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158
Preschoolers ’ Dot Enumeration Abilities Are Markers of Their Arithmetic Competence
, 2014
"... The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development. Insofar as this is correct, these abilities may be diagnostic markers of math competence in preschoolers. However, unlik ..."
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The abilities to enumerate small sets of items (e.g., dots) and to compare magnitudes are claimed to be indexes of core numerical competences that scaffold early math development. Insofar as this is correct, these abilities may be diagnostic markers of math competence in preschoolers. However
A twominute paperandpencil test of symbolic and nonsymbolic numerical magnitude processing explains variability in primary school children‟s arithmetic competence
 PloS One
, 2013
"... Recently, there has been a growing emphasis on basic number processing competencies (such as the ability to judge which of two numbers is larger) and their role in predicting individual differences in schoolrelevant math achievement. Children’s ability to compare both symbolic (e.g. Arabic numerals ..."
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Cited by 2 (1 self)
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whether both symbolic and nonsymbolic magnitude comparison are related to children’s performance on tests of arithmetic competence and whether either of these factors relate to arithmetic achievement over and above other factors such as working memory and reading ability. In order to address
Précis of "The number sense"
"... Number sense " is a shorthand for our ability to quickly understand, approximate, and manipulate numerical quantities. My hypothesis is that number sense rests on cerebral circuits that have evolved specifically for the purpose of representing basic arithmetic knowledge. Four lines of evidence ..."
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Cited by 313 (25 self)
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of evidence suggesting that number sense constitutes a domainspecific, biologicallydetermined ability are reviewed: the presence of evolutionary precursors of arithmetic in animals; the early emergence of arithmetic competence in infants independently of other abilities, including language; the existence
Cultivating competence, selfefficacy, and intrinsic interest through proximal selfmotivation.
 Journal of Personality and Social Psychology,
, 1981
"... Abstract: The present experiment tested the hypothesis that selfmotivation through proximal goal setting serves as an effective mechanism for cultivating competencies, selfpercepts of efficacy, and intrinsic interest. Children who exhibited gross deficits and disinterest in mathematical tasks pur ..."
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Cited by 295 (6 self)
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Abstract: The present experiment tested the hypothesis that selfmotivation through proximal goal setting serves as an effective mechanism for cultivating competencies, selfpercepts of efficacy, and intrinsic interest. Children who exhibited gross deficits and disinterest in mathematical tasks
Mathematics and learning disabilities
 J LEARN DISABIL
, 2004
"... Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion of underlyin ..."
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Cited by 115 (6 self)
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Between 5 % and 8 % of schoolage children have some form of memory or cognitive deficit that interferes with their ability to learn concepts or procedures in one or more mathematical domains. A review of the arithmetical competencies of these children is provided, along with discussion
Classical arithmetic is part of intuitionistic arithmetic
"... mathematics is an argument to show that the correct logic to apply in mathematical reasoning is not classical but intuitionistic. In this article I wish to cast doubt on Dummett’s conclusion by outlining an alternative, motivated by consideration of a wellknown result of Kurt Gödel, to the standard ..."
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, to the standard view of the relationship between classical and intuitionistic arithmetic. I shall suggest that it is hard to find a perspective from which to arbitrate between the competing views. Let me start, then, by stating the standard view of the relationship, with which the account I shall be canvassing
Deciding bitvector arithmetic with abstraction
 IN PROC. TACAS 2007
, 2007
"... We present a new decision procedure for finiteprecision bitvector arithmetic with arbitrary bitvector operations. Our procedure alternates between generating under and overapproximations of the original bitvector formula. An underapproximation is obtained by a translation to propositional log ..."
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Cited by 58 (24 self)
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We present a new decision procedure for finiteprecision bitvector arithmetic with arbitrary bitvector operations. Our procedure alternates between generating under and overapproximations of the original bitvector formula. An underapproximation is obtained by a translation to propositional
A mental model for early arithmetic
 Journal of Experimental Psychology: General
, 1994
"... The authors examined young children's ability to solve nonverbal calculation problems in which they must determine how many items are in a hidden array after items have been added into or taken away from it. Earlier work showed that an ability to reliably solve such problems emerges earlier tha ..."
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Cited by 52 (6 self)
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at about 2 years and should be related to overall level of intellectual competence. The authors show that the ability to reliably solve nonverbal calculation tasks emerges only after 2 years of age and that performance on nonverbal calculation problems is highly related to overall level of intellectual
On Solving Presburger and Linear Arithmetic with SAT
 In Proc. of Formal Methods in ComputerAided Design (FMCAD 2002), LNCS
, 2002
"... We show a reduction to propositional logic from quantifierfree Presburger arithmetic, and disjunctive linear arithmetic, based on FourierMotzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification problems ..."
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Cited by 27 (2 self)
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We show a reduction to propositional logic from quantifierfree Presburger arithmetic, and disjunctive linear arithmetic, based on FourierMotzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification
Deciding Disjunctive Linear Arithmetic with
, 2004
"... Abstract. Disjunctive Linear Arithmetic (DLA) is a major decidable theory that is supported by almost all existing theorem provers. The theory consists of Boolean combinations of predicates of the form Σ n j=1aj · xj ≤ b, where the coefficients aj, the bound b and the variables x1... xn are of type ..."
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Cited by 1 (0 self)
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Real (R). We show a reduction to propositional logic from disjunctive linear arithmetic based on FourierMotzkin elimination. While the complexity of this procedure is not better than competing techniques, it has practical advantages in solving verification problems. It also promotes the option
Results 1  10
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158