How well prepared are the teachers of tomorrow? An examination of prospective mathematics teachers' pedagogical content knowledge

There is a growing emphasis in the teaching profession on pedagogical content knowledge (PCK) as an important knowledge component. The study reported in this article investigates Turkish prospective mathematics teachers’ mathematics teaching knowledge in the numbers content domain. A series of 10 open-ended scenario-type questions were adopted to challenge 83 prospective mathematics teachers’ knowledge of the learner and presentation of content in the context of PCK. The participants’ responses were analysed by means of rubrics and scoring guides developed by the researchers. The results showed that many of the future teachers performed well in determining what misconceptions students might express in the given scenarios. However, a majority of the participants performed poorly on presentation of content in terms of instructional strategies. In line with these results, the authors offer some suggestions for teacher training programmes.     

A Novel Label-Free Immunosensor Based on Electrochemically Reduced Graphene Oxide for Determination of Hemoglobin A1c

Russian Journal of Electrochemistry - In this work, a novel immunosensor has been developed using an electrochemically reduced graphene oxide (ERGO) modified glassy carbon electrode (GCE) for...     

Development of All‐solid‐state Antidiabetic Drug Metformin‐selective Microsensor and its Electrochemical Applications

In this study, all‐solid‐state type potentiometric PVC membrane selective microsensor was developed for Metformin (MET) which is an antidiabetic drug active substance. Metformin‐tetraphenylborate (MET‐TPB) ion‐pair was used as an ionophore in the structure of the sensor membrane. It was determined that the sensor membrane at the ratio of 69 % o‐nitrophenyl octyl ether, 27 % polyvinyl chloride and 4 % MET‐TPB performed the best potentiometric performance. In a wide concentration range (1×10^?5–1×10^?1 mol/L), the slope, detection limit, response time, pH range, and life‐time of the sensor were determined as 55.9±1.6 mV (R²=0.996), 3.35×10^?6 mol/L, 8–10 s, pH: 3–8, and ～10 weeks, respectively. The voltammetric performances of the sensor were also investigated. The prepared microsensor was successfully utilized for the determination of Metformin in a pharmaceutical drug sample by potentiometry and voltammetry. It was observed that the obtained results were in agreement with the results obtained by the UV spectroscopy method at 95 % confidence level.     

A heat transfer problem with exponential memory and the associated thermal stresses

In this study, a heat transfer problem defined by the Caputo–Fabrizio derivative, which is known to behave by the exponential decaying law, is addressed in an axially symmetric cylindrical region. Thus, the fundamental solutions of the heat diffusion process and the associated thermal stresses are aimed to find. For this purpose, Laplace and finite Hankel integral transforms are applied according to the geometry of the region. To obtain the thermal stresses, constitutive relations of the classical thermoelasticity theory are used. The effects of fractional orders on the diffusion process are illustrated graphically using MATLAB.     

Representations of Clifford Algebras on Function Spaces on the Cantor Set

We give a representation of the (infinite-dimensional) complex Clifford algebra on the Hilbert space of square-integrable complexvalued functions on the Cantor set.     

Solid-Phase Extraction and Spectrophotometric Determination of Trace Amounts of Mercury in Natural Samples

A sensitive and selective solid phase spectrophotometric method for the determination of trace amounts of inorganic mercury is described. Hg²⁺ was sorbed on a silica gel-packed column as an Hg²⁺–N,N-bis(2-mercaptophenyl)ethanediamide (H₂L) complex. The Hg²⁺ complex was eluted from the column using 7mL of acetone. Various parameters including pH, column flow rate, and ligand concentration were optimized. The complex was found to obey Beers law from 2.3 to 73.7µgmL^–1 within the optimum range when the preconcentration factor was two. The effective molar absorption coefficient at 523nm was 1.17×10³Lmol^–1cm^–1 at 523nm. The concentration limits in Beers law dropped from 0.09 to 2.95µgmL^–1 within the optimum range when the preconcentration factor was 50. The relative standard deviation at a concentration level of 5µgmL^–1 Hg²⁺ (9 repetitive determinations) was 1.6%. The detection limits are 0.34µgmL^–1 and 0.015µgmL^–1 when the preconcentration factors are 2 and 50, respectively. The method has been used for routine determination of trace levels of Hg²⁺ in natural waters. The potential application of this method for the removal of Hg²⁺ from natural samples (sea water and lake water) spiked with 100ngmL^–1 of Hg²⁺ was studied. In order to validate the proposed method, LGC 6156 (harbour sediment – extractable metals) was analysed by this method. The results proved that excellent extraction of Hg²⁺ from both natural water samples was obtained by solid phase extraction using N,N-bis(2-mercaptophenyl) ethanediamide.     

Determination of rare earth elements in seawater by inductively coupled plasma mass spectrometry with off-line column preconcentration using 2,6-diacetylpyridine functionalized Amberlite XAD-4

An off-line column preconcentration technique using a micro-column of 2,6 diacetylpyridine functionalized Amberlite XAD-4 with inductively coupled plasma mass spectrometry (ICP-MS) as a means of detection has been developed. The aim of the method was to determine rare earth elements (REEs) (La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) in seawater. Sample solutions (2–10 mL) were passed through the column which was then washed with ultra-pure water to remove residual matrix. The adsorbed cations on the resin were eluted by using 2 mL of 0.1 mol L⁻¹ HNO₃ containing 10 ng mL⁻¹ indium as an internal standard. The eluent was analyzed for the metal concentrations using ICP-MS. Sample pH as well as the sample and eluent flow rates were optimized. The sorption capacity of resin was determined by the batch process, by equilibrating 0.05 g of the resin with solutions of 50 mL of 25 mg L⁻¹ of individual metal ions for 4 h at pH 6.0 at 26 °C. The sorption capacities for the resin were found to range between 47.3 μmol g⁻¹ (for Lu) and 136.7 μmol g⁻¹ (for Gd). Limits of detection (3σ), without any preconcentration, ranged from 2 ng L⁻¹ to 10.3 ng L⁻¹ (for Tm and Lu respectively). The proposed method was applied to the determination of REEs in seawater and tap water samples.