new chiral, enantiomerically pure, hybrid P-N ligands, namely (2R,5S)-2-phenyl-3-(2-pyridyl)-1,3-diaza-2-phosphanicyclo[3,3,0]octan-4-one (1) and (2R,5S)-2-phenyl-3-(2-pyridyl)-1,3-diaza-2-phosphanicyclo[3,3,0]octane (2), have been synthesized starting from L-proline. The two ligands differ in the presence or not of a carbonyl group in the diazaphosphane ring. Their coordination chemistry towards Pd(II) was studied by reacting them with [Pd(CH?)Cl(cod)]. A different behaviour was observed: ligand 2 shows the expected bidentate chelating behaviour leading to the mononuclear Pd-complex, while ligand 1 acts as a terdentate ligand giving a dinuclear species. The corresponding cationic derivatives were obtained from the palladium neutral complexes, both as mono- and dinuclear derivatives, and tested as precatalysts for styrene dimerization, yielding E-1,3-diphenyl-1-butene regio- and stereoselectively as the sole product. A detailed analysis of the catalytic behaviour is reported.     

Organometallic Compounds of Zinc as Selective Nucleophilic Reagents in Organic Synthesis

The ability of the Reformatsky reagent BrZnCH₂CO₂ ^tBu 1 to undergo substitution reactions has been verified with several substituted bromides.     

Microwave assisted digestion of atmospheric aerosol samples followed by inductively coupled plasma mass spectrometry determination of trace elements

A microwave digestion method in a closed vessel was developed for the determination of trace metals in atmospheric aerosols using inductively coupled plasma mass spectrometry (ICP-MS). A recovery study for the elements V, Cr, Mn, Fe, Co, Ni, Cu, Zn, As, Se, Cd, Sb, and Pb was conducted using multi-elemental standard solutions, NIST 1633b Trace Elements in Coal Fly Ash, and NIST 1648 Urban Particulate Matter. A simple digestion method using only HNO₃/H₂O₂ gave good recoveries (90%–108%) for all elements except Cr in SRM 1648, but yielded low recoveries for SRM 1633b. A more robust method using HNO₃/H₂O₂/HF/H₃BO₃ yielded higher recoveries (82%–¶103%) for the lighter elements (V – Zn) in SRM 1633b, and improved the Cr recovery in SRM 1648, but decreased the Se recovery in both SRMs. A comparative analysis of aerosol samples obtained at a remote mountain location Nathiagali, Pakistan (2.5 km above mean sea level), and Mayville, New York, downwind from the highly industrialized Midwestern United States, was carried out using Instrumental Neutron Activation Analysis (INAA) for the elements Cr, Mn, Fe, Co, Zn, As, Se, and Sb. The simple digestion method yielded excellent agreement for Cr, Fe, Zn, As, Se, and Sb, with slopes of the ICP-MS vs. INAA regressions of 0.90–1.00 and R² values of 0.96–1.00. The regressions for Mn and Co had slopes of 0.82 and 0.84 with R² values of 0.83 and 0.82, respectively. Addition of HF/H₃BO₃ did not improve the correlation for any of the elements and degraded the precision somewhat. The technique provides sensitivity and accuracy for trace elements in relatively small aerosol samples used in atmospheric chemistry studies related to SO₂ oxidation in cloud droplets. The ability to determine concentrations of a very large number of elements from a single analysis will permit source apportionment of various trace pollutants and hence strategies to control the sources of air pollution. This is particularly important as the health effects of particulate matter are increasingly recognized.     

Direct determination of the ethanol metabolites ethyl glucuronide and ethyl sulfate in urine by liquid chromatography/electrospray tandem mass spectrometry

A liquid chromatography/electrospray tandem mass spectrometry (LC/ESI-MS/MS) method for the determination in urine samples of two ethanol metabolites, ethyl glucuronide (EtG) and ethyl sulfate (EtS), was developed and validated. Pentadeuterated EtG was used as internal standard for both EtG and EtS. In addition to the surviving ions, two MS/MS reactions were monitored for each analyte, with the deprotonated molecule as precursor ion: m/z 221 --> 75, m/z 221 --> 85 (EtG), and m/z 125 --> 97, m/z 125 --> 80 (EtS). Sample pretreatment, though very simple and rapid (1:50 water dilution and centrifugation of 50 muL of urine), was found to contain the occurrence of matrix effects. The method was accurate and precise over the linear dynamic range (0.05-10 mg/L). The analytes were stable in frozen urine for at least 1 month. The assay was applied to several authentic urine samples from social drinkers and to alcoholic beverages.     

Efficient DNA Extraction and Amplification of Samples from the Archeological Site of Pompei (Italy)

Due to their growth and metabolism, microorganisms can cause severe damage to Cultural Heritage, through mechanical and chemical processes. In this paper we used molecular approaches to study bacterial communities on samples from the archeological site of Pompei (Italy). In particular four DNA extraction methods without prior cultivation of the microflora were compared. In terms of efficiency, the DNA extraction method based on the Tri-Reagent™ kit gave the best results. All extraction protocols coupled with 16S rDNA fragments PCR amplification were satisfactory; but the best results were obtained by Klentaq DNA LA Polymerase™; this enzyme can be considered an effective tool for amplification of DNA from Cultural Heritage and possibly other environmental samples.     

Polymeric nanoparticles based on polylactide and related copolymers

The preparation of nanoparticle suspensions was carried out by using commercial biodegradable polymers as poly(d,l-lactide), poly(d,l-lactide-co-glycolide) and poly(d,l-lactide-co-ϵ-caprolactone). The method of preparation was based on the controlled addition of polymer organic solution to an aqueous phase containing dispersing agents. Poly(ethylene glycol) (10, 20, and 35 kDa grade), Tween 20, and Pluronic F-127 were used as dispersing agents in the aqueous phase. Content and type of both polymeric matrix and dispersing agent resulted of paramount relevance for the attainment of monodispersed nanoparticles with average diameter of about 130 nm. The addition of a steric stabilizer allowed for nanoparticle purification and isolation while preventing their agglomeration. The best results were obtained by using 35 kDa grade poly(ethylene glycol) as dispersing agent and either mannitol or glycidylisopropylidenglyceryl-β-cyclo-dextrin as steric stabilizer. The adopted procedure afforded biodegradable nanoparticle suspensions that could be used for the incapsulation and intravenous administration of biologically active proteins and oligopeptides.