1.4 Research perspectives
A sizeable literature has accumulated over the last several decades regarding the ways in
which adults use mathematical skills or cope with mathematical tasks in both formal
(i.e., school-based) and informal (i.e., everyday or workplace) contexts. However, few
attempts have been made to synthesize this literature and examine its implications for
large-scale skills assessments. Some examples of research reports and theoretical discussions
that could be considered in this regard include: Rogoff and Lave, 1984; Resnick, 1987;
Saxe, 1988; Carraher, Schliemann, and Carraher, 1988; Scribner and Sachs, 1991;
Nunes, 1992; or Coben, 2000.
Based on an analysis of the above and related literature, Gal (1993), while at the
Numeracy Project at the National Center for Adult Literacy in the US, developed a
conceptual perspective on the nature of adults' numeracy and numerate behavior. Gal
(1993; 1997) argued that "numeracy" refers to the aggregate of skills, knowledge, and
dispositions that enable and support independent and effective management of diverse
types of quantitative situations. Gal further argued that the scope of adult numeracy is
broad in light of the need for different types of responses in different situations.
Some situations call for generative responses, i.e., computing a number or
generating an estimate or a decision. Examples are dealing with simple operations
(measuring the length of a shelf ), dealing with multi-step operations embedded in text
(such as completing a tax form) and making reasonable decisions (for example, choosing
the best loan). Other situations call for interpretive responses, i.e., making sense of
quantitative statements or data displays (as in a newspaper article reporting crime
statistics), and being able to ask critical questions about the information and arguments
presented without performing any calculations. Both types of situations, and many
mixed types, vary in terms of the literacy and communication skills they involve; in
some cases it may not be possible to separate literacy from numeracy skills. It has also
been suggested (Gal, 1997) that numerate behavior is enabled by dispositional
elements(beliefs, attitudes, habits of mind) that motivate and support effective behavior in any
given situation.
Gal (1993) also proposed that adults manage situations that call for application
of numeracy skills. A person may decide to sacrifice precision or accuracy to reduce
mental load or save time. A response may be reached in a computationally inefficient
way or be based on non-standard procedures, but this may not matter in real-life as
long as the individual expends time and effort in a way that is reasonable in light of the
demands of the situation and his or her goals. It follows that there may be important
differences between how adults respond to a school-oriented task (where adults may try
to apply only school-based, memorized procedures), and demonstrate numerate,
confident behavior in realistic situations. Cumming, Gal, and Ginsburg (1998) have
argued that many of these aspects of numerate behavior are not reflected in how tests
and test items are created and interpreted.
1.5 Assessment schemes
Some understanding of the mathematical needs of adult life can also be gleaned from
an examination of large-scale assessment efforts, used either with adults or school students.
Adult assessments. A framework developed by Kirsch and Mosenthal (see Kirsch,
Jungblut, and Mosenthal, 1998) to describe adults' literacy skills, including aspects of
adult's quantitative skills, has been widely implemented in multiple national and
international assessment projects, most recently the International Adult Literacy Survey
(IALS; see Statistics Canada and OECD, 1996, 1997). The IALS framework made
use of three literacy scales—Prose Literacy, Document Literacy, and Quantitative
Literacy—to operationalize its conception of literacy. The ALL domain of numeracy is
most closely related to the Document Literacy (DL) and Quantitative Literacy (QL)
scales, which were defined as follows.
|