Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Clinical pathways for chronic cough in children

Background Chronic cough (a cough lasting longer than four weeks) is a common problem internationally. Chronic cough has associated economic costs and is distressing to the child and to parents; ignoring cough may lead to delayed diagnosis and progression of serious underlying respiratory disease. Clinical guidelines have been shown to lead to efficient and effective patient care and can facilitate clinical decision making. Cough guidelines have been designed to facilitate the management of chronic cough. However, treatment recommendations vary, and specific clinical pathways for the treatment of chronic cough in children are important, as causes of and treatments for cough vary significantly from those in adults. Therefore, systematic evaluation of the use of evidence-based clinical pathways for the management of chronic cough in children would be beneficial for clinical practice and for patient care. Use of a management algorithm can improve clinical outcomes; such management guidelines can be found in the guidelines for cough provided by the American College of Chest Physicians (ACCP) and the British Thoracic Society (BTS). Objectives To evaluate the effectiveness of using a clinical pathway in the management of children with chronic cough. Search methods The Cochrane Register of Controlled Trials (CENTRAL), the Cochrane Airways Group Specialised Register, MEDLINE, EMBASE, review articles and reference lists of re levant articles were searched. The latest search was conducted in January 2014. Selection criteria All randomised controlled trials of parallel-group design comparing use versus non-use of a clinical pathway for treatment of chronic cough in children (< 18 years of age). Data collection and analysis Results of searches were reviewed against predetermined cr iteria for inclusion. Two review authors independently selected studies and performed data extraction in duplicate. Main results One study was included in the review. This multi-centre trial was based in five Australian hospitals and recruited 272 children with chronic cough. Children were randomly assigned to early (two weeks) or delayed (six weeks) referral to respiratory specialists who used a cough management pathway. When an intention-to-treat analysis was performed, clinical failure at six wee ks post randomisation (defined as < 75% improvement in cough score, or total resolution for fewer than three consecutive days) was significantly less in the early pathway arm compared with the control arm (odds ratio (OR) 0.35, 95% confidence interval (CI) 0.21 to 0.58). These results indicate that one additional child will be cured for e very five children treated via th e cough pathway (number needed to treat for an additional beneficial outcome (NNTB) = 5, 95% CI 3 to 9) at six weeks. Cough-specific parent-reported quality of life scores were significantly better in th e early-pathway group; the mean difference (MD) between groups was 0.60 (95% CI 0.19 to 1.01). Duration of cough post randomisation was significantly shorter in the intervention group (early-pathway arm) compared with the control group (delayed-pathway arm) (MD -2.70 weeks, 95% CI -4.26 to -1.14). Authors’ conclusions. Current evidence suggests that using a clinical algorithm for the management of children with ch r onic cough in h ospital outpatient settings is more effective than providing wait-list care. Futher high-quality randomised controlled trials are needed to perform ongoing evaluation of cough management pathways in general practitioner and other primary care settings.

What triggers problem recognition? An exploration on young Australian male problematic online gamers

Help-seeking is a complex decision-making process that first begins with problem recognition. However, little is understood about the conceptualisation of the helpseeking process and the triggers of problem recognition. This research proposes the use of the Critical Incident Technique (CIT) to examine and classify incidents that serve as key triggers of problem recognition among young Australian male problematic online gamers. The research provides a classification of five different types of triggers that will aid social marketers into developing effective early detection, prevention and treatment focused social marketing interventions.

Medical free-text to concept mapping as an information retrieval problem

Concept mapping involves determining relevant concepts from a free-text input, where concepts are defined in an external reference ontology. This is an important process that underpins many applications for clinical information reporting, derivation of phenotypic descriptions, and a number of state-of-the-art medical information retrieval methods. Concept mapping can be cast into an information retrieval (IR) problem: free-text mentions are treated as queries and concepts from a reference ontology as the documents to be indexed and retrieved. This paper presents an empirical investigation applying general-purpose IR techniques for concept mapping in the medical domain. A dataset used for evaluating medical information extraction is adapted to measure the effectiveness of the considered IR approaches. Standard IR approaches used here are contrasted with the effectiveness of two established benchmark methods specifically developed for medical concept mapping. The empirical findings show that the IR approaches are comparable with one benchmark method but well below the best benchmark.

Post-transcriptional regulation in the nucleus and cytoplasm: study of mean time to threshold (MTT) and narrow escape problem

Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via cal- culation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases,the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN : decoys are able to block binding sites on PTEN mRNAs, thereby educing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations

Atomic resolution of dielectric with low temperature coefficient

Ba(6-3x)Nd(8+2x)Ti(18)O(54) (BNTl14) is a high permittivity dielectric with low temperature coefficient (Tcf). Low coefficient of change of dielectric permittivity with temperature (Tcf) is an unusual materials property. The research is aimed at discovering how atomic structure relates to temperature coefficient. Sub-Ångström scanning transmission electron microscopy (STEM) is used to measure mixed occupancy of Nd and Ba in atomic columns. It was expected that phase separation would occur to accommodate mixing of dissimilar ions. However no evidence of phase separation was found. There is a good image match between experiment and high angle annular dark field (HAADF) simulation. Vacancies and excess Ba ions appear to be randomly arranged on the available sites which would result in distortion of TiO6 octahedra. The low Tcf may arise from TiO6 distortion.

High-resolution SNP microarray investigation of copy number variations on chromosome 18 in a control cohort

Copy number variations (CNVs) as described in the healthy population are purported to contribute significantly to genetic heterogeneity. Recent studies have described CNVs using lymphoblastoid cell lines or by application of specifically developed algorithms to interrogate previously described data. However, the full extent of CNVs remains unclear. Using high-density SNP array, we have undertaken a comprehensive investigation of chromosome 18 for CNV discovery and characterisation of distribution and association with chromosome architecture. We identified 399 CNVs, of which loss represents 98%, 58% are less than 2.5 kb in size and 71% are intergenic. Intronic deletions account for the majority of copy number changes with gene involvement. Furthermore, one-third of CNVs do not have putative breakpoints within repetitive sequences. We conclude that replicative processes, mediated either by repetitive elements or microhomology, account for the majority of CNVs in the healthy population. Genomic instability involving the formation of a non-B structure is demonstrated in one region.

Assistive classification for improving the efficiency of avian species richness surveys

Avian species richness surveys, which measure the total number of unique avian species, can be conducted via remote acoustic sensors. An immense quantity of data can be collected, which, although rich in useful information, places a great workload on the scientists who manually inspect the audio. To deal with this big data problem, we calculated acoustic indices from audio data at a one-minute resolution and used them to classify one-minute recordings into five classes. By filtering out the non-avian minutes, we can reduce the amount of data by about 50% and improve the efficiency of determining avian species richness. The experimental results show that, given 60 one-minute samples, our approach enables to direct ecologists to find about 10% more avian species.

X-ray Structure of Gelonin at 1.8 Å Resolution

Gelonin is a single chain ribosome inactivating protein (RIP) with potential application in the treatment of cancer and AIDS. Diffraction quality crystals grown using PEG3350, belong to the space group P2(1), with it a = 49.4 Angstrom b = 44.9 Angstrom, c = 137.4 Angstrom and beta = 98.4 degrees, and contain two molecules in the asymmetric unit. Diffraction data collected to 1.8 Angstrom resolution has a R(m) value of 7.3%. Structure of gelonin has been solved by the molecular replacement method, using ricin A chain as the search model. Crystallographic refinement using X-PLOR resulted in a model for which the r.m.s deviations from ideal bond lengths and bond angles are 0.012 Angstrom and 2.7 degrees, respectively The final R-factor is 18.4% for 39,806 reflections for which I > 1.0 sigma(I).The C-alpha atoms of the two molecules in the asymmetric unit superpose to within 0.38 Angstrom for 247 atom pairs. The overall fold of gelonin is similar to that of other RIPs such as ricin A chain and alpha-momorcharin, the r.m.s.d. for C-alpha superpositions being 1.3 and 1.4 Angstrom, respectively The-catalytic residues (Glu166, Arg169 and Tyr113) in the active site form a hydrogen bond scheme similar to that observed in other RIPs. The conformation of Tyr74 in the active site, however, is significantly different from that in alpha-momorcharin. Three well defined water molecules are located in the active site cavity and one of them, X319, superposes to within 0.2 Angstrom of a corresponding water molecule in the structure of alpha-momorcharin. Any of the three could be the substrate water molecule in the hydrolysis reaction catalysed by gelonin.Difference electron density for a N-linked sugar moiety has been observed near only one of the two potential glycosylation sites in the sequence. The amino acid at position 239 has been established as Lys by calculation of omit electron density maps.The two cysteine residues in the sequence, Cys44 and Cys50, form a disulphide bond, and are therefore not available for disulphide conjugation with antibodies. Based on the structure, the region of the molecule that is involved in intradimer interactions is suggested to be suitable for introducing a Cys residue for purposes of conjugation with an antibody to produce useful immunotoxins.

Palliative care problem severity score: Reliability and acceptability in a national study

Background The Palliative Care Problem Severity Score is a clinician-rated tool to assess problem severity in four palliative care domains (pain, other symptoms, psychological/spiritual, family/carer problems) using a 4-point categorical scale (absent, mild, moderate, severe). Aim To test the reliability and acceptability of the Palliative Care Problem Severity Score. Design: Multi-centre, cross-sectional study involving pairs of clinicians independently rating problem severity using the tool. Setting/participants Clinicians from 10 Australian palliative care services: 9 inpatient units and 1 mixed inpatient/community-based service. Results A total of 102 clinicians participated, with almost 600 paired assessments completed for each domain, involving 420 patients. A total of 91% of paired assessments were undertaken within 2 h. Strength of agreement for three of the four domains was moderate: pain (Kappa = 0.42, 95% confidence interval = 0.36 to 0.49); psychological/spiritual (Kappa = 0.48, 95% confidence interval = 0.42 to 0.54); family/carer (Kappa = 0.45, 95% confidence interval = 0.40 to 0.52). Strength of agreement for the remaining domain (other symptoms) was fair (Kappa = 0.38, 95% confidence interval = 0.32 to 0.45). Conclusion The Palliative Care Problem Severity Score is an acceptable measure, with moderate reliability across three domains. Variability in inter-rater reliability across sites and participant feedback indicate that ongoing education is required to ensure that clinicians understand the purpose of the tool and each of its domains. Raters familiar with the patient they were assessing found it easier to assign problem severity, but this did not improve inter-rater reliability.

How do proteins fold?

Understanding the mechanism by which an unfolded polypeptide chain folds to its unique, functional structure is a primary unsolved problem in biochemistry. Fundamental advances towards understanding how proteins fold have come from kinetic studies, Kinetic studies allow the dissection of the folding pathway of a protein into individual steps that are defined by partially-structured folding intermediates. Improvements in both the structural and temporal resolution of physical methods that are used to monitor the folding process, as well as the development of new methodologies, are now making it possible to obtain detailed structural information on protein folding pathways. The protein engineering methodology has been particularly useful in characterizing the structures of folding intermediates as well as the transition state of folding, Several characteristics of protein folding pathways have begun to emerge as general features for the folding of many different proteins. Progress in our understanding of how structure develops during folding is reviewed here.

A High-Resolution Transmission of the Precipitation Process in a Electron Microscopy Study Dilute Ti-N Alloy

The precipitation processes in dilute nitrogen alloys of titanium have been examined in detail by conventional transmission electron microscopy (CTEM) and high-resolution electron microscopy (HREM). The alloy Ti-2 at. pct N on quenching from its high-temperature beta phase field has been found to undergo early stages of decomposition. The supersaturated solid solution (alpha''-hcp) on decomposition gives rise to an intimately mixed, irresolvable product microstructure. The associated strong tweed contrast presents difficulties in understanding the characteristic features of the process. Therefore, HREM has been carried out with a view to getting a clear picture of the decomposition process. Studies on the quenched samples of the alloy suggest the formation of solute-rich zones of a few atom layers thick, randomly distributed throughout the matrix. On aging, these zones grow to a size beyond which the precipitate/matrix interfaces appear to become incoherent and the alpha' (tetragonal) product phase is seen distinctly. The structural details, the crystallography of the precipitation process, and the sequence of precipitation reaction in the system are illustrated.

A Quasi-Newton Adaptive Algorithm for Generalized Symmetric Eigenvalue Problem

In this paper, we first recast the generalized symmetric eigenvalue problem, where the underlying matrix pencil consists of symmetric positive definite matrices, into an unconstrained minimization problem by constructing an appropriate cost function, We then extend it to the case of multiple eigenvectors using an inflation technique, Based on this asymptotic formulation, we derive a quasi-Newton-based adaptive algorithm for estimating the required generalized eigenvectors in the data case. The resulting algorithm is modular and parallel, and it is globally convergent with probability one, We also analyze the effect of inexact inflation on the convergence of this algorithm and that of inexact knowledge of one of the matrices (in the pencil) on the resulting eigenstructure. Simulation results demonstrate that the performance of this algorithm is almost identical to that of the rank-one updating algorithm of Karasalo. Further, the performance of the proposed algorithm has been found to remain stable even over 1 million updates without suffering from any error accumulation problems.

Integral Formulation of the Problem of Current Distribution in Compulsator Wires of Electromagnetic Launchers and Railguns

Compulsators are power sources of choice for use in electromagnetic launchers and railguns. These devices hold the promise of reducing unit costs of payload to orbit. In an earlier work, the author had calculated the current distribution in compulsator wires by considering the wire to be split into a finite number of separate wires. The present work develops an integral formulation of the problem of current distribution in compulsator wires which leads to an integrodifferential equation. Analytical solutions, including those for the integration constants, are obtained in closed form. The analytical solutions present a much clearer picture of the effect of various input parameters on the cross-sectional current distribution and point to ways in which the desired current density distribution can be achieved. Results are graphically presented and discussed, with particular reference to a 50-kJ compulsator in Bangalore. Finite-element analysis supports the results.

High-resolution refinement of orthorhombic bovine pancreatic phospholipase A2

The X-ray structure of recombinant bovine pancreatic phospholipase A(2) (PLA2), which specifically catalyzes the cleavage of the sn-2 acylester bond of phospholipids, has been refined at 1.5 Angstrom resolution. The crystal belongs to the space group P2(1)2(1)2(1) with unit-cell parameters a = 47.12, b = 64.59 and c = 38.14 Angstrom similar to the native enzyme reported previously by Dijkstra et nl. [J. Mel. Biol. (1981), 147, 97-123]. The refinement converged to an R value of 18.4% (R-free = 22.8%) for 16 374 reflections between 10.0 and 1.5 Angstrom resolution. The surface-loop residues (60-70) art: ordered in the present orthorhombic recombinant enzyme, but disordered in the trigonal recombinant enzyme. The active-site residues, His48, Asp99, and the catalytic water superimpose well with the trigonal form. Besides the catalytic water which is hydrogen bonded to His48, it is often seen that there is a second water attached to the same N atom of His48 and simultaneously hydrogen bonded to the O atom of Asp49. It is thought that the second water facilitates the tautomerism of His48 for enzyme catalysis, The catalytic water is also hydrogen bonded to the equatorial water coordinated to the calcium ion, In addition to the equatorial water, there is also an axial calcium water and the additional structural water. These five common water molecules are hydrogen bonded to the additional 16 water molecules in the present orthorhombic structure which may further enhance the structural integrity of the active site. Besides the protein and one calcium ion, a total of 134 water molecules were located in the present high-resolution refinement.