Conceptual knowledge of decimal arithmetic

In 2 studies (Ns = 55 and 54), the authors examined a basic form of conceptual understanding of rational number arithmetic, the direction of effect of decimal arithmetic operations, at a level of detail useful for informing instruction. Middle school students were presented tasks examining knowledge of the direction of effects (e.g., "True or false: 0.77 * 0.63 > 0.77"), knowledge of decimal magnitudes, and knowledge of decimal arithmetic procedures. Their confidence in their direction of effect judgments was also assessed. The authors found (a) most students incorrectly predicted the direction of effect of multiplication and division with decimals below 1; (b) this pattern held for students who accurately compared the magnitudes of individual decimals and correctly executed decimal arithmetic operations; (c) explanations of direction of effect judgments that cited both the arithmetic operation and the numbers' magnitudes were strongly associated with accurate judgments; and (d) judgments were more accurate when multiplication problems involved a whole number and a decimal below 1 than with 2 decimals below 1. Implications of the findings for instruction are discussed

Hard lessons : Why rational number arithmetic is so difficult for so many people

Fraction and decimal arithmetic pose large difficulties for many children and adults. This is a serious problem because proficiency with these skills is crucial for learning more advanced mathematics and science and for success in many occupations. This review identifies two main classes of difficulties that underlie poor understanding of rational number arithmetic: inherent and culturally contingent. Inherent sources of difficulty are ones that are imposed by the task of learning rational number arithmetic, such as complex relations among fraction arithmetic operations. They are present for all learners. Culturally contingent sources of difficulty are ones that vary among cultures, such as teacher understanding of rational numbers. They lead to poorer learning among students in some places rather than others. We conclude by discussing interventions that can improve learning of rational number arithmetic

Predicting adaptive expertise with rational number arithmetic

Background. Adaptive expertise is a highly valued outcome of mathematics curricula. One aspect of adaptive expertise with rational numbers is adaptive rational number knowledge, which refers to the ability to integrate knowledge of numerical characteristics and relations in solving novel tasks. Even among students with strong conceptual and procedural knowledge of rational numbers, there are substantial individual differences in adaptive rational number knowledge.Aims. We aimed to examine how a wide range of domain-general and mathematically specific skills and knowledge predicted different aspects of rational number knowledge, including procedural, conceptual, and adaptive rational number knowledge.Sample. 173 6th and 7th grade students from a school in the southeastern US (51% female) participated in the study.Methods. At three time points across 1.5 years, we measured students’ domaingeneral and domain-specific skills and knowledge.Weused multiple hierarchal regression analysis to examine how these predictors related to rational number knowledge at the third time point.Result. Prior knowledge of rational numbers, general mathematical calculation knowledge, and spontaneous focusing on multiplicative relations (SFOR) tendency uniquely predicted adaptive rational number knowledge, after taking into account domain-general and mathematically specific skills and knowledge. Although conceptual knowledge of rational numbers and general mathematical achievement also predicted later conceptual and procedural knowledge of rational numbers, SFOR tendency did not.Conclusion. Results suggest expanding investigations of mathematical development to also explore different features of adaptive expertise as well as spontaneous mathematical focusing tendencies.</p

Predicting Successful Aging in a Population-Based Sample of Georgia Centenarians

Used a population-based sample (Georgia Centenarian Study, GCS), to determine proportions of centenarians reaching 100 years as (1) survivors (43%) of chronic diseases first experienced between 0–80 years of age, (2) delayers (36%) with chronic diseases first experienced between 80–98 years of age, or (3) escapers (17%) with chronic diseases only at 98 years of age or older. Diseases fall into two morbidity profiles of 11 chronic diseases; one including cardiovascular disease, cancer, anemia, and osteoporosis, and another including dementia. Centenarians at risk for cancer in their lifetime tended to be escapers (73%), while those at risk for cardiovascular disease tended to be survivors (24%), delayers (39%), or escapers (32%). Approximately half (43%) of the centenarians did not experience dementia. Psychiatric disorders were positively associated with dementia, but prevalence of depression, anxiety, and psychoses did not differ significantly between centenarians and an octogenarian control group. However, centenarians were higher on the Geriatric Depression Scale (GDS) than octogenarians. Consistent with our model of developmental adaptation in aging, distal life events contribute to predicting survivorship outcome in which health status as survivor, delayer, or escaper appears as adaptation variables late in life

Sensitivity and uncertainty analysis for the tritium breeding ratio of a DEMO fusion reactor with a helium cooled pebble bed blanket

An uncertainty analysis was performed for the tritium breeding ratio (TBR) of a fusion power plant of the European DEMO type using the MCSEN patch to the MCNP Monte Carlo code. The breeding blanket was of the type Helium Cooled Pebble Bed (HCPB), currently under development in the European Power Plant Physics and Technology (PPPT) programme for a fusion power demonstration reactor (DEMO). A suitable 3D model of the DEMO reactor with HCPB blanket modules, as routinely used for blanket design calculations, was employed. The nuclear cross-section data were taken from the JEFF-3.2 data library. For the uncertainty analysis, the isotopes H-1, Li-6, Li-7, Be-9, O-16, Si-28, Si-29, Si-30, Cr-52, Fe-54, Fe-56, Ni-58, W-182, W-183, W-184 and W-186 were considered. The covariance data were taken from JEFF-3.2 where available. Otherwise a combination of FENDL-2.1 for Li-7, EFF-3 for Be-9 and JENDL-3.2 for O-16 were compared with data from TENDL-2014. Another comparison was performed with covariance data from JEFF-3.3T1. The analyses show an overall uncertainty of ± 3.2% for the TBR when using JEFF-3.2 covariance data with the mentioned additions. When using TENDL-2014 covariance data as replacement, the uncertainty increases to ± 8.6%. For JEFF-3.3T1 the uncertainty result is ± 5.6%. The uncertainty is dominated by O-16, Li-6 and Li-7 cross-sections

Current Opinions on Optimal Management of Basilar Artery Occlusion: After the BEST of BASICS Survey

Background The best management of basilar artery occlusion (BAO) remains uncertain. The BASICS (Basilar Artery International Cooperation Study) and the BEST (Basilar Artery Occlusion Endovascular Intervention Versus Standard Medical Treatment) trials reported neutral results. We sought to understand physicians’ approaches to BAOs and whether further BAO randomized controlled trials were warranted. Methods We conducted an online international survey from January to March 2022 to stroke neurologists and neurointerventionalists. Survey questions were designed to examine clinical and imaging parameters under which clinicians would offer (or rescind) a patient with BAO to endovascular therapy (EVT) or best medical management versus enrollment into a randomized clinical trial. Results Of >3002 invited participants, 1245 responded (41.4% response rate) from 73 countries, including 54.7% stroke neurologists and 43.6% neurointerventionalists. More than 95% of respondents would offer EVT to patients with BAO, albeit in various clinical circumstances. There were 70.0% of respondents who indicated that the BASICS and BEST trials did not change their practice. Only 22.1% of respondents would perform EVT according to anterior circulation occlusion criteria. The selection of patients for BAO EVT by clinical severity, timing, and imaging modality differed according to geography, specialty, and country income level. Over 80% of respondents agreed that further randomized clinical trials for BAO were warranted. Moreover, 45.6% of respondents indicated they would find it acceptable to enroll all trial‐eligible patients into the medical arm of a BAO trial, whereas 26.3% would not enroll. Conclusion Most stroke physicians continue to believe in the efficacy of EVT in selected patients with BAO in spite of BEST and BASICS. There is no consensus on which selection criteria to use, and few clinicians would use anterior circulation occlusion criteria for BAOs. Further randomized clinical trials for BAO are warranted