Teaching Conceptual Understanding of Mathematics via a Hands-On Approach

Given the current developments in the field of mathematics instruction in the United States, conceptual understanding and a hands-on approach in mathematics are two topics of importance. Conceptual understanding of mathematics is often lacking but characterizes the core of what mathematics actually is. Using a hands-on approach presents an effective way to teach conceptual understanding of mathematics. In order to argue this, a presentation of the underlying theories of mathematical understanding and pertinent approaches is given. Then follows an investigation of three studies pertinent to using a hands-on approach in teaching conceptual understanding of mathematics: one related to implementation (Gürbüz, Çatlioğl, Bìrgìn, & Erdem, 2010), one related to tools (Özgün-Koca & Edwards, 2011), and one related to evaluation (Bartell, Webel, Bowen, & Dyson, 2013). Furthermore, an example of a hands-on mathematical activity in geometry (Tipps, Johnson, & Kennedy, 2011) which could be implemented in a real-life classroom is presented. A discussion then follows, providing interpretation and implications, such as the connection to differentiation, to teaching conceptual understanding using a hands-on approach

Association of urinary phthalate metabolite concentrations with body mass index and waist circumference: a cross-sectional study of NHANES data, 1999–2002

BACKGROUND: Although diet and activity are key factors in the obesity epidemic, laboratory studies suggest that endocrine disrupting chemicals may also affect obesity. METHODS: We analyzed associations between six phthalate metabolites measured in urine and body mass index (BMI) and waist circumference (WC) in National Health and Nutrition Examination Survey (NHANES) participants aged 6–80. We included 4369 participants from NHANES 1999–2002, with data on mono-ethyl (MEP), mono-2-ethylhexyl (MEHP), mono-n-butyl (MBP), and mono-benzyl (MBzP) phthalate; 2286 also had data on mono-2-ethyl-5-hydroxyhexyl (MEHHP) and mono-2-ethyl-5-oxohexyl (MEOHP) phthalate (2001–2002). Using multiple regression, we computed mean BMI and WC within phthalate quartiles in eight age/gender specific models. RESULTS: The most consistent associations were in males aged 20–59; BMI and WC increased across quartiles of MBzP (adjusted mean BMI = 26.7, 27.2, 28.4, 29.0, p-trend = 0.0002), and positive associations were also found for MEOHP, MEHHP, MEP, and MBP. In females, BMI and WC increased with MEP quartile in adolescent girls (adjusted mean BMI = 22.9, 23.8, 24.1, 24.7, p-trend = 0.03), and a similar but less strong pattern was seen in 20–59 year olds. In contrast, MEHP was inversely related to BMI in adolescent girls (adjusted mean BMI = 25.4, 23.8, 23.4, 22.9, p-trend = 0.02) and females aged 20–59 (adjusted mean BMI = 29.9, 29.9, 27.9, 27.6, p-trend = 0.02). There were no important associations among children, but several inverse associations among 60–80 year olds. CONCLUSION: This exploratory, cross-sectional analysis revealed a number of interesting associations with different phthalate metabolites and obesity outcomes, including notable differences by gender and age subgroups. Effects of endocrine disruptors, such as phthalates, may depend upon endogenous hormone levels, which vary dramatically by age and gender. Individual phthalates also have different biologic and hormonal effects. Although our study has limitations, both of these factors could explain some of the variation in the observed associations. These preliminary data support the need for prospective studies in populations at risk for obesity.National Institutes of Environmental Health Sciences (R21ES013724

Social disparities in exposures to bisphenol A and polyfluoroalkyl chemicals: a cross-sectional study within NHANES 2003-2006

<p>Abstract</p> <p>Background</p> <p>Bisphenol A (BPA) and polyfluoroalkyl chemicals (PFCs) are suspected endocrine disrupting compounds known to be ubiquitous in people's bodies. Population disparities in exposure to these chemicals have not been fully characterized.</p> <p>Methods</p> <p>We analyzed data from the 2003-2006 National Health and Nutrition Examination Survey. Using multivariable linear regression we examined the association between urinary concentrations of BPA, serum concentrations of four PFCs, and multiple measures of socioeconomic position (SEP): family income, education, occupation, and food security. We also examined associations with race/ethnicity.</p> <p>Results</p> <p>All four PFCs were positively associated with family income, whereas BPA was inversely associated with family income. BPA concentrations were higher in people who reported very low food security and received emergency food assistance than in those who did not. This association was particularly strong in children: 6-11 year-olds whose families received emergency food had BPA levels 54% higher (95% CI, 13 to 112%) than children of families who did not. For BPA and PFCs we saw smaller and less consistent associations with education and occupation. Mexican Americans had the lowest concentrations of any racial/ethnic group of both types of chemicals; for PFCs, Mexican Americans not born in the U.S. had much lower levels than those born in the U.S.</p> <p>Conclusions</p> <p>People with lower incomes had higher body burdens of BPA; the reverse was true for PFCs. Family income with adjustment for family size was the strongest predictor of chemical concentrations among the different measures of SEP we studied. Income, education, occupation, and food security appear to capture different aspects of SEP that may be related to exposure to BPA and PFCs and are not necessarily interchangeable as measures of SEP in environmental epidemiology studies. Differences by race/ethnicity were independent of SEP.</p

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements

Th17-skewed immune response and cluster of differentiation 40 ligand expression in canine steroid-responsive meningitis-arteritis, a large animal model for neutrophilic meningitis

Background: Steroid-responsive meningitis-arteritis (SRMA) is an immune-mediated disorder characterized by neutrophilic pleocytosis and an arteritis particularly in the cervical leptomeninges. Previous studies of the disease have shown increased levels of IL-6 and TGF-beta(1) in cerebrospinal fluid (CSF). In the presence of these cytokines, naive CD4+ cells differentiate into Th17 lymphocytes which synthesize interleukin 17 (IL-17). It has been shown that IL-17 plays an active role in autoimmune diseases, it induces and mediates inflammatory responses and has an important role in recruitment of neutrophils. The hypothesis of a Th17-skewed immune response in SRMA should be supported by evaluating IL-17 and CD40L, inducing the vasculitis. Methods: An enzyme-linked immunosorbent assay (ELISA) was performed to measure IL-17 and CD40L in serum and CSF from a total of 79 dogs. Measurements of patients suffering from SRMA in the acute state (SRMA A) were compared with levels of patients under treatment with steroids (SRMA T), recurrence of the disease (SRMA R), other neurological disorders, and healthy dogs, using the two-part test. Additionally, secretion of IL-17 and interferon gamma (IFN-gamma) from the peripheral blood mononuclear cells (PBMCs) was confirmed by an enzyme-linked immunospot (ELISpot) assay. Results: Significant higher levels of IL-17 were found in CSF of dogs with SRMA A compared with SRMA T, other neurological disorders and healthy dogs (p < 0.0001). In addition, levels of CD40L in CSF in dogs with SRMA A and SRMA R were significantly higher than in those with SRMA T (p = 0.0004) and healthy controls (p = 0.014). Furthermore, CSF concentrations of IL-17 and CD40L showed a strong positive correlation among each other (rSpear = 0.6601;p < 0.0001) and with the degree of pleocytosis (rSpear = 0.8842;p < 0.0001 and rSpear = 0.6649;p < 0.0001, respectively). IL-17 synthesis from PBMCs in SRMA patients was confirmed;however, IL-17 is mainly intrathecally produced. Conclusions: These results imply that Th17 cells are inducing the autoimmune response in SRMA and are involved in the severe neutrophilic pleocytosis and disruption of the blood-brain barrier (BBB). CD-40L intrathecal synthesis might be involved in the striking vasculitis. The investigation of the role of IL-17 in SRMA might elucidate important pathomechanism and open new therapeutic strategies

Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)