Symbolic arithmetic knowledge without instruction

This article was published in the journal, Nature [© The Nature Publishing Group]. The definitive version is available at: http://dx.doi.org/10.1038/nature05850Symbolic arithmetic is fundamental to science, technology and economics, but its acquisition by children typically requires years of effort, instruction and drill. When adults perform mental arithmetic, they activate nonsymbolic, approximate number representations and their performance suffers if this nonsymbolic system is impaired. Nonsymbolic number representations also allow adults, children, and even infants to add or subtract pairs of dot arrays and to compare the resulting sum or difference to a third array, provided that only approximate accuracy is required. Here we report that young children, who have mastered verbal counting and are on the threshold of arithmetic instruction, can build on their nonsymbolic number system to perform symbolic addition and subtraction. Children across a broad socio-economic spectrum solved symbolic problems involving approximate addition or subtraction of large numbers, both in a laboratory test and in a school setting. Aspects of symbolic arithmetic therefore lie within the reach of children who have learned no algorithms for manipulating numerical symbols. Our findings help to delimit the sources of children’s difficulties learning symbolic arithmetic, and they suggest ways to enhance children’s engagement with formal mathematics

Pleasure in decision-making situations

BACKGROUND: This study explores the role of pleasure in decision making. RESULTS: In Experiment 1, 12 subjects were presented with a questionnaire containing 46 items taken from the literature. Twenty-three items described a situation where a decision should be made and ended with a suggested solution. The other items served as filler items. The subjects were requested not to make a decision but to rate the pleasure or displeasure they experienced when reading the situation described in the item. The subjects' ratings were then compared to the decisions on the same situations made by the other subjects of the studies published by other workers. The ratings of pleasure/displeasure given by our subjects correlated significantly with the choices published by other authors. This result satisfies a necessary condition for pleasure to be the key of the decision making process in theoretical situations. In Experiment 2, a new group of 12 subjects rated their experience of pleasure/displeasure when reading various versions of 50 situations taken from daily life where an ethical decision had to be made (Questionnaire I) including 200 items. This was followed by a multiple-choice test with the 50 situations (Questionnaire II) using the same 200 items and offering the various behaviors. Subjects tended to choose ethical and unethical responses corresponding to their highest pleasure rating within each problem. In all cases the subjects' behavior was higher than chance level, and thus, followed the trend to maximize pleasure. In Experiment 3, 12 subjects reading 50 mathematical short problems followed by correct and incorrect versions of the answer to the problem (Questionnaire III), including 200 items. This was followed by a multiple-choice mathematical test with the 50 problems (Questionnaire IV) using the same 200 items and offering the correct and incorrect answers. In questionnaire IV, subjects tended to choose correct as well as incorrect responses corresponding to their highest hedonic rating within each problem. In all cases the subjects' behavior was higher than chance level, and thus, followed the trend to maximize pleasure. CONCLUSIONS: The results of the three experiments support the hypothesis according to which decisions are made in the hedonic dimension of conscious experience