Abstract:
The purpose of mathematics competitions, and in our case the South African Mathematics
Olympiad (SAMO), is to promote problem solving skills and strategies, to generate interest
and enthusiasm for mathematics and to identify the most talented mathematical minds.
SAMO is organised in two divisions – a junior and a senior division - over three rounds. We
analysed the results of the junior second round over seven years 2006-2012. Based on the
literature a mathematical content framework was developed, dividing the mathematical
content into seven broad content areas. In this paper we investigate the face validity,
diagnostic attributes and predictive criterion validity of mathematics olympiad question
papers over the period by focussing on the frequency of content area occurrence in the
different items. We also look at performance of contestants in the different content areas as a
broad diagnosis. Lastly we investigate the item performance, comparing the expected
performance by the problem committee of experts setting the question papers and the actual
performance of contestants. Topics such as numbers, algebra, patterns and functions,
measurement, applications, modelling and logic were used abundantly whereas (quite
surprisingly) there were few items on graphs, decimal fractions, spatial logic and vertices
and edges of polygons, indicating that the face validity can be improved. Contestants
performed best in items on algebra and weakest in items on statistics. The ability of the
problem committee to anticipate student item performance varied considerably and was
significantly worse in 2012 than in 2006, indicating better predictive criterion validity in
2006.
