Do Exact Calculation and Computation Estimation Reflect the Same Skills? Developmental and Individual Differences Perspectives

Groups of children in 4th, 5th, and 6th grades and college students performed exact calculation and computation estimation tasks with two-digit multiplication problems. In the former they calculated the exact answer for each problem, and in the latter they estimated whether the result of each problem was larger or smaller than a given reference number. The analyses of speed and accuracy both showed different developmental patterns of the two tasks. While the accuracy of exact calculation increased with age in childhood, the accuracy of the estimation task reached its maximum level already in 4th grade and did not change with age. The reaction time of the exact calculation task was longer than that of the estimation task. The reaction time for both tasks remained constant in childhood and decreased in adulthood, with the improvement in speed larger for the exact calculation task. Similarly, within group variability in accuracy was larger in the exact calculation task than in the computation estimation task. Finally, low correlation was found between the accuracy of the two tasks. Together, these findings suggest that exact calculation and computation estimation reflect at least in part different skills

Non-commutativity and Supersymmetry

We study the extent to which the gauge symmetry of abelian Yang-Mills can be deformed under two conditions: first, that the deformation depend on a two-form scale. Second, that the deformation preserve supersymmetry. We show that (up to a single parameter) the only allowed deformation is the one determined by the star product. We then consider the supersymmetry algebra satisfied by NCYM expressed in commutative variables. The algebra is peculiar since the supercharges are not gauge-invariant. However, the action, expressed in commutative variables, appears to be quadratic in fermions to all orders in theta.Comment: 21 pages, LaTeX; a reference adde

Autoimmune Epilepsy: Some Epilepsy Patients Harbor Autoantibodies to Glutamate Receptors and dsDNA on both Sides of the Blood-brain Barrier, which may Kill Neurons and Decrease in Brain Fluids after Hemispherotomy

Purpose: Elucidating the potential contribution of specific autoantibodies (Ab's) to the etiology and/or pathology of some human epilepsies. Methods: Six epilepsy patients with Rasmussen's encephalitis (RE) and 71 patients with other epilepsies were tested for Ab's to the –B— peptide (amino acids 372-395) of the glutamate/AMPA subtype 3 receptor (GluR3B peptide), double-stranded DNA (dsDNA), and additional autoimmune disease-associated autoantigens, and for the ability of their serum and cerebrospinal-fluid (CSF) to kill neurons. Results: Elevated anti-GluR3B Ab's were found in serum and CSF of most RE patients, and in serum of 17/71 (24%) patients with other epilepsies. In two RE patients, anti-GluR3B Ab's decreased drastically in CSF following functional-hemispherotomy, in association with seizure cessation and neurological improvement. Serum and CSF of two RE patients, and serum of 12/71 (17%) patients with other epilepsies, contained elevated anti-dsDNA Ab's, the hallmark of systemic-lupus-erythematosus. The sera (but not the CSF) of some RE patients contained also clinically elevated levels of –classical— autoimmune Ab's to glutamic-acid-decarboxylase, cardiolipin, β2-glycoprotein-I and nuclear-antigens SS-A and RNP-70. Sera and CSF of some RE patients caused substantial death of hippocampal neurons. Conclusions: Some epilepsy patients harbor Ab's to GluR3 and dsDNA on both sides of the blood-brain barrier, and additional autoimmune Ab's only in serum. Since all these Ab's may be detrimental to the nervous system and/or peripheral organs, we recommend testing for their presence in epilepsy, and silencing their activity in Ab-positive patients

Solving Math Problems Approximately: A Developmental Perspective

<div><p>Although solving arithmetic problems approximately is an important skill in everyday life, little is known about the development of this skill. Past research has shown that when children are asked to solve multi-digit multiplication problems approximately, they provide estimates that are often very far from the exact answer. This is unfortunate as computation estimation is needed in many circumstances in daily life. The present study examined 4^th graders, 6^th graders and adults’ ability to estimate the results of arithmetic problems relative to a reference number. A developmental pattern was observed in accuracy, speed and strategy use. With age there was a general increase in speed, and an increase in accuracy mainly for trials in which the reference number was close to the exact answer. The children tended to use the sense of magnitude strategy, which does not involve any calculation but relies mainly on an intuitive coarse sense of magnitude, while the adults used the approximated calculation strategy which involves rounding and multiplication procedures, and relies to a greater extent on calculation skills and working memory resources. Importantly, the children were less accurate than the adults, but were well above chance level. In all age groups performance was enhanced when the reference number was smaller (vs. larger) than the exact answer and when it was far (vs. close) from it, suggesting the involvement of an approximate number system. The results suggest the existence of an intuitive sense of magnitude for the results of arithmetic problems that might help children and even adults with difficulties in math. The present findings are discussed in the context of past research reporting poor estimation skills among children, and the conditions that might allow using children estimation skills in an effective manner.</p></div

Average number of trials per strategy by age group and distance between the reference number and the exact answer.

<p>Bars indicate standard errors computed following Loftus and Mason [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0200136#pone.0200136.ref023" target="_blank">23</a>].</p

Mean number of trials that were solved by the approximate calculation strategy (left panel) and by the sense of magnitude strategy (right panel) by age and by the distance between the exact answer and the reference number.

<p>Mean number of trials that were solved by the approximate calculation strategy (left panel) and by the sense of magnitude strategy (right panel) by age and by the distance between the exact answer and the reference number.</p