Tahany M. Gadalla

Ontario Institute for Studies in Education/University of Toronto

Efforts to ensure equity for women in scientific and technological disciplines must precede, or at least accompany, efforts to persuade them to pursue these studies. To achieve gender equity in these disciplines, factors discouraging women from full participation in them should be removed. Many psychological, sociological and institutional factors have been identified as contributors to the under-representation of women in these fields. For the aim of understanding and appraising these factors, this study offers a factual characterisation of women’s enrolment levels in mathematics, engineering, and computer science in Canadian universities and the change in these levels over the period 1972 to 1995. Findings indicate that patterns of women’s enrolment in these three disciplines are vastly different, a fact which suggests that factors specific to each discipline interact with and modify the effects of the more general sociological and psychological obstacles impeding women’s participation in them.

In 1994, twelve years after the publication of the Science Council’s "Statement of Concern," women remained very much a minority among professionals employed in the natural sciences, engineering, and mathematics. In fact, just 19% of professionals in these occupations in 1994 were women, a figure which has changed little since 1982 (15%) (Statistics Canada, 1995). In addition, it is unlikely that female representation in these occupations will increase in the near future because women continue to account for relatively small proportions of total university enrolments in these fields.

Gender imbalance in the fields of mathematics, science, and technology is an issue of educational equity. It raises the disturbing possibility that the education system functions in ways which discourage women from pursuing mathematical and scientific careers. If true, this situation is not only unethical, but it also closes an expanding job market to women and, hence, limits their career choices.

In order to achieve gender equity in mathematics and related fields, obstacles deterring women from participating in these fields must be removed. Factual characterization of the magnitude of the gender gap in these disciplines, of the change, if any, in this magnitude over time, and of the differences and similarities in the participation of women in various scientific disciplines is an essential first step toward understanding and appraising the reasons behind the paucity of women in these fields.

Studies on gender participation at the university level have traditionally contrasted the proportion of women in the combined fields of mathematics and sciences with their proportion in humanities and the social sciences. But the extent of the gender imbalance is not uniform across scientific disciplines. Hence, such clustering of disciplines does not convey an accurate account of gender imbalance in a specific discipline nor of the extent of its change in recent years. These disciplines also vary in their curricula and the type of occupations to which they lead. Hence, causes of the low participation of women in these disciplines might also vary. Examination of women's enrolment rates in mathematics, engineering and computer sciences separately will describe the gender imbalance in each of these disciplines and may also help disentangle the causes of the imbalance specific to each discipline.

The gender gap in mathematics and science participation increases at each higher level of educational achievement. This leads to having few qualified women candidates for future faculty positions who can act as role models and mentors to female students. Analysis of women's progress through the education levels in mathematics, computer science and engineering will enable us to determine at which education level women's progress is impeded in each of these three fields. Knowing where in the education pipeline these barriers might lie is a primary step on the road to removing them.

For the last two decades or so, many intervention projects have been carried out to increase young women's interests in mathematics and science and to convince them to seek careers in these fields. Little effort has been made to evaluate the effectiveness of these projects, and to assess their outcomes. Monitoring the change in women's presence in mathematics and science programs over a period of 23 years will give an accurate picture of the progress to date, hence contribute to the evaluation of these intervention efforts.

The study of past trends in enrolment provides a basis for future projections of university enrolment and of labour force supply of specific professions. These projections are used by labour market analysts. They also provide educational policy makers with information that can be used in allocating resources to various sectors of the education system.

Parity indices and adjusted participation rates were used in this work in an attempt to disentangle discipline specific and gender specific changes from the more general trend of increased enrolments in Canadian universities. Transition rates from the bachelor to the masters levels and from the masters to the doctoral levels, were used to investigate the advancement of women through these post secondary education levels in each of the three disciplines under study.

Table 1 displays data on part-time and full-time enrolment in all programs by gender and level of study in the first and the last year of the study period. The table shows that university enrolment grew from 389,793 in 72/73 to 690,713 in 94/95, a growth of about 77%. Women's share of enrolment in all programs at the bachelor level grew from 42.6% in 72/73 to 55.9% in 94/95 while their share of enrolment at the graduate levels almost doubled. At the present time, 56% of students in bachelor programs are women, enrolment in masters programs is split evenly between men and women, and in doctoral programs, 39% are women. That is, women's share of enrolment decreases as the level of study increases. Also,

women's representation is higher among part-time students compared to full-time students.

Data in table 1 also indicate that in 72/73, part-time students accounted for 25% of total enrolment at the bachelor level, 43% at the masters level, and 27% at the doctoral level. In 94/95, these percentages dropped to 21% of total enrolment at the bachelor level, 40% at the masters level, and 17% at the doctorate level. Part-time enrolment in all programs, at all levels declined from 27% in 72/73 to 22% in 94/95. In other words, more students are pursuing their university study on a full time basis.

Figure 2 represents numbers of men and women enrolled in mathematics programs in Canadian universities by level of study during the period 72/73 to 94/95. This figure illustrates

that at both the bachelor and masters levels, mathematics enrolment for men and women exhibit similar trends with varying degrees of fluctuations. In absolute numbers, the gender gaps in mathematics enrolment at these two levels have been almost constant throughout the whole period. At the doctoral level, women's enrolment increased very slightly, while men's enrolment exhibited a downward trend followed by a slow and then a rapid increase but decreased in 1993 and 1994. As a result, the gender gap in doctoral enrolment decreased and then increased back to its original size in 1972.

Table 2 provides data on 1972/73 and 1994/95 enrolment in mathematics programs by gender, level of study and registration status. As seen in this table, the number of students in mathematics programs increased considerably over the study period. Women's share of mathematics enrolment at both the bachelor and the masters levels increased by approximately 10% and at the doctoral level by about 13%.

Parity Indices. The period under study was a time of immense social and demographic change in Canada. Women have been swelling the ranks in university programs at all levels. In order to isolate the trend toward women's increased presence in mathematics from the more general trend of their increased presence in university education, parity indices for men and women at each level of study are computed and compared. Parity index is the number of students in a specified discipline expressed as a percentage of the number of students in all programs. Differences in the shapes of the parity index curves for men and women indicate gender differences in their tendency toward enroling in mathematics.

Mathematics parity indices for men and women during the study period are displayed in Figure 3. In general, the figure reveals slight negative mathematics specific changes and gender specific changes in men's favour. At the bachelor level, the parity index curves for men and women show similar, periodic changes over the study period. Men's and women's parity rise, fall, and level off over the same time periods suggesting that they are reacting to the same set of social and economic factors in the same direction. Both curves have been on the decrease since 1986 indicating that the likelihood of a bachelor student, of either sex, majoring in mathematics is on the decline.

At the masters level, both men's and women's curves exhibit a somewhat similar downward trend from 1972 to 1978 followed by a period of increase for men up to 1987 then a plateau from 1987 to 1994, while women's curve shows no particular trend during the period 1978 to 1994. In 94/95, only 0.6% of women at the masters level were majoring in mathematics as compared with 1.3% in 72/73. In other words, while women's representation in masters level programs in general increased, mathematics share of masters level students decreased. Mathematics parity for men dropped very slightly over the study period.

At the doctoral level, men's parity curve encompasses a period of moderate decrease followed by a period of slow increase and a plateau. The most striking feature of women's index curve is the apparent lack of trend over the study period. As a result, the gap between the two curves has been widening. Women's enrolment in mathematics doctoral programs has been fluctuating around 1.3% of all women’s doctoral enrolment, while the corresponding percentage for men during the last 6 years is 3.5% which is almost two and a half times that of women.

In summary, at the three levels of study, mathematics was losing students of both sexes to other programs during the period 1972 to about 1978, and although it gained some back, the proportion of university students who are in mathematics never rose back to their 1972 levels. This is particularly true at the masters level.

Adjusted Participation Rate. Adjusted participation rate provides another way of looking at the progress women made in venturing into fields perceived by many as male areas. It measures the likelihood that a woman university student will major in mathematics relative to that of a men. It is computed as the ratio of mathematics parity index for women to mathematics parity index for men. Adjusted participation rate can also be expressed as the proportion between the sex ratio of mathematics students and that of all students. Based on the assumption that men and women are able to achieve equally in mathematics, the sex ratio in mathematics should be equivalent to that in the student population in all fields. Thus, the difference between this rate and one is a measure of the disparity in the rates at which men and women major in mathematics. Adjusted participation rates at each of the three levels of study are displayed in Figure 4. The figure shows that the bachelor participation rate exhibits a slight downward trend, from 59% in 72/73 to 53% in 94/95, the masters rate a more noticeable downward trend, from 74% in 72/73 to 44% in 94/95, and the doctoral rate has been fluctuating around the 40% mark. At the three levels combined, the likelihood of a woman university student majoring in mathematics relative to that of a man has actually decreased from 58% to 51% in spite of the reported large increase in mathematics enrolment at the high school level.

Women’s Enrolment at the Present Time. Data in Tables 1 and 2 suggest the following points regarding enrolment in mathematics programs at the present time:

1. The proportion of students in both sexes enrolled in mathematics programs is very low. Of a total of 690,713 students on campus, only 10,807 are studying mathematics, that is less than 1.6%. It is worth noting that the proportion of students of both sexes enrolled in mathematics doctoral programs in 94/95, 2.5%, is higher than their proportions at the bachelor's and master's levels, 1.6% and 1.1% respectively.

2. Mathematics is still predominantly a male field especially at the graduate level with men occupying approximately 7 out of every 10 masters level seats and 8 out of every 10 doctorate seats.

3. Female to male ratio in mathematics is about one half of the female to male ratio in all programs. That is, women are only about half as likely as men to major in mathematics. This likelihood is slightly higher at the bachelor level (53%), and lower at the masters and the doctoral levels (44% and 43% respectively).

Full-time Versus Part-time Enrolment. Part-time enrolment in mathematics in 94/95 accounted for about 14% in bachelor level programs, 17% in masters level programs, and 11% in doctoral level programs. These are about one half of the corresponding percentages in all fields (corresponding percentages in all fields are 21, 40, and 17). In other words, mathematics students of both sexes tend to pursue their studies in full-time capacity, more so than students in other programs. Although women's share of part-time enrolment in all programs at each of the 3 levels is around 7 percentage points higher than their share of full-time enrolment, in mathematics programs the picture is reversed. Women's share of part-time enrolment in mathematics is about 4 points less than their share of full-time enrolment at the bachelor level, and is about the same at the masters and the doctorate levels. In other words, there is little difference in the representation of women in part-time compared to full-time study in mathematics.

Women's Movement Through Levels of Study. Women's share of mathematics enrolment at the three levels of study are 40%, 30.6%, and 21.7%, a drop of about 9 percentage points with each higher level (Table 2). Women's share of total enrolment decreases by about 6 percentage points from 55.9% to 50.2% as they move up from the bachelor to the master level, and by about 11 percentage points as they move to the doctorate level (Table 1). In other words, women's drop out rate at the masters level is higher in mathematics than in other disciplines, and the opposite is true at the doctoral level.

In an attempt to disentangle gender specific and mathematics specific differences in enrolment, transition rates from the bachelor to the masters level, and from the masters to the doctoral level for men and women are computed and displayed in Table 3. There are three caveats here. Firstly, since transition rates are not based on the same cohort, they should be interpreted with caution. In addition, since a doctorate degree typically takes longer to complete than a masters degree, enrolment in doctoral programs at any point in time could correspond to multiple cohorts of masters students. Secondly, transition rates from bachelor to masters and from masters to doctoral are difficult to interpret because some students advance to doctoral programs without going through masters programs. Thirdly, bachelor degree graduates (not students enrolled) comprise the actual pool of candidates for graduate enrolment. Thus, the comparison of transition rates, as calculated here, implies the assumption that graduation rates in these disciplines are not vastly different.

Out of all women enrolled in bachelor level programs, approximately 11% advance to the masters level; in mathematics, this ratio is only 6%. In other words, women in mathematics are less likely than women in other disciplines to make the leap to graduate studies. At the doctoral level, however, the picture is reversed. Of all women enrolled in masters level programs, approximately 30% proceed to the doctoral level; in mathematics this ratio is 67%. Put another way, once they are able to go over the hurdle of entry into graduate studies, women in mathematics are more than twice as likely as women in other disciplines to advance to the doctoral level.

Upon examining men's transition rates, it becomes apparent that they exhibit the same pattern as women's transition rates. That is, mathematics students of both sexes are less likely than students in other disciplines to make the leap to graduate studies, but once they make that leap, they are more than twice as likely to proceed to the doctoral level. Table 3 also reveals sizable gender differences in transition rates at both levels in favour of men.

Examining bachelor to doctoral transition rates, we notice that both men and women advance to the doctoral level in mathematics more than in other disciplines, with a gender difference in favour of men, starker in mathematics than in other disciplines. In particular, a female studying for a bachelor degree is half as likely as a male colleague to advance to the doctoral level while in mathematics, a female studying for a bachelor degree is about 40% as likely as a male colleague to proceed to the doctoral level. We also notice that the proportion of men in mathematics bachelor programs who go on to a doctoral program hardly changed over the study period while the proportion of women in bachelor programs who proceed to a doctoral program doubled. However, a woman in a mathematics bachelor program is still only about 40% as likely as a man to proceed to a doctoral program.

The number of men and the number of women enrolled in engineering programs in Canadian universities during the period 72/73 to 94/95 are plotted in Figure 5. This figure illustrates that at all three levels of study, the gender gap in enrolment is wider in 94/95 than in 72/73. In other words, the number of men enrolled in engineering programs has been increasing at a steeper rate than that of women. It is also apparent that in 94/95 enrolment at each of the three levels stabilized or fell slightly from its 93/94 level. In general, women's enrolment at all three levels exhibit less fluctuations than men's enrolment. Trends in men's and women's enrolment were most different at the doctoral level. In particular, number of men studying engineering declined slightly during the seventies, then increased rapidly during the eighties while the number of women showed lack of change during the 70s followed by a slight upward trend during the 80s and 90s. As a result, the gender gap in doctoral enrolment has been on the increase since 1982. In both bachelor and masters enrolment, the gender gap has been slowly and steadily increasing over the study period.

Table 4 provides data on 72/73 and 94/95 enrolment in engineering programs by gender, level of study and registration status. As seen in this table, the number of engineering students more than doubled over the study period. The number of women engineering students rose from 441 in 72/73 to 9,805 in 94/95. This corresponds to a 10 fold rise in women's share of engineering enrolment, from 1.8% in 72/73 to 17.9% in 94/95 with the highest increase at the bachelor level, from 1.7% in 72/73 to 18.4% in 94/95, and the lowest increase at the doctoral level from 2.7% in 72/73 to 10.4% in 94/95. It is interesting to note that women's share of masters and doctoral enrolment in 72/73 was higher than their share of bachelor enrolment. This means that as early as 1972, those very few women who majored in engineering tended to persevere in this field and advanced to graduate levels in

greater numbers than their men peers. In 94/95, women's portion of bachelor and masters

enrolment were about equal at 18.4% and 18.5% respectively and was eight percentage points lower, at 10.4%, of doctoral seats.

It is also apparent from Table 4 that most of the increase in women's enrolment happened in full-time enrolment. Furthermore, contrary to the situation in all disciplines where women comprise the majority of part-time enrolment, their share of part-time engineering enrolment is approximately five percentage points lower than their share of full-time enrolment at all three levels of study.

Parity Indices. Engineering parity indices, i.e. proportion of students in engineering to students in all disciplines, during the study period are displayed in Figure 6. In general, the figure reveals positive engineering specific changes for both sexes at all three levels of study

indicating that the likelihood of a university student of either sex majoring in engineering increased over the duration of the study. In addition, the fact that the parity indices for men and women exhibit different shapes reveal definite gender specificity. In particular, at all three levels of study, engineering share of university female students increased slightly and steadily during the whole period, while engineering share of male students had its ups, downs and plateaus with an overall upward trend steeper than that of women. Dissimilarities in the shapes of the parity curves for men and women together with the failure of women's parity indices to increase as much as men's suggest that men's and women's engineering enrolments were reacting to dissimilar set of influences.

At the bachelor level, engineering share of male students increased sharply between 1974 and 1979, decreased slowly during the 80s and increased very slightly in the 90s. The proportion of engineering bachelor male students to all bachelor students rose from 10.1% in 72/73 to an all time high of 14.5% in 1980 and reached 13.8% in 94/95, while the proportion for female students rose steadily from 0.2% in 72/73 to a mere 2.5% in 94/95.

At the masters level, engineering share of male students was 11.4% in 72/73. It fluctuated over the study period and reached 16.1% in 94/95. Engineering share of female masters students rose from 0.7% in 72/73 to 3.6% in 94/95.

At the doctoral level, both men's and women's parity curves show lack of apparent trend during the 70s followed by steady moderate increase during the 80s and the 90s with men's index rising much faster than women's resulting in widening the gap between the two curves. Men's share of doctoral enrolment rose from 12.5% to 20.1% over the study period while women's share rose from 1.4% to 3.7%.

Adjusted Participation Rates. Adjusted participation rates in engineering at the three levels of study are displayed in Figure 7. The most striking feature of this figure is the upward trends at the bachelor and masters levels which cover the whole study period. The figure shows that the bachelor participation rate grew from 2% in 72/73 to 18% in 94/95 and the masters rate grew from 7% to 23% while the doctoral rate grew from 12% to 18%. Adjusted participation rate at the doctoral level shows the most fluctuations, less overall increase and a plateau since 1989 to the present. Adjusted participation rate at the three levels combined rose from 2.7% to 18.1% over the study period. In other words, although the likelihood of a woman university student majoring in engineering relative to that of a man increased about 7 fold over the study period, a woman university student is still only 18% as likely as a man university student to major in engineering.

Engineering Enrolment at the Present Time. Eight percent of students of both sexes on Canadian campuses study engineering. This percentage is higher at the graduate levels than at the bachelor level. In particular, 10% of masters students and 14% of doctoral students study engineering while only 7% of bachelor students do. This means that a greater proportion of engineering students remain in the education pipeline compared to students in other fields.

Engineering is a predominantly male field. As shown in Table 4, women make up 17.9% of all engineering students; 18.4% at the bachelor level, 18.5% at the masters level, and 10.4% at the doctoral level. In spite of the ten fold rise in women's share of engineering enrolment, the female to male ratio in engineering is still less than one fifth of the female to male ratio in all fields of study. Put another way, the likelihood that a woman university student will major in engineering is less than one fifth that of a man.

Full-time Versus Part-time Enrolment. Part-time enrolment in 94/95 accounted for about 8%, 27%, and 8% in bachelor, masters, and doctoral programs respectively. These percentages are much lower than the corresponding 21%, 40%, and 17% in all fields. In other words, more students of both sexes pursue their studies in full-time capacity in engineering than in other fields.

Women's share of part-time enrolment in engineering is about 5 percentage points lower than their share of full-time enrolment at all three levels of study (Table 4). This is contrary to the situation in all fields where women's share of part-time enrolment is about 7 percentage points higher than their share in full-time enrolment.

Women's Movement Through Levels of Study. As shown in Table 4, women's share of engineering enrolment at the bachelor and masters levels are very similar, i.e. 18.4% and 18.5%, while their share at the doctoral level is 10.4%. This indicates that although graduate engineering programs do not lose women at entry into the masters level, they lose them at entry to the doctoral level. Table 5 provides another way of looking at the flow of students through levels of study by displaying the proportions of men and women engineering students moving up to higher levels of study. The table shows that in 94/95 about 16% of bachelor students of both sexes advance to a masters program, but twice as many men as women masters students advance to a doctoral program. That is, a woman engineer is just as likely as a man to move up to a masters program but is only half as likely to move up to a doctoral program. Surprisingly, in 72/73, the proportions of women engineers advancing to graduate programs were higher than those of men. While men's transition rates grew over the study period, women's rates declined substantially, especially at entry to the doctoral level. Specifically, the proportion of women doctoral to bachelor students declined from 11.3% to 4.8% while the corresponding proportion for men grew from 6.9% to 9.2% over the study period.

When comparing the proportions of students advancing to graduate levels in engineering with those in all fields (Tables 3 and 5), it becomes apparent that higher proportions of engineering students of both sexes seek graduate degrees than do students in other fields. Although fewer women than men enter the field of engineering, once women are able to go over the hurdle of entry into the field, they are more likely than women in other fields to advance to graduate studies. However, the number of men in doctoral programs as a proportion of those in bachelor programs is still twice as high as that of women, both in engineering and in all fields.

Numbers of men and women enrolled in computer science programs in Canadian universities by level of study during the period 72/73 to 94/95 are displayed in Figure 8. A noticeable characteristic of this figure is the expansion in the gender gap in enrolment at all levels of study which started in 1980 in bachelor enrolment and in 1982 in graduate programs. This expansion is the result of a faster rise in men's enrolment compared to women's enrolment, the latter showing modest increases over the study period.

Men's bachelor enrolment demonstrates a curious trend, namely, a very steep climb between 1979 and 1984 followed by a decline which lasted for about three years, a plateau and a slower climb from 1989 to the present. Women's bachelor enrolment follows the same general trend exhibited by men's enrolment but with less dramatic shifts. The decrease in bachelor enrolment between 1985 and 1988 is not reflected in graduate enrolment.

Both men's and women's masters enrolment show intervals of increase and intervals of stability over the same time periods throughout the duration of the study but the increases in women's enrolment are always lower than the increases in men's. Men's and women's doctoral enrolment remained unchanged during the 1970s then started to depart with men's enrolment rising rapidly to 93/94 then declining in 94/95 and women's enrolment rising slowly.

The numbers of students enrolled in computer science programs in 72/73 and 94/95 broken down by gender, level of study and registration status are presented in Table 6. This table shows that women's portion of computer science enrolment hardly changed over the last 23 years. In 94/95, women occupied 20.2% of all computer science places compared with 18.6% in 72/73. At the bachelor level women's portion was 20.2% in both years. At the masters level, women's enrolment rose from 13.6% in 72/73 to 22.6% in 94/95 whereas at the doctoral level, it rose from 5.3% to 16.2% during the same period. Most of the increase in women's bachelor enrolment took place in part-time enrolment. Women's portions of part-time bachelor and doctoral enrolment are higher than their portions in full-time enrolment.

Parity Indices. Men's and women's enrolment in computer science programs as a proportion of their total university enrolment are plotted in Figure 9. In general, the curves demonstrate the same features demonstrated in Figure 8 by number of students enrolled. This

means that the changes in computer science enrolment were field specific. In 94/95, 2.4% of students in Canadian universities majored in computer science compared with 0.9% in 72/73. Almost all of the increase in computer science bachelor and masters enrolment took place in the late 70s and early 80s. In doctoral programs, most of the increase took place in the second half of the 80s. This increase, however, was not the same for men and women.

Bachelor parity curves peaked in 1984, decreased sharply between 1984 and 1988, plateaud in the late 80s, and increased moderately in the 90s. The gender gap in computer science enrolment at the bachelor level expanded markedly in the 80s and 90s. While 1.2% of men and 0.4% of women university students majored in this field in 72/73, the corresponding percentages in 94/95 were 4.2 and 0.9. This corresponds to a 2.25 fold increase for women and 3.5 fold increase for men. The gender gap in enrolment in graduate programs also expanded but to a lesser extent than it did in bachelor programs. For example, proportions of men and women masters students studying computer science in 72/73 were 1.7% and 0.7%; in 94/95, they were 3.2% and 0.9%. Proportions of men and women doctoral students studying computer science increased from 1.6% and 0.4% in 72/73 to 3.1% and 0.9%, respectively, in 94/95. This corresponds to about two fold increase for men and 1.5 fold increase for women in graduate programs. It is thus evident that at all three levels of study, changes in women's parity index echo changes in men's parity index in direction albeit less dramatic in magnitude. This suggests that gender specific factors might be causing women's enrolment to be less responsive than men's to economic and social factors which influence enrolment in this discipline.

Adjusted Participation Rates. Figure 10 shows the changes in adjusted participation rates for women in the field of computer science over the duration of the study. This figure reveals a decline in women's representation in this field especially at the bachelor level. The likelihood of a woman bachelor student majoring in this field compared to that of a man declined from 34% in 72/73 to 20% in 94/95. In other words, the likelihood of a woman university student majoring in computer science as compared to that of a man dropped from 34% in 72/73 to 20% in 94/95. Put another way, in 94/95, female to male ratio in this field as compared to the same ratio in all fields was about one half its value in 72/73. Almost all of this decline took place between 1982 and 1987 following a period of healthy improvement for women in the late 70s where their level of participation relative to men's was increasing. Adjusted participation rate at the masters level fluctuated between 72/73 and 1990 with an overall downward trend from 42% to 28% and stabilized in the 90s. Adjusted participation rate at the doctoral level also fluctuated over the duration of the study but with a slight overall upward trend from 24% in 72/73 to 29% in 94/95.

The gender gap in computer science enrolment is particularly puzzling. Computer technology is a new field with no long history of sexism to overcome, and the expansion in this field occurred in the early seventies, almost at the same time as the birth of the feminist movement. At the beginning, the field was open to women but quickly became male dominated. In 1984, women constituted 28% of bachelor degree enrolment, in 1987 they constituted only 20%. And although computer science programs suffered a decline in enrolment of both sexes during this period, men's enrolment quickly bounced back, while women's enrolment never returned to the 1984 level.

Computer Science Enrolment at the Present Time. Of all students on Canadian campuses, only 2.4% study computer science. This percentage is about the same at all three levels of study. Less than 1% of women in university major in computer science. Women make up 20% of computer science bachelor enrolment, 23% of masters enrolment, and 16% of doctoral enrolment (Table 6). The female to male ratio in bachelor computer science programs is about one fifth of the female to male ratio in all fields; that is, the likelihood of a woman university student majoring in computer science is about one fifth that of a man.

Full-time Versus Part-time Enrolment. Part-time enrolment in 94/95 accounted for about 23%, 31%, and 15% in bachelor, masters, and doctoral programs respectively. These proportions are comparable to the 21%, 40%, and 17% seen in all fields. Table 6 shows that the representation of women in part-time enrolment at the bachelor and doctoral levels is higher than their representation in full-time enrolment.

Women's Movement Through Levels of Study. Table 6 shows that the percentage of women at the masters level (22.6%) is higher than that at the bachelor level (20.2%). This suggests that the proportion of women bachelor students who move up to a masters program is higher than that of men. Women's share of doctoral enrolment, however, is only 16.2% indicating that although women do not drop out of the education pipeline at entry to the masters programs, they drop out at entry to the doctoral programs.

Table 7 presents men's and women's enrolment in masters and doctoral programs as proportions of their enrolment in bachelor and masters programs in 72/73 and 94/95. The table shows that the proportion of women in the masters programs to those at the bachelor level hardly changed over the last 23 years while the proportion of doctoral to masters enrolment almost doubled. As a consequence, the proportion of doctoral to bachelor enrolment doubled from 1.7% to 3.4%. On the other hand, the proportion of men's masters to bachelor enrolment dropped from 17.8% to 9.4% while their doctoral to masters proportion increased slightly. As a consequence, the proportion of men's doctoral to bachelor enrolment dropped from 7.9% to 4.4%. Women's doctoral to bachelor enrolment (3.4%) is slightly less than men's (4.4%).

Enrolment Trends During the Period 72/73 to 94/95. During the period under study, the proportion of university students of both sexes majoring in mathematics declined from 2% to 1.6%, whereas the proportion majoring in engineering increased from 6.3% to 7.9% and the proportion majoring in computer science increased from 0.9% to 2.4%. In other words, while the field of mathematics was losing students to other disciplines, the fields of engineering and computer science were attracting more students.

Time trends of women's share of university enrolment in all programs and in each of the three fields are depicted in Figure 11. The most striking feature of this figure is the trend exhibited by the proportion of women in computer science bachelor programs where it increased steadily between 1972 and 1982, then decreased and remained almost stationary from 1987 to the present. In other words, women made good progress during the first 10 years considered in this study then turned away from this field in the late eighties and the nineties. This is unlike the trend of women's share of enrolment in engineering bachelor programs where it was steadily increasing throughout the whole period. Women's share of mathematics bachelor enrolment also increased steadily throughout the whole period but the increase is less steep than that seen in engineering. At both masters and doctoral levels, women's participation in all three fields showed some general upward trends which clearly fell below the expansion in their participation in graduate programs in other fields. In general, among the three fields under study, the representation of women is highest in mathematics followed by computer science and lowest in engineering. However, the difference between women's representation in computer science and their representation in engineering bachelor enrolment has been decreasing as a result of the increase in the numbers of women going into

engineering programs.

Table 8 displays the gain in women's share of university enrolment at the three levels of study in all programs and in each of the three disciplines in the twenty three years under study. A number of observations arise from the data in this table:

(1) Among the three fields viewed as non-traditional for women, mathematics has always been the least male dominated one.

(2) With the exception of engineering bachelor programs, the gain in women's share of university enrolment in the three disciplines at all levels fell short of their overall gain in other programs. Put another way, the proportion of women in engineering bachelor programs has been increasing at a higher rate than their proportion in total university enrolment. This is in contrast to the situation in mathematics, computer science, and engineering graduate enrolment. That is, women's representation in these programs has not been as responsive to general social and economic changes as their representation in other programs.

(3) The field of computer science has seen a dismal increase in the representation of women. This is particularly true at the undergraduate level where the proportion of women in 94/95 was exactly the same as it was in 72/73.

Review of Figures 2, 3, 5, 6, 8, and 9 reveals the following points:

(1) In all 3 fields, number of students enrolled and parity at the masters level show the most fluctuations over time. This attests to the fact that the masters degree enrolment is difficult to evaluate since it is sometimes awarded as an indicator of progress toward a doctoral degree. Also, some honour students advance to the doctoral level directly after attainment of a bachelor degree.

(2) In all 3 fields, there is a marked expansion in the gender gap in enrolment in doctoral programs from 1981 to 93/94 as a result of a faster rise in men's enrolment. This expansion is more dramatic in engineering and computer science than in mathematics. This was not the case for enrolment in all disciplines where the gender gap in doctoral enrolment remained almost unchanged from 1981 onwards. In other words, while women's doctoral enrolment in all programs was rising at the same rate as men's enrolment, in mathematics, engineering and computer science it was rising at a much slower rate than men's.

(3) Except for computer bachelor programs, enrolment in all three disciplines in 1994/95 either dropped or remained unchanged from their level in 93/94.

Comparison of adjusted participation rates in the three disciplines (Figure 4, 7, and 10) indicates that women's representation in engineering relative to their representation in all programs has been steadily increasing over the past two decades which is in contrast to the downward trend exhibited by women's participation in computer science, especially at the bachelor and masters levels, and the slight decline in the mathematics participation rates.

Enrolment at the Present Time. Eight percent of university students study engineering whereas only 1.6% study mathematics and 2.4% study computer science. Women are still under-represented in all three fields but to different degrees. Data in table 4.7 show that women's participation in mathematics (38.2%) is more than twice as high as their participation in engineering (17.9) and almost twice as high as their participation in computer science (20.2%). The disparity in women's representation in these fields persists at the graduate level where they make up 21.7%, 10.4%, and 16.2% of doctoral enrolment in mathematics, engineering, and computer science, respectively. These proportions are much less than their 39% share of doctoral enrolment in all fields.

In 1994/95, women's adjusted participation rate at all three levels combined was 21% in computer science and 18% in engineering. That is, a female university student is about one fifth as likely as a male student to major in computer science and less than one fifth as likely as a male student to major in engineering. These are much lower odds than seen in mathematics where a female student is half as likely as a male student to major in mathematics. These data do not support the assertion made by some researchers that women choose not to study in engineering or computer science because they want to avoid mathematics.

Full-time Versus Part-time Enrolment. Among the three levels of study, masters programs in all three disciplines have the highest proportions of part-time students (27% in engineering, 32% in computer science, and 17% in mathematics). Computer science has the highest proportions of part-time students of both sexes. While most of the increase in women's enrolment in mathematics and engineering over the study period occurred in full-time study, most of the increase in their enrolment in computer science occurred in part-time study; this is especially true in bachelor and doctoral programs. One might wonder whether women in part-time study are those working in low-level technical jobs in the computer industry.

Table 9 displays women's shares of part-time and full-time enrolment in all programs and in mathematics, engineering and computer science. This table indicates that women in mathematics and engineering are better represented in full-time enrolment. This is in contrast to the situation in computer science and in total university enrolment.

Table 10 displays data on enrolment by registration status viewed from a different angle. This table displays proportions of men and women university students who study on a part-time basis. As can be seen from these proportions, more than a quarter of women in computer science study on a part-time basis. This is much higher than their proportion in engineering (8.2%) and in mathematics (13.3%). This table also shows that the proportions of women in engineering and mathematics who study on a part-time basis are lower than that of men. This is also contrary to the situation in all fields and in computer science where proportions of women studying on part-time basis are higher than those of men.

Women's Movement Through Levels of Study. When comparing transition rates presented in tables 3, 5 and 7, the following points emerge:

(1) Doctoral female enrolment as a proportion of bachelor female enrolment in all three fields are higher than that in all programs; 4.0% in mathematics, 4.8% in engineering, and 3.4% in computer science compared with 3.2% in all programs, indicating that once they get over the hurdle of entry into mathematical and scientific fields, women are more likely to advance to the doctoral level than in other fields.

(2) The gender difference in the above proportion is much larger in mathematics and engineering than in computer science. That is, proportions of doctoral to bachelor enrolment for men in mathematics and engineering are twice as high as those for women, while the difference in computer science is only 1% in favour of men.

(3) While the hurdle impeding women's advancement through levels of study in mathematics seems to lie at entry to the masters level programs, in computer science and engineering it lies at entry to doctoral level programs. These fields should be examined for discipline specific factors which might help identify possible road blocks for women at these junctions.

Data in Tables 2, 4 and 6 also illustrate the different patterns in women’s representation at the three levels of study. Assuming that the proportion of students advancing to doctoral study directly after bachelor attainment is similar across all three fields, one can conclude that the pattern of women's advancement through levels of study varies across the three disciplines. While women's share of mathematics enrolment drops by about 9 percentage points at each higher level of study, women's share of engineering enrolment is the same at the bachelor and the masters levels, and their share of computer science enrolment actually increases at the masters level. At the doctoral level, women's share of engineering enrolment drops by about 8 percentage points and their share of computer science enrolment drops by about 6 percentage points.

Although women have been pursuing university education in unprecedented numbers, they continue to be under-represented in mathematics, engineering and computer science programs. Improvement in women's representation in these disciplines fell short of the improvement in their representation in other fields. Among the three fields under study, women's representation shows the most improvement in engineering, less so in mathematics and no improvement in computer science. However, the improvement is not sufficient as women are still far from achieving parity in these fields; this is most pronounced in computer science and engineering.

The field of engineering has been gaining students of both sexes from other disciplines. However, the likelihood that a woman university student will major in engineering is still less than one fifth that of a man. Representation of women in the field of computer science as compared to their representation in university education has been declining while there has been little change in mathematics.

Women occupy 20% of all computer science seats and 18% of all engineering seats in Canadian universities. These are markedly lower than the 38% in mathematics. But despite their lower representation in engineering and computer science programs, women in the latter two fields do not seem to drop out from the education pipeline at the masters level at the same rate as women in mathematics do. The proportions of women advancing to graduate studies in all three fields are higher than those in all programs. This denotes that women who do get into these male dominated fields seem to stick with them. The gender gap in the likelihood of advancing to the doctoral level is much wider in mathematics and engineering than in computer science and other fields.

In mathematics and engineering, women's representation is higher in full-time compared to part-time enrolment, at each of the three levels of study. This is in contrast to women's representation in computer science and in all programs.

It is clearly evident from the data presented in this study that women’s participation in the three disciplines under study varies a great deal. There are many differences in women’s level and trend of enrolment in part-time and full time study, in the size of the gender gap in enrolment, and in the rate at which women progress to graduate study. Thus, discipline specific factors such as curricula, topics, pedagogy, methods of instruction, context, applications, and presentation must influence women's participation in these fields in various degrees. This study shows that many more differences in levels and patterns of women’s enrolment exist among scientific and technological disciplines than can be explained by the more general factors discussed in the literature. This author proposes that discipline specific factors, such as curriculum, course content, instruction methods and context, interact with those general factors and modify their effects on women’s participation in these disciplines. Professionals in male dominated educational disciplines should take responsibility for examining their specific programs with the objective of providing an equitable learning environment for all learners.