Numeracy is a term that has been used in a variety of ways. It encompasses formal and informal mathematics, cultural practices with mathematical content, and behavior mediated by mathematical properties even when these properties are not verbally accessible. The study of numeracy explores a broad range of mathematical competencies across species, cultures, and the human lifespan. Human numeracy has universal characteristics based on biological mechanisms and developmental trajectories as well as culturally variable representation systems, practices, and values.

Studies with diverse species show that animals are sensitive to number (see Gallistel 1990 for a review). This literature suggests that there are innate capabilities that have evolved to support numeracy in humans (Gallistel and Gelman 1992). A variety of sources of evidence point to early numerical abilities in human infants (see INFANT COGNITION). For example, infants as early as the first week of life have been shown to discriminate between different small numbers (Antell and Keating 1983). The possibility that this discrimination is carried out by a cognitive mechanism encompassing several modalities has been debated (Starkey, Spelke, and Gelman 1990). In addition, studies have shown that infants have some knowledge of the effects of numerical transformations such as addition and subtraction (Wynn 1992).

Numerical competencies evident in the human infant are strong candidates for universal aspects of human numeracy. However, this does not necessarily discount the role of culture in developing human numeracy. Within the framework of EVOLUTIONARY PSYCHOLOGY, it is argued that universal characteristics of numeracy provide innate starting points for numeracy development, which, in turn, is influenced by culturally specific systems of knowledge (Cosmides and Tooby 1994). Similarly, within the neo-Piagetian framework, children are seen not simply as passing through a universal set of stages, but also as setting out on a unique cognitive journey that is guided by cultural practices (Case and Okamoto 1996). In this sense, numeracy is viewed as a cultural practice that builds on innate mechanisms for understanding quantities. The result is a conceptual structure for numeracy that reflects both universal and culture-sensitive characteristics. These conceptual structures are relatively similar across cultures that provide similar problem-solving experiences in terms of schooling and everyday life. On the other hand, mastery levels of particular tasks or skills may differ from one culture to another depending on the degree to which they are valued in each culture (Okamoto et al. 1996). In addition, cultures influence mathematical practices through the belief systems associated with numeracy, as well as through tools and artifacts (e.g., symbol systems) that support numeracy. A broad array of human activities to which mathematical thinking is applied are interwoven with cultural artifacts, social conventions, and social interactions (Nunes, Schliemann, and Carraher 1993; Saxe 1991).

Cultures have developed systems of signs that provide ways of thinking about quantitative information (see LANGUAGE AND CULTURE). Different systems shed light on different aspects of knowing. That is, they provide a means to extend the ability to deal with numbers; at the same time, they constrain numerical activities. For example, the Oksapmin of Papua New Guinea have a counting system using body parts, with no base structure, that only goes up to 27 (Saxe 1982). This way of quantifying is fully adequate for the numerical tasks of traditional life. It does not, however, facilitate easy computation or the counting of objects beyond 27. In contrast, the perfectly regular base-10 system of many Asian languages appears to make the mastery of base-10 concepts easier for children beginning school than the less regular base-10 systems of many European languages, including English (Miura et al. 1993). These various representational systems are culture-specific tools to deal with counting and computing, and all cultures seem to have them. Other culture-specific representation systems have been identified for locating (geometry, navigation), measuring, designing (form, shape, pattern), playing (rules, strategies), and explaining (Bishop 1991).

Further cultural variations in mathematical behavior are manifest in the ways that people use mathematical representations in the context of everyday activities (see SITUATED COGNITION AND LEARNING). Although they use the same counting numbers for different activities, child street vendors in Brazil were observed to use different computational strategies when selling than when doing school-like problems (Nunes, Schliemann, and Carraher 1993). While selling, they chose to use oral computation and strategies such as decomposition and repeated groupings. On school-like problems, they chose to use paper and pencil with standard algorithms and showed a markedly higher rate of error. Research in other domains, for example measurement (Gay and Cole 1967) and proportional reasoning (Nunes, Schliemann, and Carraher 1993), further confirms that informal mathematics can be effective and does not depend upon schooling for its development.

One characteristic of ethnomathematics, as informal mathematics or NAIVE MATHEMATICS is commonly called, is that the mathematics is used in pursuit of other goals rather than solely for the sake of the mathematics as in school or among professional mathematicians. As new goals arise, representational systems and practices develop to address the emergent goals. For instance, as the Oksapmin became more involved with the money economy, their "body" counting system began to change toward a base system (Saxe 1982). Although the differences between informal and school mathematics are often stressed (Bishop 1991), skills developed in the informal domain can be used to address new goals and practices in the school setting. In Liberian schools it was found that the most successful elementary students were those who combined the strategies from their indigenous mathematics with the algorithms taught in school (Brenner 1985). Similarly, Oksapmin and Brazilian children benefit from using their informal mathematics to learn school mathematics (Saxe 1985, 1991). Because conflicts between informal and school mathematics frequently arise, a number of authors have argued for building bridges between these different cultures of mathematics (Bishop 1991; Gay and Cole 1967; Gerdes 1988).

In addition to the overt mathematical
practices already described, Gerdes (1988) has described *frozen* mathematics
as the mathematics embodied in the products of a culture such as
baskets, toys, and houses. Although the history of these objects
has typically been lost, the original designers of these cultural
artifacts employed mathematical principles in their design, according
to Gerdes. Mathematical traditions embodied in these artifacts can
provide interesting mathematical investigations that help children
understand their own cultural heritage as well as contemporary school
mathematics.

The study of numeracy and culture draws from diverse disciplines within the cognitive sciences including psychology, linguistics, biology, and anthropology. The strengths of each discipline should be utilized to provide a more coherent view of what numeracy is and how it interacts with culture. Much future work remains to be done to better understand the universal and culture-specific aspects of numeracy.

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