Research
No research has been carried out on the Olympiad programs, but the availability of a very large body of statistics has allowed quite a lot of work to be done on the Australian Mathematics Competition.
The first person to research AMC data was Jo Edwards. She had a special interest in girls' results and noticed that they were not generally as high as those of boys. In fact she wrote a paper, named after the Olympic athletes Raelene, Marjorie and Betty, in which she announced the curious discovery that some of the questions which most favoured boys were those in which girls names appeared. The most outstanding one was a question which involved these athletes. We were though also to discover that mechanics was an area in which boys did best, so that was presumably a contributing factor.
After Jo died there was a bit of a vacuum, but I discussed the issue of AMC statistics with Gilah Leder, then of Monash University, and who had worked with Jo, and established a working relation with her. Over the next few years Gilah and I, and some other members of the AMF to various degrees, wrote a number of papers exploring various aspects of our statistics, to the point the Gilah and I actually won an ARC grant in 1992.
I was not interested in this research for the sake of notching up papers for my CV, but as Chair of the Problems Committee, as I was until Peter O'Halloran's death, I was interested to understand features which might help us ask better questions.
Gilah, like Jo, was also interested in gender issues, and we certainly worked that hard, but she was also interested in profiling talented students and we were also interested in risk.
Risk was a very interesting subject for us as until 2003 we had a penalty for wrong responses, to discourage guessing. Some people told us that this was unfair because it favoured boys who were more likely to guess on partial knowledge.
The best measure of risk seemed to be the Ziller statistic, and we actually used this in a paper which was published in Education Studies in Mathematics to show that actually girls took more risks before about the time of puberty and thereafter the tide swung towards boys. We also had a theory that in states in which a young transitional student around years K and 1 girls were more likely to be promoted to the next class, because they stood out in areas such as reading. We were able to get enough evidence, because we had the birthdays of each student, to show that on our entries their was a slightly higher number of girls in a class who must have been promoted.
On gender matters we got similar results to Jo, working on statistics of several years, but there was not a big difference between the results of boys and girls. We also looked at topics and found that boys' best area was still definitely mechanics, and somewhat against the general expectation, the best area for girls was geometry. I often had wondered if one of the reasons for weakening geometry was because of a perception that it favoured boys. But I realise there were other reasons.
There were papers on profiling the gifted student. This did not use the statistics but involved searching for past medallists and interviewing them.
As noted we removed the penalty for wrong responses in 2003 and so we were no longer able to investigate risk, although we had probably found the main result. But after 2003 we did go on to some interesting work with our last paper published in the Australian Mathematics Teacher in 2010.
This paper covered some extra ground. Gilah had been interested in the fact that most medallists and Olympiad team members were boys, and said it was known that in other gender comparisons such as weight and height boys had higher standard deviations than girls. So for the first time we compare standard deviations in the AMC and discovered that boys' were consistently higher. We were almost able to conclude that if we were to choose the bottom students for medals and IMO team places we would also be picking more boys than girls.
In this last paper though we had primary student data to analyse and this was as interesting as our earlier work on the Ziller statistic. We were able to see girls ahead of boys in some topics, particularly in geometry, in the primary schools. Boys still scored better in the same areas, including mechanics, but generally had higher scores than girls, but not by a significant amount. There is evidence in Australia that girls outperform boys, or at least match them, in public exams. I can only speculate here, as I am not familiar with consistently obtained data, but I suspect that girls have better organisation and study skills. And on this topic I had an interesting experience in Iran in 2005, when teaching students in teams, with some tables being teams of girls and some teams of boys. The girls always solved the problems first which indicated that communication among them was more effective. But I never followed this up.