Measuring student knowledge and skills

A task with several items
If a figure can be folded so that the two halves lie exactly on top of one another, the folding line is a line
of symmetry.
Question A
Which of the figures below have folding lines of symmetry?
Question B
Draw all the folding lines of symmetry on the square.
Question C
Which of the first eight capital letters of the alphabet have exactly two folding lines of symmetry?
Question D
John said: “I know a rule for being able to tell when a 4-sided figure has a folding line of symmetry. If the
triangles on each side of the line have the same size and shape, it has a folding line of symmetry.” Explain
why you either agree or disagree with John.

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Measuring Student Knowledge and Skills
56
OECD 1999
The following describes the composition of a typical half-hour module for the mathematical literacy
assessment in the first cycle:
– a small number (2-4) of multiple-choice or closed-constructed response items assessing
Competency Classes 1 or 2;
– a small number (1-2) of problems each containing two or three items in one context assessing
Competency Classes 1 or 2;
– one block consisting of several items positioned in one context. The items would start with rela-
tively straightforward tasks assessing Competency Class 1 and then progress to more complex
ones assessing Competency Class 3.
Reporting scales
To meet the aims of OECD/PISA, the development of scales describing student achievement is
essential. The process of developing the scales will be iterative, in that initial proposals that are based
on past experience and research in the field of learning and cognitive development in mathematics will
be further developed on the basis of empirical evidence collected during the PISA field trial.
The choice of reporting scales for mathematical literacy as a minor domain has yet to be made. The
most obvious choices are to report: i) a single mathematical literacy scale; ii) a separate scale for each of
the big ideas; or iii) a separate scale for each of the three competency classes. This choice between these
three alternatives will be made after the field trial data has been analysed.
The results of OECD/PISA will be more informative if, for at least some of the items, marks are
awarded not only for “correct” answers but also for the different strategies used by the students. It would
not be surprising, for example, if students in two countries had the same score on the mathematical lit-
eracy scale, but differed greatly in how they had reached this level of mathematical literacy: in one coun-
try, students may rely more on formal strategies and routines, while in the other country more informal,
common-sense strategies may be used.