(1996). The role of anterior ectosylvian cortex in cross-modality orientation and approach behavior. Whether or not schooling is offered, children and adults all over the world develop an intuitive, naive mathematics. As long as number-relevant examples are part of their culture, people will learn to reason about and solve addition and subtraction problems with positive natural numbers. They also will rank order and compare continuous amounts, if they do not have to measure with equal units. The notion of equal units is hard, save for the cases of money and time. Universally, and without formal instruction, everyone can use money. Examples abound of child candy sellers, taxicab drivers, fishermen, carpenters, and so on developing fluent quantitative scripts, including one for proportional reasoning. Of note is that almost always these strategies use the natural numbers and nonformal notions of mathematical operations. For example, the favored proportions strategy for Brazilian fishermen can be dubbed the " integer proportional reasoning " : the rule for reasoning is that one whole number goes into another X number of times and there is no remainder. Intuitive mathematics serves a wide range of everyday math tasks. For example, Liberian tailors who have no schooling can solve arithmetic problems by laying out and counting familiar objects, such as buttons. Taxicab drivers and child fruit vendors in Brazil invent solutions that serve them well (Nunes, Schliemann, and Carraher 1993). Two kinds of theories vie for an account of the origins and acquisition of intuitive arithmetic. One idea is that knowledge of the counting numbers and their use in arithmetic tasks builds from a set of reinforced bits of learning about situated counting number routines. Given enough learning opportunities, principles of counting and arithmetic are induced (Fuson 1988). Despite the clear evidence that there are pockets of early mathematical competence, young children are far from perfect on tasks they can negotiate. Additionally, the range of set sizes and tasks they can deal with is limited. These facts constitute the empirical foundation for the " bit-bit " theory and would seem to constitute a problem for the " principle-first " account of intuitive mathematics , which proposes an innate, domain-specific, learning enabling structure. Although skeleton-like to start, such a structure serves to draw the beginning learner's attention to seek out, attend to, and assimilate number-relevant data— be these in the physical, social, cultural and mental environ-ments—that are available for the …
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