• PISA focuses on how students understand, use, and apply mathematical skills and mathematize problems that are related to the formal school mathematics curriculum the students were expected to cover as part of their studies.
• PISA puts only partial emphasis on the realism of tasks. Given that students have limited world experience, tasks can be contrived or use formal symbolism that assesses mostly formal knowledge of what was taught in schools.
• The PISA mathematical assessment is not explicitly interested either in tasks where mathematical information is embedded in text (realistic or otherwise), or in the influence of literacy skills on mathematical performance (despite the inclusion of the term "literacy" in "mathematical Literacy").

Nationally-recognized standardized tests used in several countries to assess the mathematical knowledge of adults are often in line with school-based assessments. For example, the GED test in the U.S. (used to grant a high-school equivalency diploma to adults who did not formally graduate from high-school), and the National Vocational Qualifications system in the U.K., both use items with characteristics that are more in line with school-related assessments of mathematical knowledge than with the QL scale. These tests rely heavily on multiple-choice questions, employ some tasks requiring manipulation of numbers without a meaningful context, and require the use of some formal mathematical notations in formulas, either memorized or provided as part of the test.

School-oriented assessments point to some general areas of mathematical knowledge and skill that both school graduates as well as early school leavers may need to have to effectively cope with the various challenges of adult life. Reviewing the PISA, the Third International Mathematics and Science Study (TIMSS), and similar assessments highlights the fact that some important mathematical skills and knowledge that these assessments aim to capture were not captured by the QL scale of IALS. For example, knowledge of "big ideas" related to shape and geometry or to chance and statistics, knowledge of measurement systems, or the ability to "model" the mathematical aspects of certain situations were not included.

The above discussion is not meant to be a comprehensive review of current large-scale assessments of schooling-related mathematical skills (see Robitaille and Travers, 1992), nor a criticism of the QL scale of the IALS assessment framework. It simply reiterates that all assessments make conscious decisions regarding the (mathematical) skills that are important to assess, and that consequently the forms of assessment chosen carry not only advantages, but also disadvantages. The philosophy behind the design of mathematical assessments for PISA, GED, and similar assessments is based on assumptions about what it means to "know math" or "be able to do math" in a schooling context; hence, the assessment design assumes that it is legitimate to use a certain degree of formalization of math symbols and to present contrived math tasks. This assumption does not fit the assessment of skills of adults who may have been out of school for many years.