DL:
The knowledge and skills required to locate and use information contained in various formats (including job applications, payroll forms, transportation schedules, maps, tables, and graphics).
QL:
The knowledge and skills required to apply arithmetic operations, either alone or sequentially, to numbers embedded in printed materials (such as balancing a check book, figuring out a tip, completing an order form, or determining the amount of interest on a loan).

QL tasks as well as some DL tasks have addressed important aspects of people's mathematical knowledge and skills. For example, DL tasks required respondents to identify, understand, and interpret information given in various lists, tables, charts and displays; this information sometimes included quantitative information, such as numbers or percents. QL tasks required respondents to apply arithmetical operations learned mostly in elementary grades. However, these tasks did not require respondents to cope with other types of mathematical information (e.g., measurements, shapes) or with information whose processing does not require comprehension of text. In addition, tasks used in both scales called for a limited range of responses, i.e., exact computations or specific types of interpretations. Thus, while such tasks and responses are important by themselves, they represent only a subset of the much wider range of tasks and responses that are typical of many everyday and work tasks, such as sorting, measuring, estimating, conjecturing, or using models (e.g., formulas).

School assessments. IALS' central mission was assessing facets of real-world literacy, hence the QL scale focused on application of basic mathematical operations in response to functional tasks using realistic texts. Large-scale assessments of mathematical skills aimed at younger populations usually take quite different approaches. Selected such assessments, associated with the ongoing PISA (Project for International Student Assessment), organized by the OECD, and with the GED test in the US, are reviewed below. These assessments are reviewed to highlight issues that can inform the content of an assessment of adult numeracy skills, as well as to shed light on areas where an assessment of adult numeracy has to deviate from familiar forms of assessments that are common with school-age populations.

The PISA survey has developed a framework for assessing Mathematical Literacy, defined as follows:

An individual's ability to identify, to understand, to make well-founded judgments about, and to act towards the roles that mathematics plays in dealing with the world, as needed for that individual's current and future life as a constructive, concerned, and reflective citizen (PISA Mathematics Functional Expert Group, 1998).

This definition shows some overlap and consistency with the conception of numeracy used in the present framework as well as with broader conceptions of literacy as adopted by IALS and ALL. Yet, some key differences seem to include the following: