11. Selection of items for the Main Numeracy assessment

Following the above analyses, 40 items were chosen that together satisfy several requirements or goals that are outlined below. Information about the extent to which the selected 40 items satisfy these requirements is briefly described.

11.1 Facet coverage in scale

A primary goal for the items selected for the Main study is that they represent the various aspects of four facets outlined as part of the numeracy construct, so that the scale overall offers respondents an opportunity to demonstrate a variety of numeracy skills, tested within a range of realistic contexts.

Mathematical Idea and Type of Response. The first focus in selecting items was on covering the two key facets of "mathematical idea" (Facet 3) and "type of response" (Facet 2). A desired mix of the categories within these two facets was created and is listed in Table 3, and items of varying levels of difficulty were chosen to fit within that mix.

It should be noted that the categories within the facets are not mutually exclusive; that is, an item whose primary task involves "dimension" may also require dealing with "quantity" and one that requires interpretation may also involve estimation. Hence, the percentages in Table 3 are not absolute, as items could be classified in more than one way, depending on which of their several key demands are taken into consideration.

Contexts. Another consideration in selecting items for the Main study was to achieve a desirable mix of the contexts from which the tasks are drawn (Facet 1 in Table 1). Nearly half, 45%, of the 40 items chosen are situated in Everyday Life contexts, 25% are from situations that represent participation in the Larger Society, 20% are from the world of Work, and 10% represent more formal tasks that may be helpful in Further Learning.

Representations. A final concern was to vary the types of stimuli that were included in the final scale. Each type of stimuli listed in the description (Facet 4 in Table 1) is present in the 40 items, i.e., pictures, numbers and symbols, formulae, diagrams and maps, graphs, tables, and, of course, text. With respect to text, the 40 items selected include stimuli (and questions) that span the range from minimum text dependency to higher levels of dependency, as shown in Table 4. The level of literacy/ text dependence of the stimulus and the question is an important consideration, especially when comparisons are made to the QL scale used in IALS, where stimuli were often quite heavily text-based and required considerable literacy skills.