When using sample data to decide whether two populations differ, laypeople attend to the difference between group means, but largely overlook within-group variability (Obrecht, Chapman, & Gelman, 2007). We show, first, that laypeople know about and use story-implied variability when making pairwise comparisons. Then we demonstrate that participants' sensitivity to variance in a dataset is boosted when presented in a context that implies consistent variance information. Statistical data were couched in stories about electrical conductivity measurements obtained from element samples (low-variability (...) category) or body weight measurements from samples of peoples (high-variability category). We manipulated, between participants, whether the data variance matched or mismatched the story-implied variability. Participants who received data in a matching context showed high sensitivity to variance, while those in the mismatching condition did not. Laypeople use statistical data to make reasonable inferences when those data are provided in a context that makes sense. (shrink)

Number concepts must support arithmetic inference. Using this principle, it can be argued that the integer concept of exactly ONE is a necessary part of the psychological foundations of number, as is the notion of the exact equality - that is, perfect substitutability. The inability to support reasoning involving exact equality is a shortcoming in current theories about the development of numerical reasoning. A simple innate basis for the natural number concepts can be proposed that embodies the arithmetic principle, supports (...) exact equality and also enables computational compatibility with real- or rational-valued mental magnitudes. (shrink)

‘Number sense’ is a short‐hand 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 suggesting that number sense constitutes a domain‐specific, biologically‐determined 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 of a homology (...) between the animal, infant, and human adult abilities for number processing; and the existence of a dedicated cerebral substrate. In adults of all cultures, lesions to the inferior parietal region can specifically impair number sense while leaving the knowledge of other cognitive domains intact. Furthermore, this region is demonstrably activated during number processing. I postulate that higher–level cultural devel‐opments in arithmetic emerge through the establishment of linkages between this core analogical representation and other verbal and visual representations of number notations. The neural and cognitive organization of those representations can explain why some mathematical concepts are intuitive, while others are so difficult to grasp. Thus, the ultimate foundations of mathematics rests on core representations that have been internalized in our brains through evolution. (shrink)