On recognizing and formulating mathematical problems

When mathematics is used to help people cope with real-life situations, a three-stage intellectual process is involved. First, a person becomes aware of a problem-situation which stimulates him to generate a problem-statement, a verbal story-problem. This may be in writing, expressed orally, or merely thought and evidenced by other behavior. Second, he transforms the verbal problem-statement into a mathematical formulation. Third, he analyzes this mathematically stated problem into subproblems to which the solution is more immediate.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43864/1/11251_2004_Article_BF00052419.pd

Face scanning and spontaneous emotion preference in Cornelia de Lange syndrome and Rubinstein-Taybi syndrome

Background Existing literature suggests differences in face scanning in individuals with different socio-behavioural characteristics. Cornelia de Lange syndrome (CdLS) and Rubinstein-Taybi syndrome (RTS) are two genetically defined neurodevelopmental disorders with unique profiles of social behaviour. Methods Here, we examine eye gaze to the eye and mouth regions of neutrally expressive faces, as well as the spontaneous visual preference for happy and disgusted facial expressions compared to neutral faces, in individuals with CdLS versus RTS. Results Results indicate that the amount of time spent looking at the eye and mouth regions of faces was similar in 15 individuals with CdLS and 17 individuals with RTS. Both participant groups also showed a similar pattern of spontaneous visual preference for emotions. Conclusions These results provide insight into two rare, genetically defined neurodevelopmental disorders that have been reported to exhibit contrasting socio-behavioural characteristics and suggest that differences in social behaviour may not be sufficient to predict attention to the eye region of faces. These results also suggest that differences in the social behaviours of these two groups may be cognitively mediated rather than subcortically mediated

On the Validation of Computer Science Theories

We address normatively the demarcation problem for Computer Science: How can Computer Science research be conducted scientifically? First we attempt to delimit the subject matter of Computer Science, and conclude that it is not computers but programs. Since programs are not physical objects, it is difficult to see how they can be studied empirically. The rest of the paper is devoted to an explanation of how this can be done. This method is first illustrated by a hypothesis of narrow scope, analogous to a physical law. Next it is illustrated by a theory of wide scope — the Turing Machine model of computers. The approach is summarized in the conclusions.Chief of Naval Researc