‘Mathematics A is intended for students who will have little further education in mathematics in their academic studies, but who must be able to use mathematics as an instrument to a certain extent. In particular, we have in mind those who have to prepare themselves for the fact that subjects outside the traditional sciences are more frequently being approached with the use of mathematics. This means that students must learn to be able to assess the value of a mathematically tinged presentation in their education. To do this they must become familiar with the current mathematical use of language, with formulations in formula language, and with divergent forms of mathematical representation. Furthermore, they must learn to work with mathematical models and be able to assess the relevance of these models.’ (HEWET-report 1980)
It will be clear that in mathematics A the emphasis lies on applications of mathematics and mathematical models more than on ‘pure’ and abstract mathematics, and also more on the processes to come to an answer than on the answer (the product) itself. Alas: Mathematics A quickly reverted to a rather meagre reflection of what it intended to be, it didn’t really meet the initial objectives as cited above. In the central final examinations at the end of VWO (grade 12) for mathematics A the open ended problems generally ask of the students only to do a calculation, draw a graph, read a graph, substitute a few values in a formula and more of that kind of triviality. Trivialities as viewed from the perspective of the objectives of mathematics A. That many of the questions are not trivial for many students is an entirely different matter, although not completely unrelated. Mathematics A has only had a short time to prove its ‘process character’. The emphasis on the ‘products’ quickly pushed aside reasoning and interpretation. This phenomenon was foreseen, but has evidently been inescapable. An explanation for this can lie in the traditional image of ‘what a (school)mathematical problem is like’, but also in the lack of courage to meet the challenge of giving students tasks in which they really are confronted with open ended problems. The assessment by the expert, the teacher, cannot be entirely objective for such open ended problems and that seems to be a weighty argument for not including any ‘higher level’ problems in the central written examination.
The Mathematics A-lympiad owes its existence, at least in its conception, to
the presumption of the correctness of the above hypothesis. The idea was that
it would be good for mathematics A if a ‘task’ was designed that attempted to
encompass the original objectives of mathematics A.
The members of the committee formed to design such a ‘task’ knew that this would
be risky and difficult right from the start. But the concern that mathematics
A as a subject was being threatened, or at least was not been done justice,
the desire to investigate what free forms of tasks, including teamwork, would
yield, and the curiosity about what students can and cannot do, overcame the
anticipated problems.
It now seems that the limit has more or less been reached. The number of participating schools in the Netherlands seems almost stable. We cannot yet draw any conclusion about the number of participating teams. Surveys have shown increasing numbers of schools are participating in the competition with their complete grade 11.
Since the school year 1997-’98, Curaçao has also participated in the Mathematics A-lympiad. It is a natural choice for the schools in the Dutch Antilles to participate as they follow exactly the same curriculum as schools in the Netherlands. They even use the same books. As is the case in Denmark the local mathematics teachers determine which team wrote the best paper in the qualifying round. This team is then invited to the final round in the Netherlands.
Over the last ten years the competition has grown from 14 teams from 14 schools in the Netherlands to more than 1000 teams from more than 150 schools in the Netherlands, Denmark and Curaçao. And we do not believe that this is the end.
The ‘problem solving’ or ‘modelling’ component is contained in the mathematics
curriculum in many foreign countries. Working on these skills is often put on
the shelf, because textbooks often don’t provide good examples of appropriate
tasks and teachers do not know how they are supposed to deal with this. If no
structural support is provided, this component is likely to disappear from the
curriculum: it will not be practised and will certainly not be assessed.
The Mathematics A-lympiad fills this ‘gap’ perfectly by providing appropriate
tasks to practice these skills. This is both the case in the Netherlands as
well as in the other participating countries. The contents of the mathematics
curricula do not need to be exactly the same. In the Mathematics A-lympiad these
other ‘higher order’ skills are being used.
Over the next few years we expect greater participation from abroad.
In brief: the network meetings are very valuable for exchanging information. In order to give the network function more shape, a newsletter is also sent out twice a year containing as much latest news and information as possible.
In the early years of the Mathematics A-lympiad it was exceptional in mathematics
education to call on skills such as problem-solving, reading, writing, doing
research, forming arguments, reasoning, critically reviewing mathematical models,
mathematisation, teamwork, planning: the full range of general and mathematical
skills. In the Mathematics A-lympiad these skills have acquired a fixed place
in a lot of schools in The Netherlands.
That the ‘experiment’ set up 10 years ago has succeeded, can be seen in the
‘products’. Students prove to be able to produce papers of a high quality in
response to the task in a very short period of time, showing a good command
of mathematical and general skills. Papers that often surprise the real ‘professionals’.
All in all a great deal of experience has been acquired in the Mathematics A-lympiad on all aspects of assessing general and mathematical skills by means of a larger open ended assignment. Internationally there is also considerable interest in evaluating these attempts to operationalise the ‘higher order skills’. The limitations and undesired effects of traditional testing are acknowledged and recognised. Many people are in search of suitable tests/tasks that fit within the bounds of ‘fixed time’ and ‘paper and pencil’, but which also attempt to assess the process goals and higher order skills.
The A-lympiad takes its name from the subject, mathematics A – and rightly so. The concern that mathematics A would not be able to develop into a fully-fledged subject if the testing was not appropriate has turned out to be right. Fitting the philosophy of mathematics A into the fixed examination standards has turned out to be a difficult exercise (or too difficult).
But the A-lympiad also has nothing (further) to do with mathematics A. How else could one explain that Denmark may soon overtake the Netherlands in the number of schools and in quality of the papers– if the trend continues? And other countries are also showing an interest. No, the A in mathematics A stands for Aanleiding (reason for) in Dutch and for Applications abroad. This type of mathematics is precisely the mathematics that many students will deal with later on in society: solving more complex problems in teams where technical tricks alone will not do. The only thing that shows where the roots of the A-lympiad lie is the choice of contexts, contexts -by the way- that students with more scientific interests are happy to get to grips with. That does not alter the fact that a more technical oriented A-lympiad fitting the goals and content of mathematics B would seem to be very desirable next to the existing A-lympiad.
This publication contains greatly needed information for teachers who can help students to prepare properly for the A-lympiad – as a competition, as a school exam, or simply as an extra activity. The Netherlands knows that many countries are looking this way: how will it be further developed? When will there be an English and a Spanish version? How are we going to tackle the organisational problems? Over the next five years the A-lympiad must show that it has grown up and become valuable, and must also be cross-border in the geographic sense. Because mathematics A was only the impulse.