Problem Posing: A Neglected Component in Mathematics Courses for Prospective Elementary and Middle School Teachers

The purpose of this article is to describe a scheme which is designed to guide the prospective teacher beyond the point of proficiency as a student solving given problems. By experiencing several stages of inquiry, the scheme provides a mechanism where by the prospective teacher advances toward assuming the role of a teacher posing his or her own problems. Although the scheme has been developed within the context of a standard mathematics course for preservice teachers, the ideas set forth are equally appropriate for incorporation within a science course for prospective teachers.     

Problem Formulation: Insights from Student Generated Questions

This article describes an exploration of one facet of problem formulation. Prospective elementary and secondary teachers were presented with a mathematical situation consisting of data and conditions, but no questions were presented. They were asked to create questions that could be answered using the given information. In the spirit of exploration, this paper analyzes the student-formulated questions from two perspectives—the nature of the information contained within the questions posed and the responses which those questions elicited. A careful analysis of questions posed by students will enable education professionals to understand and promote better problem posing in mathematics classrooms.     

Calculating the Green's function for the Helmholtz equation by the method of the fifth parameter

Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 31, No. 12, pp. 1507–1512, December, 1988.     

Reactivity of the cadmium ion in concentrated phosphoric acid solutions

The solvation transfer coefficients which characterize the changes of ion reactivity with phosphoric acid concentration have been calculated for cadmium from the constants of the successive chloride complexes, and for silver and diethyldithiophosphate from potentiometric measurements. They evidence the strong desolvation of the cadmium species in concentrated phosphoric acid media, causing a remarkable increase of its reactivity. They allow the results of liquid-liquid extraction, precipitation and flotation reactions to be correctly interpreted and their changes to be foreseen when the reagents are modified.     

Confirmation of avermectin residues in food matrices with negative-ion atmospheric pressure chemical ionization liquid chromatography/mass spectrometry

A multi-residue LC/MS method has been developed to confirm avermectin drug residues in several food matrices. Ivermectin (IVR), doramectin (DOR), eprinomectin (EPR) and moxidectin (MOX) are confirmed using atmospheric pressure chemical ionization (APCI) with negative ion detection and selected ion monitoring of three to four ions for each compound. The drug residues are extracted from tissue or milk using previously published procedures. IVR and DOR are confirmed at 20 ppb levels in fortified salmon muscle; IVR is also confirmed in tissue from salmon dosed with the drug. Residues of DOR, IVR, and EPR are confirmed in fortified milk at the 20 ppb level and in fortified beef liver at 40 ppb. Residues of MOX can also be confirmed in these matrices, but at slightly higher levels (40-80 ppb).     

Evaluation of chelation concentration and cation separation of actinides at ultra-trace levels in urine matrix

Summary The feasibility of measuring picogram levels of actinides in a urine matrix using ion chromatography coupled on-line to an inductively coupled plasma quadrupole mass spectrometer (IC-Q-ICPMS) was investigated. A chelation column for separation of matrix ions and preconcentration of the actinides was combined with a cation-exchange column for separation of the actinides. Sample preparation required simple addition of ammonium acetate to adjust the pH of the urine matrix. Spike solutions containing ²³² Th, ²³⁷Np, ²³⁸U, ²³⁹Pu, and ²⁴¹Am were added to undiluted urine, diluted urine (1 : 9) and water. Results showed that this approach enhanced the signal sensitivities of all the tested actinides over two orders of magnitude in the water matrix, while certain elements (especially Am) can still be effectively concentrated in undiluted urine.     

Simultaneous determination of residues of chloramphenicol, florfenicol, florfenicol amine, and thiamphenicol in shrimp tissue by gas chromatography with electron capture detection

A gas chromatographic (GC) method is presented for determining residues of chloramphenicol (CAP), florfenicol (FF), florfenicol amine (FFa), and thiamphenicol (TAP) in shrimp tissues, with meta-nitrochloramphenicol (mCAP) as the internal standard. The composited shrimp is extracted with basic ethyl acetate, followed by an acetonitrile-basic ethyl acetate mixture. This extract is centrifuged, filtered, evaporated, and reconstituted in water; the reconstituted extract is acidified, defatted with hexane, and passed through a propylsulfonic acid (PRS) and C18 solid-phase extraction (SPE) system. The C18 SPE column is eluted with methanol, and the PRS SPE column is eluted with basic MeOH plus counter ion. The combined eluates are evaporated, reconstituted in acetonitrile, and derivatized with Sylon BFT. After derivatization, the addition of toluene directly to the sample, followed by the addition of basic water, quenches the derivatization process. After centrifugation, the organic layer is carefully removed, and the analytes are determined by GC with electron capture detection. Shrimp tissues were fortified with fenicols (i.e., CAP, FF, FFa, and TAP) at 5, 10, 20, 40, and 80 ng/mL. Overall recoveries were 88, 101, 91, and 84% with overall interassay (between-day) variabilities (i.e., relative standard deviations) of 5.3, 9.4, 12.8, and 7.4% for CAP, FF, FFa, and TAP, respectively. The method detection limits were calculated as 0.7, 1.4, 2.4, and 1.3 ng/g (ppb) for CAP, FF, FFa, and TAP, respectively, based on a 10 g sample. The quantitation limit as determined empirically by this method is the lower limit of the standard curve, which is about 5 ng/g (ppb) for each analyte.