Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Comparison of decision tree, support vector machines, and Bayesian network approaches for classification of falls in Parkinson’s disease

Being able to accurately predict the risk of falling is crucial in patients with Parkinson’s dis- ease (PD). This is due to the unfavorable effect of falls, which can lower the quality of life as well as directly impact on survival. Three methods considered for predicting falls are decision trees (DT), Bayesian networks (BN), and support vector machines (SVM). Data on a 1-year prospective study conducted at IHBI, Australia, for 51 people with PD are used. Data processing are conducted using rpart and e1071 packages in R for DT and SVM, con- secutively; and Bayes Server 5.5 for the BN. The results show that BN and SVM produce consistently higher accuracy over the 12 months evaluation time points (average sensitivity and specificity > 92%) than DT (average sensitivity 88%, average specificity 72%). DT is prone to imbalanced data so needs to adjust for the misclassification cost. However, DT provides a straightforward, interpretable result and thus is appealing for helping to identify important items related to falls and to generate fallers’ profiles.

Written numeracy assessment in the early years: The challenges of pronouns and noun groups

We examine the challenges of pronouns and noun groups in the Australian Curriculum, Assessment and Reporting Authority’s (ACARA) Year 3 National Assessment Program - Literacy and Numeracy (NAPLAN) Numeracy Example Test (ACARA, 2015a). Framed by discourses of Literacy as a General Capability (ACARA, 2015b) in the Australian Curriculum: Mathematics (ACARA, 2015c), the pronouns and noun groups used in the Example Test are mapped onto the Australian Curriculum: English Content Descriptions (ACARA, 2015d). The findings are that some of the pronouns and noun groups used in the Example Test are more complex than what Year 3 children are expected to achieve in the Australian Curriculum: English. We thus stress the need for early years teachers of mathematics to account for the unique mathematical register of written mathematics problems so that young children are not only prepared for high-stakes written numeracy assessments, but are also enabled as a numerically literate citizen.

Functional evaluation of genetic variants associated with endometriosis near GREB1

STUDY QUESTION: Do DNA variants in the growth regulation by estrogen in breast cancer 1 (GREB1) region regulate endometrial GREB1 expression and increase the risk of developing endometriosis in women? SUMMARY ANSWER: We identified new single nucleotide polymorphisms (SNPs) with strong association with endometriosis at the GREB1 locus although we did not detect altered GREB1 expression in endometriosis patients with defined genotypes. WHAT IS ALREADY KNOWN: Genome-wide association studies have identified the GREB1 region on chromosome 2p25.1 for increasing endometriosis risk. The differential expression of GREB1 has also been reported by others in association with endometriosis disease phenotype. STUDY DESIGN, SIZE, DURATION: Fine mapping studies comprehensively evaluated SNPs within the GREB1 region in a large-scale data set (>2500 cases and >4000 controls). Publicly available bioinformatics tools were employed to functionally annotate SNPs showing the strongest association signal with endometriosis risk. Endometrial GREB1 mRNA and protein expression was studied with respect to phases of the menstrual cycle (n = 2-45 per cycle stage) and expression quantitative trait loci (eQTL) analysis for significant SNPs were undertaken for GREB1 [mRNA (n = 94) and protein (n = 44) in endometrium]. PARTICIPANTS/MATERIALS, SETTING, METHODS: Participants in this study are females who provided blood and/or endometrial tissue samples in a hospital setting. The key SNPs were genotyped using Sequenom MassARRAY. The functional roles and regulatory annotations for identified SNPs are predicted by various publicly available bioinformatics tools. Endometrial GREB1 expression work employed qRT-PCR, western blotting and immunohistochemistry studies. MAIN RESULTS AND THE ROLE OF CHANCE: Fine mapping results identified a number of SNPs showing stronger association (0.004 < P < 0.032) with endometriosis risk than the original GWAS SNP (rs13394619) (P = 0.034). Some of these SNPs were predicted to have functional roles, for example, interaction with transcription factor motifs. The haplotype (a combination of alleles) formed by the risk alleles from two common SNPs showed significant association (P = 0.026) with endometriosis and epistasis analysis showed no evidence for interaction between the two SNPs, suggesting an additive effect of SNPs on endometriosis risk. In normal human endometrium, GREB1 protein expression was altered depending on the cycle stage (significantly different in late proliferative versus late secretory, P < 0.05) and cell type (glandular epithelium, not stromal cells). However, GREB1 expression in endometriosis cases versus controls and eQTL analyses did not reveal any significant changes. LIMITATIONS, REASONS FOR CAUTION: In silico prediction tools are generally based on cell lines different to our tissue and disease of interest. Functional annotations drawn from these analyses should be considered with this limitation in mind. We identified cell-specific and hormone-specific changes in GREB1 protein expression. The lack of a significant difference observed following our GREB1 expression studies may be the result of moderate power on mixed cell populations in the endometrial tissue samples. WIDER IMPLICATIONS OF THE FINDINGS: This study further implicates the GREB1 region on chromosome 2p25.1 and the GREB1 gene with involvement in endometriosis risk. More detailed functional studies are required to determine the role of the novel GREB1 transcripts in endometriosis pathophysiology. STUDY FUNDING/COMPETING INTERESTS: Funding for this work was provided by NHMRC Project Grants APP1012245, APP1026033, APP1049472 and APP1046880. There are no competing interests.

No evidence for genetic association with the let-7 microRNA-binding site or other common KRAS variants in risk of endometriosis

STUDY QUESTION Is there a contribution of the minor allele at the KRAS single nucleotide polymorphism (SNP) rs61764370 in the let-7 microRNA-binding site to endometriosis risk? SUMMARY ANSWER We found no evidence for association between endometriosis risk and rs61764370 or any other SNPs in KRAS. WHAT IS KNOWN ALREADY The rs61764370 SNP in the 3' untranslated region of the KRAS gene is predicted to disrupt a complementary binding site (LCS6) for the let-7 microRNA, and was recently reported to be at a high frequency (31%) in 132 women of varying ancestry with endometriosis compared with frequencies in a database of population controls (up to 7.6% depending on ancestry), suggesting a strong effect of this KRAS SNP in the aetiology of endometriosis. STUDY DESIGN, SIZE AND DURATION This was a case-control study with a total of 11 206 subjects. The study was performed between February 2012 and July 2012. PARTICIPANTS/MATERIALS, SETTINGAND METHODS We first investigated a possible association between common markers in KRAS and endometriosis risk from our genome-wide association (GWA) data in 3194 surgically confirmed endometriosis cases and 7060 controls of European ancestry. Although rs61764370 was not genotyped on the GWA arrays, five SNPs typed in the study were highly correlated with this variant. The rs61764370 and two SNPs highly correlated with rs61764370 were then genotyped in 933 endometriosis cases and 952 controls using the Sequenom MassARRAY platform. MAIN RESULTS AND THE ROLE OF CHANCE There was no evidence for an association between rs61764370 and endometriosis risk P = 0.411 and odds ratio = 1.10 (95% confidence intervals: 0.88-1.36). We also found no evidence for an association between the highly correlated SNP rs17387019 and endometriosis. Their minor allele frequencies in cases and controls were of 0.087-0.091 similar to the population frequency reported previously for this variant in controls. Analyses of endometriosis cases with revised American Fertility Society stage III/IV disease also showed no evidence for an association between these SNPs and endometriosis risk. LIMITATIONS AND REASONS FOR CAUTION The GWA and genotyped data sets were not independent since individuals and cases from some families overlap. Controls in our GWA study were not screened for endometriosis. WIDER IMPLICATIONS OF THE FINDINGS The key SNP, rs61764370, was genotyped in a subset of samples. Our results do not support the suggestion that carrying the minor allele at rs61764370 contributes to a significant number of endometriosis cases and rs61764370 is, therefore, unlikely to be a useful marker of endometriosis risk. STUDY FUNDING/COMPETING INTEREST(S) The research was funded by grants from the Australian National Health and Medical Research Council and Wellcome Trust. None of the authors has competing interests for the study.

What does “futility” mean? An empirical study of doctors’ perceptions

Objective(s) To describe how doctors define and use the terms “futility” and “futile treatment” in end-of-life care. Design, Setting, Participants A qualitative study using semi-structured interviews with 96 doctors across a range of specialties who treat adults at the end of life. Doctors were recruited from three large Australian teaching hospitals and were interviewed from May to July 2013. Results Doctors’ conceptions of futility focused on the quality and chance of patient benefit. Aspects of benefit included physiological effect, weighing benefits and burdens, and quantity and quality of life. Quality and length of life were linked, but many doctors discussed instances when benefit was determined by quality of life alone. Most doctors described the assessment of chance of success in achieving patient benefit as a subjective exercise. Despite a broad conceptual consensus about what futility means, doctors noted variability in how the concept was applied in clinical decision-making. Over half the doctors also identified treatment that is futile but nevertheless justified, such as short-term treatment as part of supporting the family of a dying person. Conclusions There is an overwhelming preference for a qualitative approach to assessing futility, which brings with it variation in clinical decision-making. “Patient benefit” is at the heart of doctors’ definitions of futility. Determining patient benefit requires discussions with patients and families about their values and goals as well as the burdens and benefits of further treatment.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Implicit difference approximation for the time fractional diffusion equation

In this paper, we consider a time fractional diffusion equation on a finite domain. The equation is obtained from the standard diffusion equation by replacing the first-order time derivative by a fractional derivative (of order $0<\alpha<1$ ). We propose a computationally effective implicit difference approximation to solve the time fractional diffusion equation. Stability and convergence of the method are discussed. We prove that the implicit difference approximation (IDA) is unconditionally stable, and the IDA is convergent with $O(\tau+h^2)$, where $\tau$ and $h$ are time and space steps, respectively. Some numerical examples are presented to show the application of the present technique.

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.