Outcomes from skills projects conducted in the United States illustrate workplace perspectives regarding mathematical skills needed by workers. Following earlier research by a task force of the American Society of Training and Development (Carnevale, Gainer, and Meltzer, 1990), the Secretary of Labor's Commission on Achieving Necessary Skills (SCANS) (Packer, 1997) has differentiated between mastery of basic arithmetical skills and much broader and flexible understanding of principles and underlying ideas, subsumed under the notion of mathematical skills:

SCANS arithmetical skills: Performs basic computations; uses basic numerical concepts such as whole numbers and percentages in practical situations; makes reasonable estimates and arithmetic results without a calculator; and uses tables, graphs, diagrams and charts to obtain or convey quantitative information.

SCANS mathematical skills: Approaches practical problems by choosing appropriately from a variety of mathematical techniques; uses quantitative data to construct logical explanations for real world situations; expresses mathematical ideas and concepts orally and in writing; and understands the role of chance in the occurrence and prediction of events. (SCANS, 1991, p. 83)

Based on a later survey of employers, industry trainers, and educators, among others, Forman and Steen (1999) similarly argued that quantitative skills desired by employers are much broader than mere facility with the mechanics of addition, subtraction, multiplication, and division and familiarity with basic number facts; they also include some knowledge of statistics, probability, mental computation strategies, some grasp of proportional reasoning or modeling relationships, and broad problem-solving and communication skills about quantitative issues. Buckingham (1997), who studied what she called "specific and generic numeracies of the workplace" in some manufacturing industries in Australia, concluded that workplace numeracy is now about making decisions in the face of uncertainty in real situations, and that it encompasses far more than the basic skills traditionally associated with the term numeracy (as this term had been used in Australia).

Outcomes from skills projects are echoed in educational specifications. For example, basic skills projects in the United Kingdom and Australia influenced vocational education frameworks that name numeracy as an important skill, and describe stages or levels of accomplishment (Australian Education Council, 1992). The National Council for Vocational Qualifications Core Skills in the United Kingdom identified five levels of numeracy skill (Oates, 1992) that are closely linked to the sequence of content in the national school mathematics curriculum.

1.2 Broader life purposes

Since numeracy involves action in the real world, it is important to reflect on the kinds of purposes served by people's ability to act in a numerate way. Since people's numeracy is related to and may at times depend on people's literacy skills or other lifeskills, the purposes served by numeracy are expected to parallel those served by adults' literacy.