How does imposing a step-by-step solution method impact students’ approach to mathematical word problem solving?

This paper presents the second phase of a larger research program with the purpose of exploring the possible consequences of a gap between what is done in the classroom regarding mathematical word problem solving and what research shows to be effective in this particular field of study. Data from the first phase of our study on teachers’ self-proclaimed practices showed that one-third of elementary teachers from the region of Quebec require their students to follow a specific sequential problem-solving method, known as the ‘what I know, what I look for’ method. These results led us to hypothesize that the observed gap may have an impact on students’ comprehension of mathematical word problems. The use of this particular method was the foundation for us to study, in the second phase, the effect of the imposition of this sequential method on students’ literal and inferential understanding of word problems. A total of 278 fourth graders (9–10 years old) solved mathematical word problems followed by a test to assess their understanding of the word problems they had just solved. The results suggest that the use of this problem solving method does not seem to improve or impair students’ understanding. From a more fundamental point of view, our study led us to the conclusion that the way word problem solving is addressed in the mathematics classroom, through sequential and inflexible methods, does not help students develop their word problem solving competence.     

Special Lagrangian Submanifolds with Isolated Conical Singularities. II. Moduli spaces

This is the second in a series of five papers studying special Lagrangiansubmanifolds (SLV m-folds) X in (almost) Calabi–Yau m-folds M with singularities x ₁ , ..., x _n locally modelled on specialLagrangian cones C ₁, ..., C _n in ^m with isolated singularities at 0.Readers are advised to begin with Paper V.This paper studies the deformation theory of compact SL m-folds X in Mwith conical singularities. We define the moduli space _X of deformations of X in M, and construct a natural topology on it. Then we show that _X is locally homeomorphic to the zeroes of a smooth map : _{X X} between finite-dimensional vector spaces.Here the infinitesimal deformation space _X depends only on the topology of X, and the obstruction space _X only on the cones C ₁, ..., C _n at x ₁, ..., x _n . If the cones C _i are stable then _X is zero, and _X is a smooth manifold. We also extend our results to families of almost Calabi–Yau structures on M.     

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.     

Stability properties of a nonstandard finite difference scheme for a hantavirus epidemic model

This paper studies the stability properties of a nonstandard finite difference (NSFD) scheme used to simulate the dynamics of a mouse population model in hantavirus epidemics. It is shown that this difference scheme and the underlying system of differential equations have the same dynamics. The proof uses the fact that the total population obeys the logistic equation, as well as techniques from calculus, graphical analysis, and dynamical systems.     

Stability and fragmentation of organic silicon functionalizations studied by laser desorption mass spectrometry

A method is introduced to investigate organic functionalizations on silicon by laser-induced thermal desorption (LITD), where well-ordered Si(1 1 1)-(1 × 1):H(D) surfaces are used to determine the desorption temperature as a function of laser fluence. To demonstrate the potential of this technique silicon surfaces with ultrathin oxide layers were functionalized with organic end groups. The species desorbed with focused XeCl laser pulses were monitored at an oblique angle and their time-of-flight (TOF) distributions were measured with a quadrupole mass analyzer after electron impact ionization. By assuming a negligible contribution of the oxide and organic layers to the heating effect, the TOF temperatures measured for Si(1 1 1)-(1 × 1):H(D) could be used to determine the mass of the desorbed species. Detailed results are presented for dimethylsilyl (DMS), bromomethyldimethylsilyl (BMDMS), and chloromethyldimethylsilyl (CMDMS) terminated surfaces which were prepared by silanization with suitable chloro and disilazane compounds. While for the DMS termination dimethylsilanol (76 u) is desorbed as a single species, clearly identifying the terminating group, in the case of BMDMS and CMDMS further fragmentation of the end group occurs at the surface.     

Development of an enzymatic microreactor based on microencapsulated laccase with off-line capillary electrophoresis for measurement of oxidation reactions

Microencapsulation is used here as a new technique to immobilize enzymes in a microreactor coupled off-line to capillary electrophoresis (CE), allowing the determination of enzymatic reaction products. The redox enzyme laccase was encapsulated using the method of interfacial cross-linking of poly(ethyleneimine) (PEI). The 50 μm diameter capsules were slurry packed from a suspension into a capillary-sized reactor made easily and quickly from a short length of 530 μm diameter fused-silica tubing. The volume of the bed of laccase microcapsules in the microreactor was in the order of 1.1 μL through which 50 μL of the substrate o-phenylenediamine (OPD) was flowed. The oxidation product 2,3-diaminophenazine (DAP) and the remaining OPD were quantified by CE in a pH 2.5 phosphate buffer. Peak migration time reproducibility was in the order of 0.4% RSD and peak area reproducibility was less than 1.7% RSD within the same day. Using the OPD peak area calibration curve, a conversion efficiency of 48% was achieved for a 2-min oxidation reaction in the microreactor.     

Experimental and computational studies of the macrocyclic effect of an auxiliary ligand on electron and proton transfers within ternary copper(II)-Histidine complexes

The dissociation of [Cu^II(L)His]^•2+ complexes [L=diethylenetriamine (dien) or 1,4,7-triazacyclononane (9-aneN₃)] bears a strong resemblance to the previously reported behavior of [Cu^II(L)GGH]^•2+ complexes. We have used low-energy collision-induced dissociation experiments and density functional theory (DFT) calculations at the B3LYP/6-31+G(d) level to study the macrocyclic effect of the auxiliary ligands on the formation of His^•+ from prototypical [Cu^II(L)His]^•2+ systems. DFT revealed that the relative energy barriers of the same electron-transfer (ET) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ are very similar, with the ET reactions of [Cu^II(9-aneN₃)His]^•2+ leading to the generation of two distinct His^•+ species; in contrast, the proton transfer (PT) dissociation pathways of [Cu^II(9-aneN₃)His]^•2+ and [Cu^II(dien)His]^•2+ differ considerably. The PT reactions of [Cu^II(9-aneN₃)His]^•2+ are associated with substantially higher barriers (>13 kcal/mol) than those of [Cu^II(dien)His]^•2+. Thus, the sterically encumbered auxiliary 9-aneN₃ ligand facilitates ET reactions while moderating PT reactions, allowing the formation of hitherto nonobservable histidine radical cations.     

trans‐Decahydronaphthalene (decalin) from powder diffraction data

The title compound, C₁₀H₁₈, a decalin stereoisomer, crystallizes with Z′ = 0.5 in the space group P2₁/n. The trans‐decalin molecule is located on an inversion centre with both rings in a chair conformation, making for a quasi‐flat overall shape. Despite the absence of hydrogen bonds, it crystallizes easily. In this work the unknown crystal structure of trans‐decalin has been solved and refined using X‐ray powder diffraction data.