Connected Tasks: The Building Blocks of Reasoning and Proof

Do you find it challenging to find mathematical tasks that promote reasoning in your classroom? What type of tasks do you feel are the most important for children to investigate? Finding patterns, and making and justifying conjectures are considered the building blocks of mathematical reasoning and proof. Curriculum revisions in the United States and Australia place increased emphasis on problem solving and reasoning in the primary school curriculum (National Council of Teachers of Mathematics [NCTM], 2000; Australian Curriculum, Assessment and Reporting Authority [ACARA], 2010). A number of curriculum resources for teachers are available (e.g., NCTM, 1993; Sullivan & Lilburn, 1997) but under current reform efforts, primary teachers require additional ideas to extend problem solving and reasoning in their classrooms

Prospective elementary teachers use of representation to reason algebraically

We used a teaching experiment to evaluate the preparation of preservice teachers to teach early algebra concepts in the elementary school with the goal of improving their ability to generalize and justify algebraic rules when using pattern-finding tasks. Nearly all of the elementary preservice teachers generalized explicit rules using symbolic notation but had trouble with justifications early in the experiment. The use of isomorphic tasks promoted their ability to justify their generalizations and to understand the relationship of the coefficient and y-intercept to the models constructed with pattern blocks. Based on critical events in the teaching experiment, we developed a scale to map changes in preservice teachers’ understanding. Features of the tasks emerged that contributed to this understanding

Associations between cardiorespiratory fitness, physical activity and clustered cardiometabolic risk in children and adolescents: the HAPPY study

Clustering of cardiometabolic risk factors can occur during childhood and predisposes individuals to cardiometabolic disease. This study calculated clustered cardiometabolic risk in 100 children and adolescents aged 10-14 years (59 girls) and explored differences according to cardiorespiratory fitness (CRF) levels and time spent at different physical activity (PA) intensities. CRF was determined using a maximal cycle ergometer test, and PA was assessed using accelerometry. A cardiometabolic risk score was computed as the sum of the standardised scores for waist circumference, blood pressure, total cholesterol/high-density lipoprotein ratio, triglycerides and glucose. Differences in clustered cardiometabolic risk between fit and unfit participants, according to previously proposed health-related threshold values, and between tertiles for PA subcomponents were assessed using ANCOVA. Clustered risk was significantly lower (p < 0.001) in the fit group (mean 1.21 ± 3.42) compared to the unfit group (mean -0.74 ± 2.22), while no differences existed between tertiles for any subcomponent of PA. Conclusion These findings suggest that CRF may have an important cardioprotective role in children and adolescents and highlights the importance of promoting CRF in youth

Fine-mapping, novel loci identification, and SNP association transferability in a genome-wide association study of QRS duration in African Americans

The electrocardiographic QRS duration, a measure of ventricular depolarization and conduction, is associated with cardiovascular mortality. While single nucleotide polymorphisms (SNPs) associated with QRS duration have been identified at 22 loci in populations of European descent, the genetic architecture of QRS duration in non-European populations is largely unknown. We therefore performed a genome-wide association study (GWAS) meta-analysis of QRS duration in 13,031 African Americans from ten cohorts and a transethnic GWAS meta-analysis with additional results from populations of European descent. In the African American GWAS, a single genome-wide significant SNP association was identified (rs3922844, P = 4 × 10−14) in intron 16 of SCN5A, a voltage-gated cardiac sodium channel gene. The QRS-prolonging rs3922844 C allele was also associated with decreased SCN5A RNA expression in human atrial tissue (P = 1.1 × 10−4). High density genotyping revealed that the SCN5A association region in African Americans was confined to intron 16. Transethnic GWAS meta-analysis identified novel SNP associations on chromosome 18 in MYL12A (rs1662342, P = 4.9 × 10−8) and chromosome 1 near CD1E and SPTA1 (rs7547997, P = 7.9 × 10−9). The 22 QRS loci previously identified in populations of European descent were enriched for significant SNP associations with QRS duration in African Americans (P = 9.9 × 10−7), and index SNP associations in or near SCN5A, SCN10A, CDKN1A, NFIA, HAND1, TBX5 and SETBP1 replicated in African Americans. In summary, rs3922844 was associated with QRS duration and SCN5A expression, two novel QRS loci were identified using transethnic meta-analysis, and a significant proportion of QRS–SNP associations discovered in populations of European descent were transferable to African Americans when adequate power was achieved

Loci influencing blood pressure identified using a cardiovascular gene-centric array

Blood pressure (BP) is a heritable determinant of risk for cardiovascular disease (CVD). To investigate genetic associations with systolic BP (SBP), diastolic BP (DBP), mean arterial pressure (MAP) and pulse pressure (PP), we genotyped 50 000 single-nucleotide polymorphisms (SNPs) that capture variation in 2100 candidate genes for cardiovascular phenotypes in 61 619 individuals of European ancestry from cohort studies in the USA and Europe. We identified novel associations between rs347591 and SBP (chromosome 3p25.3, in an intron of HRH1) and between rs2169137 and DBP (chromosome1q32.1 in an intron of MDM4) and between rs2014408 and SBP (chromosome 11p15 in an intron of SOX6), previously reported to be associated with MAP. We also confirmed 10 previously known loci associated with SBP, DBP, MAP or PP (ADRB1, ATP2B1, SH2B3/ATXN2, CSK, CYP17A1, FURIN, HFE, LSP1, MTHFR, SOX6) at array-wide significance (P 2.4 10(6)). We then replicated these associations in an independent set of 65 886 individuals of European ancestry. The findings from expression QTL (eQTL) analysis showed associations of SNPs in the MDM4 region with MDM4 expression. We did not find any evidence of association of the two novel SNPs in MDM4 and HRH1 with sequelae of high BP including coronary artery disease (CAD), left ventricular hypertrophy (LVH) or stroke. In summary, we identified two novel loci associated with BP and confirmed multiple previously reported associations. Our findings extend our understanding of genes involved in BP regulation, some of which may eventually provide new targets for therapeutic intervention.</p

New genetic loci link adipose and insulin biology to body fat distribution.

Body fat distribution is a heritable trait and a well-established predictor of adverse metabolic outcomes, independent of overall adiposity. To increase our understanding of the genetic basis of body fat distribution and its molecular links to cardiometabolic traits, here we conduct genome-wide association meta-analyses of traits related to waist and hip circumferences in up to 224,459 individuals. We identify 49 loci (33 new) associated with waist-to-hip ratio adjusted for body mass index (BMI), and an additional 19 loci newly associated with related waist and hip circumference measures (P < 5 × 10(-8)). In total, 20 of the 49 waist-to-hip ratio adjusted for BMI loci show significant sexual dimorphism, 19 of which display a stronger effect in women. The identified loci were enriched for genes expressed in adipose tissue and for putative regulatory elements in adipocytes. Pathway analyses implicated adipogenesis, angiogenesis, transcriptional regulation and insulin resistance as processes affecting fat distribution, providing insight into potential pathophysiological mechanisms