The conception of numeracy developed for ALL is built upon recent research and work done in several countries on functional demands of different life contexts, on the nature of adults' mathematical and statistical knowledge and skills, and on how such skills are applied or used in different circumstances. In light of the general intention of the ALL survey to provide information about a diverse set of lifeskills, this framework defines numeracy as follows:

Numeracy is the knowledge and skills required to effectively manage and respond to the mathematical demands of diverse situations.

However, since an assessment can only examine observed behavior, not internal processes or capacities, this framework uses a more detailed definition of "numerate behavior" as a means to guide the development of items for the survey.

Numerate behavior is observed when people manage a situation or solve a problem in a real context; it involves responding to information about mathematical ideas that may be represented in a range of ways; it requires the activation of a range of enabling knowledge, factors, and processes.

Both definitions above use broad concepts and terms whose specific meanings and underlying components are explained in more detail later in this document. The definitions imply that numeracy can be viewed as a functional competency that is somewhat different from the traditional notion of "knowing mathematics" in that it relates to the capacity to act and bring one's knowledge (mathematical and other) to bear on tasks in context.

Numeracy is assessed in the ALL survey by presenting to respondents short tasks with mathematical content that are embedded in real-life contexts. As illustrated by the sample items in Appendix 1, tasks require that respondents activate a range of knowledge and skills, and respond to different situations by computing, estimating, understanding notions of shape, length, volume, monetary units, measuring, understanding some statistical ideas, or interpreting simple formulas. Respondents are encouraged to use the tools provided, paper and pencil, a ruler and a four-function calculator, whenever they wish. Numeracy and its assessment is thus broader in scope than Quantitative Literacy, as defined in IALS, which refers to a person's ability to apply arithmetic operations to numbers embedded in print materials.

About this report

This report describes key stages in the development of the Numeracy assessment scale for the ALL survey that took place between 1998 and early 2003, in three parts:

Part A presents a conceptual discussion of the numeracy construct and its facets, examines approaches to assessment of mathematical skills, and reviews issues that influenced the item development process. This section includes most of the text that appeared in the original Numeracy framework published in 1999 on the ALL (then ILSS) website. Editorial changes were made to streamline the presentation and to respond to comments from external reviewers, but the material was kept mostly intact since it served as the conceptual foundation from which item development progressed starting in 1998.

Part B describes the development of the item pool and scoring guidelines, and the feasibility studies that led to the selection of 80 items for a Pilot study that took place in 2002.

Part C outlines the design of the ALL Pilot study and presents key results, on the basis of which 40 Numeracy items were selected for the main ALL assessment in 2003. Two appendices contain sample Numeracy items that have been released to the public (Appendix 1) and details of a scheme of complexity factors that was used to inform the evaluation of difficulty levels of items during the item development process (Appendix 2).