Thirty years after: the lives of former winners of Mathematical Olympiads.

Of all the methods for identifying gifted students, mathematical Olympiads probably boast the longest and most illustrious history. Speaking about their importance, people ordinarily bring up various major mathematicians who, in their school years, won this or that Olympiad. Sometimes they also mention their less successful peers who showed great promise in childhood. This article attempts to trace the lives not of just one or two people, but of an entire group of former Olympiad participants. How did their lives turn out? What became of those who were considered especially gifted in childhood? How do they view the role of the Olympiads in their lives? These are the questions to which answers were sought. Former participants of Russian (to be precise, St. Petersburg) Olympiads were tracked down and two surveys were conducted--one in 1991 and another in 2001. The opportunity to follow the changes in their lives during this fateful decade in Russian history also appears important.

Mathematical Olympiads in St. Petersburg and Russia 

Let us briefly review the history of mathematical Olympiads in Russia and in St. Petersburg (1) (Fomin, 1994; Kukushkin, 1996). The St. Petersburg Olympiads are the oldest in Russia. First conducted in 1934, they have taken place, annually ever since, with a break during the war years. These Olympiads are conducted by official city referees who follow the general guidelines of all Russian Olympiads--at least since such guidelines were first introduced--but remain largely independent in their decisions and in developing the problems for participants. The St. Petersburg Olympiad has two rounds--a written round for each district and an oral round that is citywide. Actually, there are officially three rounds--the third round takes place in schools and its intended purpose is to select the most capable students. In reality, however, the district-wide round is frequently attended by anyone who wants to take part, as well as by those who were advised to do so by a teacher. Each of the rounds is conducted separately for each grade; thus, those participating in the district-wide round--say, seventh-graders from all the schools in the district (30-40 schools)--gather together in one of the schools where they are offered assignments that are identical for the entire city. The district-wide round takes place on the same day in all districts. The work of the participants is checked in the district and then checked again by the official city referees. As a result, approximately 100-120 participants are selected for the citywide round. The oral citywide round is peculiar to St. Petersburg--it is written in other cities. The belief is that students will react better and faster in a conversational setting. In order to avoid making subjective judgments, it is recommended that problems be heard not by one referee, but by at least two (this rule, however, is not always obeyed in practice). The winners are identified by the results of this round and given awards--first, second, and third places, as well as first-and second-degree honorable mentions. The number of winners and the distribution of the awards can vary within a range that is quite broad. There have been years when about half of the participants were winners, and other years when the winners were very few. Ideally, winners are ranked according to the following principle: those who solved all 6 of the problems win first places, those who solved 5 win second places, and so on. But in practice this principle is not always followed. Sometimes the first place is also awarded to those students who have solved 5 problems, sometimes the referees give different weights to different problems, and so on.

An all-Russian Olympiad appeared in 1961, and an Olympiad for the entire Soviet Union in 1967. Since then, selecting participants for these Olympiads has become one of the most important tasks of the official city referees. Accordingly, it has been common practice for several decades (with a brief interruption during 1984-1990) to conduct a so-called qualifying or concluding round among the winners of the citywide round. This usually means those who won first and second places.

After another selection from among the winners of the all-Russian (all-Soviet Union) Olympiad, a team is formed to represent Russia (the USSR) at the International Olympiad. Students from St. Petersburg have been widely represented in the Russian team in recent decades--in fact, a certain St. Petersburg phenomenon has materialized, when approximately half of the Russian team, as well as a certain portion of the teams of several other countries including the US, have consisted of students from St. Petersburg. In most recent years, however, the situation has changed somewhat. At least one reason for this is the fact that the traditions and methods of working with gifted students common in St. Petersburg (Fomin, Genkin & Itenberg, 1996) have been adopted in a number of other cities, which now successfully compete with St. Petersburg.

The Characteristics of Olympiad Problems and Conflicting Views of Olympiads

Over the course of many years, hundreds of wonderful problems have been collected from mathematical Olympiads (Berlov, Ivanov & Kohas', 1998; Fomin, 1994; Fomin et al., 1996). Naturally, it is impossible to characterize them in a few words. Traditionally, the connection of these problems to the school math curriculum is quite strong; the problems that are assigned require a considerable familiarity with elementary geometry and algebra, and in the upper classes a knowledge of calculus as well. At the same time, these problems are intended to test a student's capacity for independent creative thinking and not merely his or her assimilation of the materials in his textbooks. The need to invent "unschool-like" problems using classroom materials over many years has led to the development of a special field, Olympiad Mathematics, which studies a broad variety of techniques and strategies. In the opinion of many teachers, familiarity with this field has become in recent years a sine qua non for anyone aspiring to win a mathematical Olympiad. Obviously, the strategies employed in mathematical Olympiads cannot themselves be grasped without mathematical abilities. Nonetheless, today the general view among teachers is that the role of the Olympiad itself in identifying mathematical aptitude is diminishing. In their opinion, the Olympiad has turned into a competition to determine who is best prepared, in which a gifted participant who has not been sufficiently trained in solving specific Olympiad-style problems has no chance of winning.

It is interesting to note that when the mathematical Olympiads were first conceived, a decision was made not to allow the winners of one Olympiad to participate in next year's Olympiad, precisely in order to prevent any "professionalization" among the students and to stop them from concentrating excessively on Olympiad problems. Subsequently, however, this rule withered away, while the appearance of the all-Russian and other Olympiads further reinforced their athletic, competitive aspect.

In order to grasp the general context in which the Olympiads take place, it is important to note that there exist long-standing traditions of instruction in mathematical circles--free optional math classes for students from different schools, which meet after school, usually several times a week. A considerable amount of time is devoted in mathematical circles to Olympiad problems (Fomin et al., 1996). The role of specialized math schools, which first appeared at the beginning of the 1960s (Karp, 1992; Vogeli, 1997), is also significant. Students with the greatest aptitude for mathematics usually attend such schools for their last 2-4 years, and in such schools special attention has always been paid to mathematical Olympiads. In St. Petersburg, three schools were considered the best: No. 30, No. 45, and No. 239.

Survey Participants and Survey Procedures

The decision was made to track down former Olympiad participants and to try to evaluate how their lives turned out, to what degree they can be considered successful, and also to learn how they themselves view and rate their education. A group of students from the classes of 1969-73 was chosen--that is, people born in 1952-56--in other words, people who entered active life at the end of the brief years of Soviet liberalization and who were formed during the so-called period of stagnation. The survey was begun in 1991, when these people were 35-40 years old.

The list of winners prepared for the survey was formed by writing out the names of all of the winners of the St. Petersburg Olympiad who appear in the surviving archival records, starting from 1968 (the choice of year was dictated by technical reasons). Thus, the list of winners from the class of 1969 includes the winners of two Olympiads; the list of winners from the class of 1970 includes the winners of three Olympiads, and so on.

This provided 354 names, which were distributed as shown in Table 1 (first place winners (P1) include all those who won first place at least once, second place winners (P2) include all those who won second place at least once and who never won first place).

The attempt was made to determine the addresses of these people, which presented considerable problems since the only information available about them was their names and years of birth. In Russia, when a person comes of age, he or she registers in his or her place of residence. This provided some means of tracking people down, but it was usually impossible to locate people with very common last names. In addition, quite a large number of them turned out to be inaccessible because they had emigrated; the late 80s and early 90s were a period of mass emigration. Throughout the search the attempt was made to follow a single principle: to locate people based exclusively on the records available to the author of the survey. Thus, so that the selected group of names should not distort reality, the author did not allow himself to turn to various well-known mathematicians who had been winners of Olympiads if their addresses were or became easily accessible only as a result of their fame, and not in the same way as all the others. The final tally consisted of 148 people. Their distribution is given in Table 2.

All of these people were sent questionnaires about their education and employment. The survey included questions about the name of the respondent, his or her age, and his or her education. Respondents were also asked about their place of work (first and current), about their professional field, about any honorary titles that they had received, and about their published work. They were asked to evaluate on a scale from 1 to 5 (with 5 being "excellent" and 1 "very bad") the mathematical education they had received in school, and the education they had received after graduating from high school. In addition, the 1991 questionnaire asked respondents to list the names of any math teachers who had left a positive impression; the names (numbers) of the schools where these teachers had taught; and the names of the instructors of the mathematical circles that the respondents had attended. The following questions were also asked:

* Have you yourself ever taught in a school, a mathematical circle, a college, and so on?

* After graduating from school, did you ever help to organize and conduct a mathematical Olympiad?

In conclusion, respondents were invited to write out their observations about mathematical education and to express their views on the problems confronting Russian education in general.

Table 3 shows the distribution of obtained responses (in absolute numbers and as percentages of the figures in Table 2).

Ten years later, in 2001, a second survey was carried out--all those who responded to the 1991 questionnaire were sent another one. The 2001 questionnaire repeated the questions from 1991, except for those marked with bullets, and in addition contained the following new questions, which were relevant because of current discussions or because of changes that had taken place:

* Do you agree with the view that Russian mathematical education requires radical reforms? Why do you hold this opinion?

* There is a view that because of their cut-throat, competitive nature, the Olympiads do more harm than good. Do you agree with this view? Why?

* Was winning an Olympiad beneficial (practically, psychologically, or otherwise) for you personally?

* How would you characterize your current financial position in comparison to what it was ten years ago? a) Radically improved b) Somewhat improved

c) Same as before d) Somewhat deteriorated e) Radically deteriorated.

Unfortunately, the population under investigation had shrunk even further: 2 people had died, and the new addresses of 9 more could not be determined--7 of them had emigrated to the US, 2 to Germany. Table 4 shows the distribution of the obtained responses (in absolute numbers and as percentages of those who responded in 1991 as reported in Table 3).

While it is obviously impossible automatically to generalize the results of the sample to all former Olympiad participants (it may be assumed that those of them who were less successful were in general less inclined to report where they work, etc.), nevertheless, it seems that these results can be considered sufficiently characteristic and indicative of certain existing tendencies.

A Characterization of the Group Surveyed

The respondents' level of education, both in 1991 and in 2001, was quite high. All of the respondents received a higher education, an over-whelming majority of them at prestigious schools.

Table 5 describes the findings about the academic degrees held by those surveyed. It should be kept in mind that there are two academic degrees in Russia--candidate of science degree, equivalent to a Ph.D., and a doctor of science degree, which is higher. Previously, Russia did not have a bachelor's or a master's degree: graduates were simply given a single diploma after completing their higher education.

Table 6 includes the findings about the respondents' employment. Under "industry" the so-called "departmental institutes" were included, that is, institutes conducting research in applied fields within a framework of production. It should be noted that among the 2001 respondents, 4 are currently working outside Russia, and 4 more work in Russia but in foreign firms.

The respondents were found to be quite active in producing publications. Table 7 includes the findings about their numbers of published papers.

Most of the respondents were graduates of the three top specialized math schools (see Table 8). (It should be kept in mind that the statistics in the archives in some cases erroneously named earlier schools that the winners attended--not the math schools that they were attending at the time of the Olympiad. Questionnaire responses allowed this to be corrected. It is possible that the general statistics about those who graduated from these schools as given in Tables 1 and 2 are somewhat lower than the actual number of graduates.) Table 5 includes the levels of education attained by the graduates of these three schools. Thus, in the group surveyed, the graduates of the three most famous schools have clearly achieved more than the graduates of other schools (as a rule, also specialized math schools). In each group there were only two people employed in academic institutions who did not graduate from these three schools. As far as can be judged by informal statistics and conversations with teachers, the overall achievements after school for graduates of these three schools are lower than achievements of the former winners of Olympiads.

As the findings show (see Table 5), the group surveyed has raised its level of education over the past 10 years (5 people received a doctor of science degree, 1 a candidate of science degree). No less significant are the changes in the financial situation that took place over these turbulent years in Russian history. Thirteen respondents reported that, over the past 10 years, there was a radical improvement in their financial situation, 9 reported that it was somewhat improved, and 1 reported that it was the same. Four respondents reported that their financial situations had deteriorated somewhat and 1 reported that his financial situation had deteriorated radically.

For the small group of those who did not graduate from the top three schools the picture is even more clear-cut. Four members of this group reported that their financial situations had radically improved over the past 10 years. Two of them reported a somewhat improved financial situation and 1 reported that his financial situation had deteriorated somewhat. No members of this group reported that their financial situation remained the same or radically deteriorated over the past 10 years.

Responses about Issues in Education

Virtually all those surveyed give an extremely high appraisal of the education they received in secondary school. Some of them add, though, that they mean only their specialized math schools, which they attended in their final years, while the schools they attended prior to that were hardly satisfactory. Such an assessment was given both in 1991 and in 2001. The situation with colleges is rather different: they are evaluated lower, and the assessment given in 1991 is noticeably lower than the one given ten years later. This becomes particularly vivid when one compares the answers that the same people gave in the two surveys. In 1991, 11 respondents rated their college lower than they did in 2001. The people surveyed were invited to rate their college on a scale from 1 to 5, with 5 as the best. The numerical statistics obtained are included in Table 9.

It should be noted that some respondents gave an additional rating to their math circles and also to their graduate schools. Math circle ratings were usually more reserved; there were more 4's than 5's, and some 3's as well. Among graduate schools ratings, more than half were 2's and 3's.

Most of the respondents from 2001 expressed a negative view of the reforms in mathematics education: 19 respondents consider the reforms unnecessary and 5 respondents give no answer. Only 6 respondents consider the reforms necessary, specifying that what is necessary is providing schools with technical equipment (2 respondents), that the reforms should not be radical and should not affect specialized math schools (1 respondent), that reforms are needed only because the level of education has dropped and needs to be brought up to what it used to be (1 respondent), and finally that reforms are called for because schools are governed by mindless routine (1 respondent). The 1991 questionnaire did not include a direct question about the need for reforms; nonetheless, the respondents viewed reforms in a much more positive light. Their open responses frequently mentioned the various shortcomings of public education, its tediousness, its dryness, and its monotony. The main change that was recommended by the respondents was an increase in the number of math schools and greater specialization in general.

Finally, let us examine the 2001 respondents' attitudes to mathematical Olympiads. As may have been expected, virtually all of the respondents expressed their disagreement with the view that the competitive side of the Olympiads does the student as much harm as good. Only 2 of the respondents stated that Olympiads disorient the student, instilling false values and leading to overwork. Judging by certain details of the responses, it appears that these statements were based on the respondents' observation of their children, rather than on their own experience. In response to the question about the benefit of the mathematical Olympiads to them personally, the majority of those surveyed stated that they consider them beneficial. The respondents emphasized the psychological impact of the Olympiads as a stimulus to further work and as a criterion of what has been achieved, as well as the opportunity to make friends, and finally the chance simply to enjoy a victory.

Some Conclusions

An intensive mathematical education constitutes an important aspect of Russian educational culture, and the graduates of prestigious specialized math schools forma noticeable proportion of the Russian intelligentsia. It is easy to name graduates from such schools who went on to become delegates in the Russian parliament, or editors of the largest Russian newspapers; these graduates also constitute about 90% of the faculty of the math department of St. Petersburg University. As a consequence, an analysis of the lives and opinions of the winners of mathematical Olympiads is interesting from two angles. In terms of education, it reveals what became of those who were considered most likely to succeed by the recognized standards of the prevalent methodology. And it is interesting from a broader point of view as well, suggesting insights about the lives and opinions of those involved in math and applied sciences in general.

Clearly, the statistics cited above can in no way be considered exhaustive, if only because of their unquestionable incompleteness. For example, as already stated, no questionnaires were sent to many of the more famous mathematicians of this generation who attended schools in St. Petersburg (Leningrad). All the same, it seems that there exists a basis for certain conclusions.

The respondents' views on education, and especially on mathematical education, are conservative. The ideal is seen as the preservation and expansion of the system in existence during the respondents' school years, and the obvious changes that have taken place since that time are simply not taken into account. It is curious that in 1991, in keeping with the dominant mood in intellectual circles, these very views acquired a reformist tinge, while ten years later, again in keeping with the spirit of the times, they became frankly conservative. The math school culture, unfortunately little known in the West (Vogeli, 1997), seems to the respondents to answer all questions.

This is not surprising. The people surveyed clearly belong, on the whole, to the ranks of those who successfully build their lives and careers and successfully make use of new opportunities as they arise (which, of course, confirms the effectiveness of the operating system of selection). Not many people in Russia today could say that their financial situation has radically improved over the past 10 years. At the same time, it is evident that this well-being is in many respects connected with the demands of foreign (Western) organizations, not Russian ones. A number of people have left the academic sphere for business. Many members of the group surveyed chose to emigrate. The number of winners of the St. Petersburg Olympiads who live in the US today is not that much smaller than the number living in Russia.

It is quite difficult to make any judgments concerning the mechanisms responsible for achieving success. There are grounds for assuming that the most important step in the development of an academic or other career on the part of former winners of mathematical Olympiads was entering a prestigious school. This in itself was partly the cause of their good performance in the Olympiad, as well as, most significantly, a choice of direction and the first step in that direction. The statistics about Olympiad winners who did not attend the top three schools are unfortunately too sparse, but the fact that their financial situation has noticeably improved in recent years, when opportunities for further advancement have opened up, deserves consideration.

Responses to the questionnaires also reveal the important role of individual teachers. Sometimes it is even noticeable in the statistics (for example, an increase in the number of Olympiad winners from one of the schools outside the top three during the tenure there of one or another teacher).

It may be noted in conclusion that today, with mathematical Olympiads held everywhere in the world, it would be interesting to compare the statistics reported here with statistics obtained from other countries. Such an investigation, along with a repetition of the survey in Russia with other age groups, would shed light on the process of identifying and developing mathematical talents in different countries, and help us to understand the peculiarities of different cultures of mathematical education.

Table 1
St. Petersburg Olympiad Winners 1969-1974

Class of   Total   P1   P2    P3   From    From    From     From Other
                                   HS#30   HS#45   HS#239    Schools

1969         78     8   15    55    23      14       21        20
1970         42     4   25    13    10      13        7        12
1971         69    10   17    42    16      20       11        22
1972         86    11   15    60    13      11       13        49
1973         79    10   22    47    16      12        8        43

Total       354    43   94   217    78      70       60       146

Note: P1=First Place Winners; P2=Second Place Winners; P3=Third Place
Winners.

Table 2
Located Sample of Olympiad Winners 1969-1973

Class of   Total   P1   P2   P3   From    From    From     From Other

                                  HS#30   HS#45   HS#239     Schools

1969         36     3   10   23    11       7       8          10
1970         17     2    7    8     4       5       3           5
1971         26     2   10   14     6       7       6           7
1972         34     3    7   24     6       3       4          21
1973         35     4    8   23     5       6       3          21

Total       148    14   42   92    32      28      24          64

Note: P1=First Place Winners; P2=Second Place Winners; P3=Third Place
Winners.

Table 3
Distribution of 1991 Survey Responses

                                          Percent of Subjects
                                          (in Table 2)
Class of   Total   P1   P2   P3   Total    P1     P2     P3

1969         15     1    5    9   41.7    33.3    50    39.1
1970          9     1    5    3   52.9     50    71.4   37.5
1971         11     2    3    6   42.3    100     30    42.9
1972         14     1    3   10   41.2    33.3   42.9   41.7
1973          9     2    0    7   25.7     50      0    30.4

Total        58     7   16   35   39.9     50    38.1   38.0

Note: P1=First Place Winners; P2=Second Place Winners; P3=Third Place
Winners.

Table 4
Distribution of 2001 Survey Responses

                               Percent of 1991
                               Responses
Class of   Total   P1   P2   P3   Total    P1     P2     P3

1969         10     1    4    5   66.7    100     80    55.6
1970          5     1    3    1   55.6    100     60    33.3
1971          7     1    2    4   63.6    50     66.7   66.7
1972          6     0    2    4   42.9     0     66.7    40
1973          2     0    0    2   22.2     0      --    28.0

Total        30     3   11   16   51.7    42.9   68.8   45.7

Note: P1=First Place Winners; P2=Second Place Winners; P3=Third Place
Winners.

Table 5
Academic Degrees Held by Survey Respondents

                            Total   Doctor of   Candidate     No
                                    Science    of Science   Doctoral
                                                             Degree

1991 Group                    58        1          30          27
2001 Group                    30        5          14          11
1991 Group from the Top 3     41        1          26          14
  Schools
1991 Group from Other         17        0           4          13
  Schools
2001 Group from the Top 3     23        4          12           7
  Schools
2001 Group from Other          7        1           2           4
  Schools

Table 6
Survey Respondent Employment

             Total     Academic     Industry    Politics    Other
                     Institutions                         Professions

1991 Group     58         25           28          2           1
2001 Group     30         12           15          1           1

             Unemployed     Not
                          Given

1991 Group       1          1
2001 Group       1          0

Table 7
Survey Respondent Publications

             Total    0   1-5   6-15   16-25   Over 25   Publications
                                                         Exist, Number
                                                           Not Given

1991 Group     58    10    4     14      10       14           6
2001 Group     30     7    1      2       2       14           4

Table 8
Survey Respondent Schools Attended

             Total    From     From     From     From
                     School   School   School    Other
                      # 30     # 45     # 239   Schools

1991 Group     58      18       11       12        17
2001 Group     30      11        5        7         7

Table 9
Quality of Mathematical Education

               School        College
Rating        5   4   3    5    4    3   No Answer Given

1991 Group   52   5   1   19   22   16         0
2001 Group   24   4   0   16   12    0         2

Note: Schools and colleges were rated on a 1-5 scale; 5 highest.

(1) The city was called Leningrad during the Soviet period and its historical name, St. Petersburg, was restored only in 1991. Throughout the article, only this current name will be used. The name of the country, Russia, also reappeared after a long absence only in 1991, after the collapse of the Soviet Union. Before this time, Russia was merely the Soviet Union's largest republic, and in fact it held its own Olympiads, although it did not send its team to compete in the International Olympiads--the international team was drawn from the entire Soviet Union.

REFERENCES

Berlov, S.L., Ivanov, S. V., K., & Kohas', K. P. (1998). St. Petersburg Mathematical Olympiads. (Peter-burgskie Matematicheskie Olimpiady) St. Petersburg: Lan'.

Fomin, D. V. (1994) St. Petersburg Mathematical Olympiads. (Sankt-Peterburgskie Matematicheskie Olimpiady) St. Petersburg: Politechnika.

Karp, A. (1992). Math tutor available.... (Dayu Uroki Matematiki ...) Moscow: Prosveschenie.

Kukushkin, B. (1996) The Olympiad movement in Russia. International Journal of Educational Research, 25 (6), 553-562.

Fomin, D., Gengkin, S., & Itenberg, I. (1996). Mathematical circles: Russian experience (M. Saul, trans.). Providence, RI: American Mathematical Society.

Vogeli, B. R. (1997). Special secondary schools for the mathematically and scientifically talented. An international panorama. New York: Teachers College Columbia University 

Dr. Alexander Karp is an assistant professor of mathematics education at Teachers College, Columbia University. He holds a Ph.D. in Mathematics Education from St. Petersburg Pedagogical University. He has authored more than 60 publications, including textbooks, collections of problems, and research papers on the education of the talented. His scholarly interests also include the history of mathematics education, assessment in mathematics education, and teaching students who display a lack of motivation in studying mathematics.