Measuring student knowledge and skills

A mathematics essay task
The four pyramids show the population of the Netherlands.
The first two show the actual population in 1950 and 1986.
The last two show the expected population for 2000 and 2035.
Discuss the extent to which the information provided in these population pyramids suggests an aging of
the population in the Netherlands; where appropriate use alternative graphical displays to support your
argument.
Figure 20.
A mathematics essay task

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Considerations for Future Survey Cycles of OECD/PISA
81
OECD 1999
– all students must complete the assessment within a fixed time limit;
– the assessment is oriented more towards finding out what students do not know rather than what they
do know;
– usually the assessment is based on the “lower” goal activities of computation and comprehension;
– the assessment consists of open questions; and
– marks are as objective as they can be.
The second stage compensates for the elements missing from the first stage. The characteristics of the second
stage are that:
– the assessment is undertaken with no time limit;
– the assessment may be completed at home;
– the assessment emphasises what students know rather than what they do not know;
– much attention is given to higher-order activities: interpretation, reflection, communication, etc.;
– the structure of the assessment is more open, consisting of questions calling for long answers, including
essays; and
– marking can be difficult and less objective.
Production items
Assessment procedures should provide students with the opportunity to demonstrate their abilities, and
should be considered an integral part of the learning-teaching process. The use of students’ own productions is not new,
and there exists considerable experience with this form of assessment. Treffers (1987) introduced a distinction
between construction and production. Free construction offers the greatest scope in terms of freedom for students
to demonstrate their own thoughts and abilities. It can involve:
– solving relatively open problems which invite the production of divergent responses because they admit dif-
ferent solutions, often at varying levels of mathematisation;
– solving incomplete problems which, before they can be solved, require students to search for and obtain data
and references;
– contriving one’s own problems (easy, moderate, difficult), written in the form of a test paper or a book of prob-
lems about a topic for the next cohort of students (Streefland, 1990).
These possible formats, and others, should be explored further for use in OECD/PISA in the years to come.

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OECD PUBLICATIONS, 2, rue André-Pascal, 75775 PARIS CEDEX 16
PRINTED IN FRANCE
(96 1999 05 1 P) ISBN 92-64-17053-7 – No. 50619 1999

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