Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

Caterpillar Track Complexes in Template‐Directed Synthesis and Correlated Molecular Motion

Small alterations to the structure of a star‐shaped template totally change its mode of operation. The hexapyridyl template directs the conversion of a porphyrin dimer to the cyclic hexamer, but deleting one pyridine site changes the product to the cyclic decamer, while deleting two binding sites changes the product to the cyclic octamer. This surprising switch in selectivity is explained by the formation of 2:1 caterpillar track complexes, in which two template wheels bind inside the nanoring. Caterpillar track complexes can also be prepared by binding the hexapyridyl template inside the 8‐ and 10‐porphyrin nanorings. NMR exchange spectroscopy (EXSY) experiments show that these complexes exhibit correlated motion, in which the conrotatory rotation of the two template wheels is coupled to rotation of the nanoring track. In the case of the 10‐porphyrin system, the correlated motion can be locked by binding palladium(II) dichloride between the two templates.     

Biofunctionalization of Polyoxometalates with DNA Primers,Their Use in the Polymerase Chain Reaction (PCR) and Electrochemical Detection of PCR Products

The bioconjugation of polyoxometalates (POMs), which are inorganic metal oxido clusters, to DNA strands to obtain functional labeled DNA primers and their potential use in electrochemical detection have been investigated. Activated monooxoacylated polyoxotungstates [SiW₁₁O₃₉{Sn(CH₂)₂CO}]^8? and [P₂W₁₇O₆₁{Sn(CH₂)₂CO}]^6? have been used to link to a 5′‐NH₂ terminated 21‐mer DNA forward primer through amide coupling. The functionalized primer was characterized by using a battery of techniques, including electrophoresis, mass spectrometry, as well as IR and Raman spectroscopy. The functionality of the POM‐labeled primers was demonstrated through hybridization with a surface‐immobilized probe. Finally, the labeled primers were successfully used in the polymerase chain reaction (PCR) and the PCR products were characterized by using electrophoresis.     

Ultrafast delocalization of excitation in synthetic light-harvesting nanorings

Rings of chlorophyll molecules harvest sunlight remarkably efficiently during photosynthesis in purple bacteria. The key to their efficiency lies in their highly delocalized excited states that allow for ultrafast energy migration. Here we show that a family of synthetic nanorings mimic the ultrafast energy transfer and delocalization observed in nature. π-Conjugated nanorings with diameters of up to 10 nm, consisting of up to 24 porphyrin units, are found to exhibit excitation delocalization within the first 200 fs of light absorption. Transitions from the first singlet excited state of the circular nanorings are dipole-forbidden as a result of symmetry constraints, but these selection rules can be lifted through static and dynamic distortions of the rings. The increase in the radiative emission rate in the larger nanorings correlates with an increase in static disorder expected from Monte Carlo simulations. For highly symmetric rings, the radiative rate is found to increase with increasing temperature. Although this type of thermally activated superradiance has been theoretically predicted in circular chromophore arrays, it has not previously been observed in any natural or synthetic systems. As expected, the activation energy for emission increases when a nanoring is fixed in a circular conformation by coordination to a radial template. These nanorings offer extended chromophores with high excitation delocalization that is remarkably stable against thermally induced disorder. Such findings open new opportunities for exploring coherence effects in nanometer molecular rings and for implementing these biomimetic light-harvesters in man-made devices.     

Tuning the Photo-electrochemical Performance of RuII-Sensitized Two-Dimensional MoS2

Covalently tethering photosensitizers to catalytically active 1T-MoS₂ surfaces holds great promise for the solar-driven hydrogen evolution reaction (HER). Herein, we report the preparation of two new Ru^II-complex-functionalized MoS₂ hybrids [Ru^II(bpy)₂(phen)]-MoS₂ and [Ru^II(bpy)₂(py)Cl]-MoS₂. The influence of covalent functionalization of chemically exfoliated 1T-MoS₂ with coordinating ligands and Ru^II complexes on the HER activity and photo-electrochemical performance of this dye-sensitized system was studied systematically. We find that the photo-electrochemical performance of this Ru^II-complex-sensitized MoS₂ system is highly dependent on the surface extent of photosensitizers and the catalytic activity of functionalized MoS₂. The latter was strongly affected by the number and the kind of functional groups. Our results underline the tunability of the photovoltage generation in this dye-sensitized MoS₂ system by manipulation of the surface functionalities, which provides a practical guidance for smart design of future dye-sensitized MoS₂ hydrogen production devices towards improved the photofuel conversion efficiency.     

Reversible addition–fragmentation chain transfer polymerization of alkyl‐2‐cyanoacrylates: An assessment of livingness

Alkyl 2‐cyanoacrylates (CAs) are primarily used as instant adhesives, including those sold under the Loctite brand. The adhesive action can be inhibited with acid stabilizers allowing radical polymerization to be employed. The following article details the first attempted controlled/living radical polymerization of alkyl CAs: Reversible addition fragmentation chain transfer (RAFT) polymerization mediated by a poly(methyl methacrylate) dithiobenzoate macroRAFT agent for three different CA monomers (ethyl 2‐cyanoacrylate, n‐butyl 2‐cyanoacrylate, and 2‐phenylethyl cyanoacrylate) allowed the preparation of the first block copolymers of this challenging but commercially important monomer class. Nevertheless, GPC with UV detection indicated significant loss of the RAFT end‐group for all three CAs limiting control/living character. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1397–1408     

Facile Electrochemical Hydrogenation and Chlorination of Glassy Carbon to Produce Highly Reactive and Uniform Surfaces for Stable Anchoring of Thiolated Molecules

Carbon is a highly adaptable family of materials and is one of the most chemically stable materials known, providing a remarkable platform for the development of tunable molecular interfaces. Herein, we report a two‐step process for the electrochemical hydrogenation of glassy carbon followed by either chemical or electrochemical chlorination to provide a highly reactive surface for further functionalization. The carbon surface at each stage of the process is characterized by AFM, SEM, Raman, attenuated total reflectance (ATR) FTIR, X‐ray photoelectron spectroscopy (XPS), and electroanalytical techniques. Electrochemical chlorination of hydrogen‐terminated surfaces is achieved in just 5 min at room temperature with hydrochloric acid, and chemical chlorination is performed with phosphorus pentachloride at 50 °C over a three‐hour period. A more controlled and uniform surface is obtained using the electrochemical approach, as chemical chlorination is observed to damage the glassy carbon surface. A ferrocene‐labeled alkylthiol is used as a model system to demonstrate the genericity and potential application of the highly reactive chlorinated surface formed, and the methodology is optimized. This process is then applied to thiolated DNA, and the functionality of the immobilized DNA probe is demonstrated. XPS reveals the covalent bond formed to be a C?S bond. The thermal stability of the thiolated molecules anchored on the glassy carbon is evaluated, and is found to be far superior to that on gold surfaces. This is the first report on the electrochemical hydrogenation and electrochemical chlorination of a glassy carbon surface, and this facile process can be applied to the highly stable functionalization of carbon surfaces with a plethora of diverse molecules, finding widespread applications.     

Ion‐Transfer Electrochemistry of Rat Amylin at the Water–Organogel Microinterface Array and Its Selective Detection in a Protein Mixture

The behavior of proteins and polypeptides at electrified aqueous–organic interfaces is of benefit in label‐free detection strategies. In this work, rat amylin (or islet amyloid polypeptide) was studied at the interface formed between aqueous liquid and gelled organic phases. Amylin is a polypeptide that is co‐secreted with insulin from islet beta‐cells and is implicated in fibril formation. In this study, rat amylin was used, which does not undergo aggregation. The polypeptide underwent an interfacial transfer process, from water to the gelled organic phase, under applied potential stimulation. Cyclic voltammetry revealed steady‐state forward and peak‐shaped reverse voltammograms, which were consistent with diffusion‐controlled water‐to‐organic transfer and thin‐film stripping or desorptive back‐transfer. The diffusion‐controlled forward current was greater when amylin was present in an acidic aqueous phase than when it was present in an aqueous phase at physiological pH; this reflects the greater charge on the polypeptide under acidic conditions. The amylin transfer current was concentration dependent over the range 2–10 μM , at both acidic and physiological pH. At physiological pH, amylin was selectively detected in the presence of a protein mixture, which illustrated the bioanalytical possibilities for this electrochemical behavior.     

Electrochemical genosensor based on three-dimensional DNA polymer brushes monolayers

A new approach to the three dimensional integration of short DNA strands at gold electrode surfaces via the in situ formation of DNA-acrylamide conjugates is presented. Surface initiated atom transfer radical polymerisation was employed to grow acrylamide brushes co-polymerised in the presence of acrylamide modified DNA probes. This strategy was demonstrated for the realisation of biofunctionalised thin polymer films capable of binding its complementary 105-base DNA amplicon. The synthesised brushes were characterised using atomic force microscopy, attenuated total reflectance spectroscopy and electrochemical impedance spectroscopy. Once characterised, the polymer brushes were applied to the quantitative detection of target DNA using an enzyme labelled reporter DNA probe in a sandwich-type format.