Froebel Gifts: A Tool to Reinforce Conceptual Knowledge of Fractions

In this manuscript, we review Froebel Gifts and its use as an effective, practical tool to teach and reinforce conceptual knowledge that students should acquire regarding fractions. Furthermore, we set forth and examine the different techniques and methods that can be used to explore this manipulative as a teaching material, and end focusing on the fifth Froebel Gift and several practical and interesting activities that can be developed with this material in class

“From School of Crisis to Distinguished”: Using Maslow\u27s Hierarchy in a Rural Underperforming School

Despite conditions that would work against a small and rural school in an impoverish rural area of the United States, Fairway Elementary School has managed to excel in its accountability measures. Through interviews with faculty, staff, teachers, students, and parents of children at Fairway Elementary School a model was developed through the lens of Maslow’s Hierarchy of Needs. It was found that a new administrator at the school started with the physiological needs of the children and are now working within the esteem stage of Maslow’s Hierarchy. Details from each stage of the hierarchy are provided as a promising practice for other rural schools. Fairway Elementary continues to succeed in their efforts to improve not only student achievement, but the culture of their school within an impoverished community

An Analysis of Graduate Teaching Assistants’ Noticing Skills During Calculus and Physics Tutoring Scenarios

Professional noticing of mathematical thinking, as defined by Jacobs, Lamb, and Philipp (2010) can be broken down into three components: attending to relevant cues, interpreting the mathematical understanding, and deciding the next best instructional steps. Most research on this topic has been conducted with elementary children. However, there is a gap in the research on professional noticing at more advanced levels, particularly college students. The purpose of this study was to take the concept of professional noticing and apply it to mathematics education at the post-secondary level. Specifically, the question we sought to answer in this study was: To what extent do mathematics and physics Teaching Assistants (TAs) attend and interpret student thinking when making decisions in their classroom? Mathematics and Physics TAs (n = 20) participated in this study focusing on their professional noticing skills when analyzing a college student struggling with two calculus-based problems. Results show that the TAs struggle most with interpreting student understanding and that those with more experience are better at deciding the next steps. Additionally, there is some data to support that knowledge of the content can impact their decision-making skills

Climate impacts associated with reduced diet diversity in children across nineteen countries

It is widely anticipated that climate change will negatively affect both food security and diet diversity. Diet diversity is especially critical for children as it correlates with macro and micronutrient intake important for child development. Despite these anticipated links, little empirical evidence has demonstrated a relationship between diet diversity and climate change, especially across large datasets spanning multiple global regions. Here we use survey data from 19 countries and more than 107,000 children, coupled with 30 years of precipitation and temperature data, to explore the relationship of climate to child diet diversity while controlling for other agroecological, geographic, and socioeconomic factors. We find that higher long-term temperatures are associated with decreases in overall child diet diversity, while higher rainfall in the previous year, compared to the long-term average, is associated with greater diet diversity. Examining six regions individually, we find that five have significant reductions in diet diversity associated with higher temperatures while three have significant increases in diet diversity associated with higher precipitation. In some regions, the statistical effect of climate on diet diversity is comparable to or greater than other common development efforts including those focused on education, improved water and toilets, and poverty reduction. These results suggest that warming temperatures and increasing rainfall variability could have profound short- and long-term impacts on child diet diversity, potentially undermining widespread development interventions aimed at improving food security

Decimal Dilemmas: Interpreting and Addressing Misconceptions

In this article, a student's misconception of multiplication and division of decials is analyzed and findings are presented from preservice teachers’ interpretation of that misconception. The authors then highlight common decimal misconceptions, outline two strategies for addressing such misconceptions in the classroom, and include final remarks connecting the professional noticing framework with addressing misconceptions in mathematics

Teaching Mathematics with Technology: TPACK and Effective Teaching Practices

This paper examines how 17 secondary mathematics teacher candidates (TCs) in four university teacher preparation programs implemented technology in their classrooms to teach for conceptual understanding in online, hybrid, and face to face classes during COVID-19. Using the Professional Development: Research, Implementation, and Evaluation (PrimeD) framework, TCs, classroom mentor teachers, field experience supervisors, and university faculty formed a Networked Improvement Community (NIC) to discuss a commonly agreed upon problem of practice and a change idea to implement in the classroom. Through Plan-Do-Study-Act cycles, participants documented their improvement efforts and refinements to the change idea and then reported back to the NIC at the subsequent monthly meeting. The Technology Pedagogical Content Knowledge framework (TPACK) and the TPACK levels rubric were used to examine how teacher candidates implemented technology for Mathematics conceptual understanding. The Mathematics Classroom Observation Protocol for Practices (MCOP2) was used to further examine how effective mathematics teaching practices (e.g., student engagement) were implemented by TCs. MCOP2 results indicated that TCs increased their use of effective mathematics teaching practices. However, growth in TPACK was not significant. A relationship between TPACK and MCOP2 was not evident, indicating a potential need for explicit focus on using technology for mathematics conceptual understanding

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering

We analyze the anisotropic clustering of massive galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) sample, which consists of 264,283 galaxies in the redshift range 0.43 < z < 0.7 spanning 3,275 square degrees. Both peculiar velocities and errors in the assumed redshift-distance relation ("Alcock-Paczynski effect") generate correlations between clustering amplitude and orientation with respect to the line-of-sight. Together with the sharp baryon acoustic oscillation (BAO) standard ruler, our measurements of the broadband shape of the monopole and quadrupole correlation functions simultaneously constrain the comoving angular diameter distance (2190 +/- 61 Mpc) to z=0.57, the Hubble expansion rate at z=0.57 (92.4 +/- 4.5 km/s/Mpc), and the growth rate of structure at that same redshift (d sigma8/d ln a = 0.43 +/- 0.069). Our analysis provides the best current direct determination of both DA and H in galaxy clustering data using this technique. If we further assume a LCDM expansion history, our growth constraint tightens to d sigma8/d ln a = 0.415 +/- 0.034. In combination with the cosmic microwave background, our measurements of DA, H, and growth all separately require dark energy at z > 0.57, and when combined imply \Omega_{\Lambda} = 0.74 +/- 0.016, independent of the Universe's evolution at z<0.57. In our companion paper (Samushia et al. prep), we explore further cosmological implications of these observations.Comment: 19 pages, 11 figures, submitted to MNRAS, comments welcom

Global, regional, and national burden of neurological disorders, 1990–2016 : a systematic analysis for the Global Burden of Disease Study 2016

Background: Neurological disorders are increasingly recognised as major causes of death and disability worldwide. The aim of this analysis from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2016 is to provide the most comprehensive and up-to-date estimates of the global, regional, and national burden from neurological disorders. Methods: We estimated prevalence, incidence, deaths, and disability-adjusted life-years (DALYs; the sum of years of life lost [YLLs] and years lived with disability [YLDs]) by age and sex for 15 neurological disorder categories (tetanus, meningitis, encephalitis, stroke, brain and other CNS cancers, traumatic brain injury, spinal cord injury, Alzheimer's disease and other dementias, Parkinson's disease, multiple sclerosis, motor neuron diseases, idiopathic epilepsy, migraine, tension-type headache, and a residual category for other less common neurological disorders) in 195 countries from 1990 to 2016. DisMod-MR 2.1, a Bayesian meta-regression tool, was the main method of estimation of prevalence and incidence, and the Cause of Death Ensemble model (CODEm) was used for mortality estimation. We quantified the contribution of 84 risks and combinations of risk to the disease estimates for the 15 neurological disorder categories using the GBD comparative risk assessment approach. Findings: Globally, in 2016, neurological disorders were the leading cause of DALYs (276 million [95% UI 247–308]) and second leading cause of deaths (9·0 million [8·8–9·4]). The absolute number of deaths and DALYs from all neurological disorders combined increased (deaths by 39% [34–44] and DALYs by 15% [9–21]) whereas their age-standardised rates decreased (deaths by 28% [26–30] and DALYs by 27% [24–31]) between 1990 and 2016. The only neurological disorders that had a decrease in rates and absolute numbers of deaths and DALYs were tetanus, meningitis, and encephalitis. The four largest contributors of neurological DALYs were stroke (42·2% [38·6–46·1]), migraine (16·3% [11·7–20·8]), Alzheimer's and other dementias (10·4% [9·0–12·1]), and meningitis (7·9% [6·6–10·4]). For the combined neurological disorders, age-standardised DALY rates were significantly higher in males than in females (male-to-female ratio 1·12 [1·05–1·20]), but migraine, multiple sclerosis, and tension-type headache were more common and caused more burden in females, with male-to-female ratios of less than 0·7. The 84 risks quantified in GBD explain less than 10% of neurological disorder DALY burdens, except stroke, for which 88·8% (86·5–90·9) of DALYs are attributable to risk factors, and to a lesser extent Alzheimer's disease and other dementias (22·3% [11·8–35·1] of DALYs are risk attributable) and idiopathic epilepsy (14·1% [10·8–17·5] of DALYs are risk attributable). Interpretation: Globally, the burden of neurological disorders, as measured by the absolute number of DALYs, continues to increase. As populations are growing and ageing, and the prevalence of major disabling neurological disorders steeply increases with age, governments will face increasing demand for treatment, rehabilitation, and support services for neurological disorders. The scarcity of established modifiable risks for most of the neurological burden demonstrates that new knowledge is required to develop effective prevention and treatment strategies. Funding: Bill & Melinda Gates Foundation

Crowdsourcing hypothesis tests: Making transparent how design choices shape research results

To what extent are research results influenced by subjective decisions that scientists make as they design studies? Fifteen research teams independently designed studies to answer fiveoriginal research questions related to moral judgments, negotiations, and implicit cognition. Participants from two separate large samples (total N > 15,000) were then randomly assigned to complete one version of each study. Effect sizes varied dramatically across different sets of materials designed to test the same hypothesis: materials from different teams renderedstatistically significant effects in opposite directions for four out of five hypotheses, with the narrowest range in estimates being d = -0.37 to +0.26. Meta-analysis and a Bayesian perspective on the results revealed overall support for two hypotheses, and a lack of support for three hypotheses. Overall, practically none of the variability in effect sizes was attributable to the skill of the research team in designing materials, while considerable variability was attributable to the hypothesis being tested. In a forecasting survey, predictions of other scientists were significantly correlated with study results, both across and within hypotheses. Crowdsourced testing of research hypotheses helps reveal the true consistency of empirical support for a scientific claim.</div

Global age-sex-specific fertility, mortality, healthy life expectancy (HALE), and population estimates in 204 countries and territories, 1950-2019 : a comprehensive demographic analysis for the Global Burden of Disease Study 2019

Background: Accurate and up-to-date assessment of demographic metrics is crucial for understanding a wide range of social, economic, and public health issues that affect populations worldwide. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 produced updated and comprehensive demographic assessments of the key indicators of fertility, mortality, migration, and population for 204 countries and territories and selected subnational locations from 1950 to 2019. Methods: 8078 country-years of vital registration and sample registration data, 938 surveys, 349 censuses, and 238 other sources were identified and used to estimate age-specific fertility. Spatiotemporal Gaussian process regression (ST-GPR) was used to generate age-specific fertility rates for 5-year age groups between ages 15 and 49 years. With extensions to age groups 10–14 and 50–54 years, the total fertility rate (TFR) was then aggregated using the estimated age-specific fertility between ages 10 and 54 years. 7417 sources were used for under-5 mortality estimation and 7355 for adult mortality. ST-GPR was used to synthesise data sources after correction for known biases. Adult mortality was measured as the probability of death between ages 15 and 60 years based on vital registration, sample registration, and sibling histories, and was also estimated using ST-GPR. HIV-free life tables were then estimated using estimates of under-5 and adult mortality rates using a relational model life table system created for GBD, which closely tracks observed age-specific mortality rates from complete vital registration when available. Independent estimates of HIV-specific mortality generated by an epidemiological analysis of HIV prevalence surveys and antenatal clinic serosurveillance and other sources were incorporated into the estimates in countries with large epidemics. Annual and single-year age estimates of net migration and population for each country and territory were generated using a Bayesian hierarchical cohort component model that analysed estimated age-specific fertility and mortality rates along with 1250 censuses and 747 population registry years. We classified location-years into seven categories on the basis of the natural rate of increase in population (calculated by subtracting the crude death rate from the crude birth rate) and the net migration rate. We computed healthy life expectancy (HALE) using years lived with disability (YLDs) per capita, life tables, and standard demographic methods. Uncertainty was propagated throughout the demographic estimation process, including fertility, mortality, and population, with 1000 draw-level estimates produced for each metric. Findings: The global TFR decreased from 2·72 (95% uncertainty interval [UI] 2·66–2·79) in 2000 to 2·31 (2·17–2·46) in 2019. Global annual livebirths increased from 134·5 million (131·5–137·8) in 2000 to a peak of 139·6 million (133·0–146·9) in 2016. Global livebirths then declined to 135·3 million (127·2–144·1) in 2019. Of the 204 countries and territories included in this study, in 2019, 102 had a TFR lower than 2·1, which is considered a good approximation of replacement-level fertility. All countries in sub-Saharan Africa had TFRs above replacement level in 2019 and accounted for 27·1% (95% UI 26·4–27·8) of global livebirths. Global life expectancy at birth increased from 67·2 years (95% UI 66·8–67·6) in 2000 to 73·5 years (72·8–74·3) in 2019. The total number of deaths increased from 50·7 million (49·5–51·9) in 2000 to 56·5 million (53·7–59·2) in 2019. Under-5 deaths declined from 9·6 million (9·1–10·3) in 2000 to 5·0 million (4·3–6·0) in 2019. Global population increased by 25·7%, from 6·2 billion (6·0–6·3) in 2000 to 7·7 billion (7·5–8·0) in 2019. In 2019, 34 countries had negative natural rates of increase; in 17 of these, the population declined because immigration was not sufficient to counteract the negative rate of decline. Globally, HALE increased from 58·6 years (56·1–60·8) in 2000 to 63·5 years (60·8–66·1) in 2019. HALE increased in 202 of 204 countries and territories between 2000 and 2019