Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

In Response: "Oral versus IV treatment for catheter-related bloodstream infections - by Burke A. Cunha"

In his letter Cunha suggests that oral antibiotic therapy is safer and less expensive than intravenous therapy via central venous catheters (CVCs) (1). The implication is that costs will fall and increased health benefits will be enjoyed resulting in a gain in efficiency within the healthcare system. CVCs are often used in critically ill patients to deliver antimicrobial therapy, but expose patients to a risk of catheter-related bloodstream infection (CRBSI). Our current knowledge about the efficiency (i.e. costeffectiveness) of allocating resources toward interventions that prevent CRBSI in patients requiring a CVC has already been reviewed (2). If for some patient groups antimicrobial therapy can be delivered orally, instead of through a CVC, then the costs and benefits of this alternate strategy should be evaluated...

Integrin-linked kinase as a target for ERG-mediated invasive properties in prostate cancer models

Approximately half of prostate cancers (PCa) carry TMPRSS2-ERG translocations; however, the clinical impact of this genomic alteration remains enigmatic. Expression of v-ets erythroblastosis virus E26 oncogene like (avian) gene (ERG) promotes prostatic epithelial dysplasia in transgenic mice and acquisition of epithelial-to-mesenchymal transition (EMT) characteristics in human prostatic epithelial cells (PrECs). To explore whether ERG-induced EMT in PrECs was associated with therapeutically targetable transformation characteristics, we established stable populations of BPH-1, PNT1B and RWPE-1 immortalized human PrEC lines that constitutively express flag-tagged ERG3 (fERG). All fERG-expressing populations exhibited characteristics of in vitro and in vivo transformation. Microarray analysis revealed >2000 commonly dysregulated genes in the fERG-PrEC lines. Functional analysis revealed evidence that fERG cells underwent EMT and acquired invasive characteristics. The fERG-induced EMT transcript signature was exemplified by suppressed expression of E-cadherin and keratins 5, 8, 14 and 18; elevated expression of N-cadherin, N-cadherin 2 and vimentin, and of the EMT transcriptional regulators Snail, Zeb1 and Zeb2, and lymphoid enhancer-binding factor-1 (LEF-1). In BPH-1 and RWPE-1-fERG cells, fERG expression is correlated with increased expression of integrin-linked kinase (ILK) and its downstream effectors Snail and LEF-1. Interfering RNA suppression of ERG decreased expression of ILK, Snail and LEF-1, whereas small interfering RNA suppression of ILK did not alter fERG expression. Interfering RNA suppression of ERG or ILK impaired fERG-PrEC Matrigel invasion. Treating fERG-BPH-1 cells with the small molecule ILK inhibitor, QLT-0267, resulted in dose-dependent suppression of Snail and LEF-1 expression, Matrigel invasion and reversion of anchorage-independent growth. These results suggest that ILK is a therapeutically targetable mediator of ERG-induced EMT and transformation in PCa.

Manuel Aires Mateus : an architecture for the art of life [曼努埃尔·艾利斯·马特乌斯：建筑，为了生活的艺术]

This text is the outcome of a conversation with Manuel Aires Mateus (Aires Mateus Arquitectos) and discusses the importance of architecture and memory in contemporary architectural productions

Taxonomic review of the chironomid genus Cricotopus v.d. Wulp (Diptera: Chironomidae) from Australia : keys to males, females, pupae and larvae, description of ten new species and comments on Paratrichocladius Santos Abreu

The Australian species of the Orthocladiinae genus Cricotopus Wulp (Diptera: Chironomidae) are revised for larval, pupal, adult male and female life stages. Eleven species, ten of which are new, are recognised and keyed, namely Cricotopus acornis Drayson & Cranston sp. nov., Cricotopus albitarsis Hergstrom sp. nov., Cricotopus annuliventris (Skuse), Cricotopus brevicornis Drayson & Cranston sp. nov., Cricotopus conicornis Drayson & Cranston sp. nov., Cricotopus hillmani Drayson & Cranston, sp. nov., Cricotopus howensis Cranston sp. nov., Cricotopus parbicinctus Hergstrom sp. nov., Cricotopus tasmania Drayson & Cranston sp. nov., Cricotopus varicornis Drayson & Cranston sp. nov. and Cricotopus wangi Cranston & Krosch sp. nov. Using data from this study, we consider the wider utility of morphological and molecular diagnostic tools in untangling species diversity in the Chironomidae. Morphological support for distinguishing Cricotopus from Paratrichocladius Santo-Abreu in larval and pupal stages appears lacking for Australian taxa and brief notes are provided concerning this matter.

Drug administration guides in dysphagia

Aim: The aim of this evaluation was to evaluate the use of Individualised Medication Administration Guides (IMAGs) for patients with dysphagia on one stroke ward over a 6month period. Background: Patients with dysphagia (PWD) are more likely to suffer an administration error than patients without swallowing difficulties. To both standardise and improve medicines administration to patients with dysphagia I-MAGs were introduced on one stroke ward over a 6 month period. Methods: A software package supported with data on current national guidelines on the administration of medicines to PWD was designed by a specialised pharmacist in dysphagia to enable him to create individualised medication administration guides for patients with dysphagia which stated how each medicine should be optimally prepared and administered. On completion of the pilot service a questionnaire was given to all nurses, pharmacist and speech and language therapists who had experienced the I-MAGs. All the professionals received the same questionnaire but questions relevant only to their practice were added to the nurse’s questionnaire. Results: Of 26 Healthcare professionals (HCPs) approached, 19 returned completed questionnaires. Higher variability was found in the 13 responses from the nurse respondents than in the ones from the 3 pharmacist and the 3 SALTs. 8 (61%) of the nurses felt more confident in their practice when I-MAGs were in place. 10 (76%) of the nurses admitted that the guides could sometimes increase the time of the administration, but saw that it made practice safer. All the pharmacists considered the recommendations in the guides useful and all the respondents with the exception of one nurse (12:13) would like this service to continue. Conclusion: I-MAGs were well received on the ward and they support individualised care for patients with dysphagia. But the guides needed additional pharmacist input and greater nursing time. Research to determine the cost effectiveness of I-MAGs is needed.

Implementation of individualised medication administration guides for patients with dysphagia: Results from a pilot controlled trial

Introduction Patients with dysphagia (PWDs) have been shown to be four times more likely to suffer medication administration errors (MAEs).1 2 Individualised medication administration guides (I-MAGs) which outline how each formulation should be administered, have been developed to standardise medication administration by nurses on the ward and reduce the likelihood of errors. This pilot study aimed to determine the recruitment rates, estimate effect on errors and develop the intervention to design a future full scale randomised controlled trial to determine the costs and effects of I-MAG implementation. Ethical approval was granted by local ethics committee. Method Software was developed to enable I-MAG production (based on current best practice)3 4 for all PWDs on two care of the older person wards admitted during a six month period from January to July 2011. I-MAGs were attached to the medication administration record charts to be utilised by nurses when administering medicines. Staff training was provided for all staff on the intervention wards. Two care of the older person wards in the same hospital were used for control purposes. All patients with dysphagia were recruited for follow up purposes at discharge. Four ward rounds at each intervention and control ward were observed pre and post I-MAG implementation to determine the level of medication administration errors. NHS ethical approval for the study was obtained. Results 164 I-MAGs were provided for 75 patients with dysphagia (PWDs) in the two intervention wards. At discharge, 23 patients in the intervention wards and 7 patients in the control wards were approached for recruitment of which 17 (74%) & 5 (71.5%) respectively consented. Discussion Recruitment rates were low on discharge due to the dysphagia remitting during hospitalisation. The introduction of the I-MAG demonstrated no effect on the quality of administration on the intervention ward and interestingly practice improved on the control ward. The observation of medication rounds at least one month post I-MAG removal may have identified a reversal to normal practice and ideally observations should have been undertaken with I-MAGs in place. Identification of the reason for the improvement in the control ward is warranted.

Inability to swallow tablets is common and cause for concern

We naturally chew food before swallowing, but tablets and capsules require a complicated, conscious mechanism to over-ride the need to chew and the gag reflex, designed to eject foodstuffs that are not adequately chewed...

Inappropriate formulation choices in the administration of medication to elderly patients with dysphagia in nursing homes

Inappropriate food or medication texture in patients with dysphagia is the most significant risk factor for pneumonia. Dysphagia is prevalent within care homes for the older person as it is largely found in conditions associated with ageing. This study was designed to determine the appropriateness of medication formulation choices in elderly patients with dysphagia in care homes.

Nurses’ views on the implementation of Individualised Medication Administration Guides in patients with dysphagia in care homes

As conditions such as stroke, cancer, Parkinson's disease and Huntingdon's chorea are commonly found in care homes between 15% and 30% of residents in care homes have been found to have difficulties in swallowing their medicines.To address the difficulties associated with administering medicines to patients who cannot swallow (with dysphagia), Individualised Medication Administration Guides (I-MAGs) were introduced by a specialised pharmacist in Care for Elderly wards in a general hospital in East Anglia. The guides contained detailed information about how to administer each medication and they were individualised to the needs of the patient. The I-MAGs were printed in green forms and attached to the medication chart in order to be used in conjunction with it. The ward nurses reported an increase in their confidence when administering medication when I-MAGs were present in the ward. Some patients with I-MAG were discharged to care homes where the I-MAG might have been equally useful. However, the design of such guides is not known to be suitable for care homes environment where they have never been used before. This study aims to explore the opinions of nurses and carers within care homes on the relevance and acceptability of individualised medication administration guides for patients with dysphagia (PWD).

Medicines related dysphagia in primary care: The prevalence of and impact on community pharmacists

Dysphagia is a common and problematic symptom characterised by varying degrees of difficulty swallowing food, fluids and medicines of differing consistencies. International primary care based studies have identified that between 1 in 4 and 1 in 5 patients have some form of dysphagia, it can affect medicines taking behaviour and healthcare professionals are largely unaware of this1,2. Similar research has not been undertaken in the UK. Adherence related pharmacy based services in the UK provide an opportunity for community pharmacists to identify the problem and facilitate better medicines use. The aim of this pilot study was to estimate the level of patient reported dysphagia in older persons using community pharmacies in the UK, describe how it affects their medicine taking behaviour and identify whether advanced pharmacy services are related to improved awareness of this.

ERAP2 is associated with ankylosing spondylitis in HLA-B27-positive and HLA-B27-negative patients

The association of endoplasmic reticulum aminopeptidase 2 (ERAP2) with ankylosing spondylitis (AS) was recently described in the large International Genetics of AS Consortium Immunochip study...

Association of IL23R and ERAP1 genes with ankylosing spondylitis in a Portuguese population

Objective: Association between ankylosing spondylitis (AS) and two genes, ERAP1 and IL23R, has recently been reported in North American and British populations. The population attributable risk fraction for ERAP1 in this study was 25%, and for IL23R, 9%. Confirmation of these findings to ERAP1 in other ethnic groups has not yet been demonstrated. We sought to test the association between single nucleotide polymorphisms (SNPs) in these genes and susceptibility to AS among a Portuguese population. We also investigated the role of these genes in clinical manifestations of AS, including age of symptom onset, the Bath Ankylosing Spondylitis Disease Activity, Metrology and Functional Indices, and the modified Stoke Ankylosing Spondylitis Spinal Score. Methods: The study was conducted on 358 AS cases and 285 ethnically matched Portuguese healthy controls. AS was defined according to the modified New York Criteria. Genotyping of IL23R and ERAP1 allelic variants was carried out with TaqMan allelic discrimination assays. Association analysis was performed using the Cochrane-Armitage and linear regression tests of genotypes as implemented in PLINK for dichotomous and quantitative variables respectively. A meta-analysis for Portuguese and previously published Spanish IL23R data was performed using the StatsDirect® Statistical tools, by fixed and random effects models. Results: A total of 14 nsSNPs markers (8 for IL23R, 5 for ERAPl, 1 for LN-PEP) were analysed. Three markers (2 for IL23R and 1 for ERAP1) showed significant single-locus disease associations, confirming that the association of these genes with AS in the Portuguese population. The strongest associated SNP in IL23R was rs1004819 (OR=1.4, p=0.0049), and in ERAP1 was rs30187 (OR=1.26, p=0.035). The population attributable risk fractions in the Portuguese population for these SNPs are 11% and 9.7% respectively. No association was seen with any SNP in LN-PEP, which flanks ERAP1 and was associated with AS in the British population. No association was seen with clinical manifestations of AS. Conclusions: These results show that IL23R and ERAP1 genes are also associated with susceptibility to AS in the Portuguese population, and that they contribute a significant proportion of the population risk for this disease.

Spectrum of ankylosing spondylitis in Portugal. Development of BASDAI, BASFI, BASMI and mSASSS reference centile charts

The availability of population-specific normative data regarding disease severity measures is essential for patient assessment. The goals of the current study were to characterize the pattern of ankylosing spondylitis (AS) in Portuguese patients and to develop reference centile charts for BASDAI, BASFI, BASMI and mSASSS, the most widely used assessment tools in AS. AS cases were recruited from hospital outpatient clinics, with AS defined according to the modified New York criteria. Demographic and clinical data were recorded. All radiographs were evaluated by two independent experienced readers. Centile charts for BASDAI, BASFI, BASMI and mSASSS were constructed for both genders, using generalized linear models and regression models with duration of disease as independent variable. A total of 369 patients (62.3% male, mean ± (SD) age 45.4 ± 13.2 years, mean ± (SD) disease duration 11.4 ± 10.5 years, 70.7% B27-positive) were included. Family history of AS in a first-degree relative was reported in 17.6% of the cases. Regarding clinical disease pattern, at the time of assessment 42.3% had axial disease, 2.4% peripheral disease, 40.9% mixed disease and 7.1% isolated enthesopatic disease. Anterior uveitis (33.6%) was the most common extra-articular manifestation. The centile charts suggest that females reported greater disease activity and more functional impairment than males but had lower BASMI and mSASSS scores. Data collected through this study provided a demographic and clinical profile of patients with AS in Portugal. The development of centile charts constitutes a useful tool to assess the change of disease pattern over time and in response to therapeutic interventions.