Performance and Perception: Exploring Gender Gaps in Human Capital Skills

Performance and Perception: Exploring Gender Gaps in Human Capital SkillsAuthor(s): Victor ThiessenSource: The Canadian Journal of Sociology / Cahiers canadiens de sociologie, Vol. 32, No. 2(Spring, 2007), pp. 145-176Published by: Canadian Journal of SociologyStable URL: http://www.jstor.org/stable/20460630 .

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Performance and Perception: Exploring Gender Gaps in Human Capital Skills*

Victor Thiessen

Abstract: Why do young women rate their numeric skills lower than their male counterparts, despite the fact that their actual performance equals, or exceeds, those of young men? This puzzle

is explored using the 2000 Youth in Transition Survey of 23,592 Canadians aged eighteen to

twenty years. The surprisingly simple and paradoxical answer consists of two factors. First, it is

precisely because on average young women have greater human capital skills that they rate their

numeric skills as lower. That is, since young women's math performance is at a level comparable

to that of young men, but their language performance exceeds their math performance, they

devalue their numeric skills because their linguistic skills are better. Second, young women

discriminate more among their various skills than young men, apparently basing their self

assessments on relative marks, whereas young men seem to generalize their skill assessments on

the basis of their highest mark.

Resume6: Pour quelle raison les jeunes femmes cotent-elles leurs competences numeriques a un

niveau inf6rieur a celles de leurs homologues masculins, malgre le fait que leur performance reelle

est egale ou sup6rieure a celle des jeunes gens ? Ce mystere a e explore au moyen de 1'Enquete

aupres des jeunes en transition de 2000 a laquelle 23 592 Canadiens ages de dix huit a vingt ans

ont particip6. La r6ponse qui, etonnamment est a la fois simple et paradoxale, comporte en deux

facteurs. D'abord, c'est justement parce qu'en moyenne les jeunes femmes ont des competences

sup6rieures en capital humain qu'elles cotent leurs competences numeriques a un niveau inferieur.

* I want to thank the editor of The Canadian Journal of Sociology, Nico Stehr, and the anony mous reviewers, as well as my colleagues Howard Ramos and Richard Apostle, for their

helpful suggestions and criticisms of earlier drafts of this paper. I am grateful to SSHRC and

Statistics Canada for funding this research and providing access to the data through the Atlantic

Research Data Centre.

Canadian Journal of Sociology/Cahiers canadiens de sociologie 32(2) 2007 145



146 Canadian Journal of Sociology

C'est-a-dire qu'etant donne que leur performance en mathematiques est comparable a celle des

jeunes gens, mais que leur performance linguistique depasse celle en mathematiques, elles depre

cient leurs competences numeriques parce que leurs competences linguistiques sont meilleures. Ensuite, les jeunes femmes discriminent davantage les diverses competences que les jeunes gens,

basant apparemment leur autoevaluation sur les notes relatives, alors que les jeunes gens semblent

plut6t generaliser l'evaluation de leurs competences en fonction de la note la plus elevee.

Introduction

In a comparative cross-national assessment, students in the United States ranked

first for self-perceived math ability and South Korea last, whereas in actual

performance, South Koreans ranked first and the United States close to last

(Educational Testing Service 1992). While this discrepancy is dramatic, it

highlights the main questions addressed in this paper: What is the relationship

between performance and perception, and what inferences can be made about

the dynamics by which young people arrive at self-perceptions of their human

capital skills? At the heart of these questions lies a puzzle: Why do young

women rate their numeric skills lower than their male counterparts, despite the

fact that their actual performance equals or exceeds those of young men? This

puzzle is explored with respect to gender gaps in both the actual and perceived

performance of young Canadians on a variety of human capital skills. More

specifically, it addresses the relationships between marks received in high

school and self-assessed skills, and how these relationships differ between females and males.

In this paper I explore gender gaps in human capital skills in the Youth in

Transition Survey (YITS), a large (N=23,592), nationally representative sample

of eighteen- to twenty-year old Canadians. Investigating gender gaps in this

sample has several advantages. First, young people will have been fully exposed

to the effects of public education. In Canada, as in most industrialized countries,

human capital skills are developed primarily in educational institutions. Hence

it is reasonable to expect that performance measures in schools will constitute

a primary mechanism through which young people assess their various human

capital skills.

Second, gender gaps in human capital skills should be a relatively tractable

problem in such a sample, since many of the most important sociological

background characteristics should be irrelevant with respect to this topic. This

is because in a large random sample of a relatively homogeneous age group, one

would expect background characteristics on statistical grounds to be evenly

distributed between males and females. For example, the distribution of parental

education or household income should be approximately the same for young

men and women. If the genders do not differ on socio-economic characteristics,

then social advantages accruing on those bases cannot logically account for any

gender differences in human capital skills.



Exploring Gender Gaps in Human Capital Skills 147

Third, as will become apparent later, it is crucial for the topic at hand to

document self-assessed skills in relation to all combinations of marks in English

and math. Even with the large sample size, certain combinations of marks occur

rather infrequently. Fourth, the measures of self-assessed skills available in this data set are more

comprehensive than those used in previous studies; they include self-assess ments on six domains, rather than the typical focus on math and language skills.

It also differs in the format used to elicit such information. These differences

permit an assessment of the generalizability of previous findings. Finally, this age group is located at the juncture where crucial decisions and

life course transitions are in the process of being made. These include whether

to pursue further education, in what programs or fields of study, and ultimately

what occupations to enter. In making these decisions and transitions, both

performance and perception of human capital skills are likely to play decisive

roles.'

Review of literature

Scholars have invested considerable energy documenting gender gaps and their

trends in a variety of human capital skills. This has produced an impressive and

relatively consistent set of findings that have refined our understanding of the

processes of human capital skill development, especially during the schooling years. For good reasons, much of the research has relied on carefully con

structed and internationally comparable achievement test scores in mathematics,

reading, and science. Arguably, objective achievement in these skill domains

constitutes the clearest marker of the stock of human capital skills necessary for

competitive advantage in knowledge-based societies.

Recent research shows that although a unitary concept of perceived academic

ability, or academic self-concept, is seductively appealing, its use masks

important relationships (Correll 2001; Marsh and Ayotte 2003; Marsh and Hau

2004; Marsh et al. 2005). These studies indicate that academic self-concept

should be divided into at least two components: math and language. The impor

tance of this distinction was made manifest in attempts to resolve an empirical

1. I could have chosen to analyse the follow-up to the Canadian PISA 2000 survey, since self

assessed skill items were administered in the follow-up survey. It has the advantage of being

age-homogeneous (all respondents were fifteen years old in 2000). Analyses of this data set by the author reveal 1) similar gender gaps in self-assessed skills, 2) a virtually identical

underlying skill perception space, and 3) similar relationships between marks in English and

math as the ones reported in this paper. However, the psychometric properties of the skill

assessment items were somewhat inferior in that sample. Additionally, it is arguably a less

representative sample because of the added attrition that plagues all longitudinal data sets.




puzzle: While there is a strong correlation between math and language

performance on standardized tests or course marks (typically 0.5 or higher), the

correlation between math and language self-concepts is usually low, often

approaching zero (Marsh and Hau 2004). The resolution to this puzzle came

when multivariate analyses showed strong positive associations between per

formance in one domain and self-assessed ability in that domain, but simulta

neous weaker negative associations between performance in one domain (such

as math) and self-assessments in the other (such as language skills) when

performance in both domains are included as independent variables. Marsh and

Hau's (2004) interpretation is that individuals use both an external standard

(how good am I in math compared to others) and an internal standard (am I

better in math or in language tasks). On the basis of the first Program for

International Student Assessment (PISA) surveys, Marsh and Hau (2004)

document that these simultaneous positive and negative associations hold for

both math and language self-assessments in almost all of the twenty-six parti

cipating countries. The above findings imply that performance and perception in both domains

should be analyzed simultaneously. One shortcoming of most research is that

each skill domain, such as math or reading, typically is analyzed independently

of other domains. When considered within the same study, they are still

analyzed sequentially rather than simultaneously, or aggregated into an average

score (for examples of the latter, see Lee 1993; Muller 1993). That is, statistically there is a single dependent variable representing one skill domain.

Correll (2001) is a notable exception, assessing the relationships between math

and reading achievement with math and linguistic facility self-concepts in one

simultaneous regression equation. For certain important questions, various skill

domains must be analysed simultaneously, since the configuration of human

capital skills may be of crucial import.

A second shortcoming is that insufficient attention has been placed on the

relationship between self-assessments and performance. Where the relationship

has been examined, it takes the form of examining the extent of congruence

between perceived competence on a given human capital skill and test scores (or

course marks) tapping that skill. Since moderately strong relationships between

perceived competence and actual performance have generally been found

(Correll 2001; Marsh and Hau 2004; Marsh et al. 2005; Zhang 1999), a

premature conclusion has been formed that the relationship between perception

and performance is not problematic. This conclusion is premature since few

studies have investigated whether incongruencies between perception and per

formance are systematic; only if they are random would they not be problem

atic. My argument is that puzzles and paradoxes emerge precisely in divergen

cies between performance and perception and that these need to be understood

if we wish to understand the dynamics of human behaviour. This paper intends




to show that, although a high correspondence between perception and perform ance in human capital skills exists, there are also systematic disjunctures

between the two that are of theoretical, policy, and practical relevance.

With respect to causality, longitudinal research supports the conclusion of

reciprocal effects between performance and perception; that is, good perfor mance leads to higher self-assessments, which in turn (through increased interest and effort) subsequently improve performance (Bouchey and Harter 2005; Marsh, Hau, and Kong 2002; Marsh et al. 2005). This paper focuses on

the first link in the causal chain and therefore uses an "effects" terminology.

Nevertheless, the point of view I take does not fit squarely within a causal

framework; I assume that individuals utilize a variety of internal and external

cues and self-enhancement strategies to arrive at cognitions about their skills.

Marks do not "cause" individuals to form a particular self-assessment, for

example, since individuals may choose to discount the validity of poor marks,

as will be argued later on.

Gender gaps in human capital skills

The empirical literature consistently finds that women outperform men in la nguage tasks. This is so regardless of whether the measure of performance is

standardized reading achievement tests (Correll 2001; Ma 2000; OECD 2001;

Willms 2004) or language marks (Correll 2001; Duckworth and Seligman 2006;

Durik, Vida, and Eccles 2006; Finnie, Lascelles, and Sweetman 2005; Hagan

1991; Skaalvik 2004). In contrast to women's substantially higher performance

in reading and language, their self-assessed language skills are usually only

slightly higher than that of men: Durik, Vida, and Eccles (2006), Skaalvik

(2004), and Watt (2004) find no statistically significant gender difference,

Marsh and Ayotte (2003) report a weak but statistically significant difference

in favour of women, while Correll (2001) reports a more substantial difference.

Gender differences with respect to math performance are more complicated.

On standardized math tests, men perform better than women (Lau 2004; Lauzon

1999; Ma 2000; OECD 2001). However, this gender difference in math is much

smaller than in language (approximately one-third as large) and appears to be

decreasing over time (OECD 2001). Furthermore, this difference is almost

entirely due to a disproportionate number of men at the very highest levels of

math performance. That is, more men than women are found at the higher levels

of math achievement, and this gender difference increases with an increasing

performance level (Benbow and Stanley 1980; 1983; Lauzon 1999; OECD

2001; Penner 2003). Except at the highest (most difficult) levels, no appreciable

sex differences in math performance are found (OECD 2001; Spencer, Steele,

and Quinn 1999), and even at the highest level, the gender gap is declining

(Spelke 2005). Turning to math marks, recent research indicates that women




perform at least as well as men (Correll 2001; Duckworth and Seligman 2006;

Hagan 1991; Marsh et al. 2005; Skaalvik 2004). Yet, despite comparable or near

comparable performance, women rate their math skills substantially lower than

men (Correll 2001; Fredricks and Eccles 2002; Marsh and Ayotte 2003; Marsh

et al. 2005; Skaalvik 2004; Watt 2004).

Sociological explanations for the gender gap in math self-assessed skills are

based on the premise that in Western societies math ability is considered to be

sex-typed (Correll 2001). When women and men assess their own math skills,

they utilize these cultural cues as an additional source of information about their

own skills. The result is that men are more likely to overestimate - and women

to underestimate - their math skills, after controlling for actual performance.

Similarly, technology is generally considered a male domain. Hence it is not

surprising that men consider their computer skills higher than do women, even

after controlling for the amount of experience with computers (Volman and van

Eck 2001). In general the gender gap in perceived skills is largest on male-typed

tasks (Beyer 1998; Chan et al. 2000).

If beliefs about sex-type of task are to provide a plausible explanation, it

follows that tasks in which females are thought to be superior should result in

men underestimating theirperformance more than women. This expectation has

not been systematically investigated, but the limited available evidence fails to

support this expectation (Beyer 1998). It seems that on female-typed tasks, men

expect to perform on a par with women, while on male-typed tasks they expect

to perform better than women. This asymmetry suggests a gender modesty

explanation: given identical performance, men will judge their performance

higher than women. Hagan's (1991) findings indirectly support the gender

modesty hypothesis, since he found no gender difference in academic self

confidence, while at the same time in his sample girls' marks in both math and

English were higher than those of boys. Chan et al. (2000) provide evidence for

a small gender modesty effect. Of the twelve subject areas for which perceived

ability was measured, males did not rate themselves below the mid-point on any

subject, whereas females did so in three areas: computer science, engineering,

and physics. A point whose significance will be discussed later is that these

researchers found much greater variation in the self-ratings of females than that

of males. That is, females differentiated between their various abilities more

than males did.

Attribution theory provides a more psychological framework for understand

ing some of the conditions under which perception is incongruent with

performance. One hypothesis that has received some empirical support is that

personal success tends to be attributed to personal attributes, whereas failure

tends to be attributed to the environment. Both Lauzon (1999) and Stipek and

Gralinski (1991) document that high performing students tended to believe that

talent and ability were needed to achieve excellence in math and science; in




contrast, low performing students were more likely to believe that luck and

memorization were required. In a different context Krahn and Bowlby (2000)

found that young people with higher occupational achievements were somewhat more likely to attribute their success to their education, while those with lower occupational success were somewhat more likely to attribute their life outcomes to the changing economy. Weiner et al. (1971:102) report experimental evidence supporting the hypothesis that "success is more likely to be attributed to internal

factors than is failure, while there is a tendency to attribute failure to external

sources." One consequence of this is that poor marks should be discounted more

in assessing one's skills than solid marks, an expectation that I will call the

discounting failure hypothesis. One variant of attribution theory focuses on the fact that females are more

self-disciplined and put more effort into their school work than males (Duck

worth and Seligman 2006). As a result, when they assess their performance they

are more likely to attribute their success to effort rather than ability. The idea

that success is attributed to different factors than attributions of failure

nevertheless remains contested. Bempechat and Drago-Severson (1999:290) conclude that an "extensive literature on the relationship between attributions and academic achievement has repeatedly shown that higher achievement, in

mathematics as well as other subjects, is positively correlated with attributions

to ability, not effort; lower achievement is negatively correlated with attribu tions to ability, not effort."

Data and Measures

The data come from cycle 1 of YITS, administered between January and April

2000 to residents of the ten Canadian provinces who turned eighteen to twenty

years of age during 1999. The sample is based on the Labour Force Survey

(LFS), which employs probability sampling in a stratified, multistage design. As

with the LFS, the sampling frame excludes persons living in Yukon, Nunavut,

and the Northwest Territories or First Nations reserves, as well as full-time

members of the armed forces and inmates of institutions. Computer-assisted

telephone interviews were completed with 23,592 youth, yielding a response

rate of 80.9%. Systematic non-response rates by province, age, gender, and date

of LFS household data were taken into account in post-stratification weighting.2

Skill domains

Among the most important self-perceptions young people possess concern their

stock of human capital skills and the composition of those skills, such as which

2. Further methodological details can be found in Statistics Canada (2003).




skills they possess in particular abundance. These perceptions are arguably the

base upon which they make decisions about which educational pathways and

which occupational careers are possible and desirable. In a knowledge-intensive

society, it is believed that writing, reading and oral communication abilities,

new ways to solve problems, using numerical information to figure out practical

problems, and facility with computers are key to accessing valued resources.

Self-assessed skills for these six skill domains were measured through the

following questions:

How would you rate your ...

Ability to use a computer. For example, using software applications, programming, using a

computer to find or process infornation.

Writing abilities. For example, writing to get across information or ideas to others, editing

writing to improve it. Reading abilities. For example, understanding what you read and identifying the most

important issues, using written material to find infonnation.

Oral communication abilities. For example, explaining ideas to others, speaking to an

audience, participating in discussions. Ability to solve new problems. For example, identifying possible causes, planning strategies or thinking of new ways to solve problems.

Mathematical abilities. For example, using formulas to solve problems, interpreting graphs

or tables, using math to figure out practical things in everyday life.

Five response categories, ranging from "poor" to "excellent" were provided.

These measures of self-assessed skills have both advantages and disadvantages

relative to those used in other nationally-representative surveys. On the positive

side, they tap self-assessment on skills beyond that of math and English. Also,

they focus attention on skills, rather than on the marks they expect to get in

these two subjects, which some, such as Correll (2001) do. On the negative side,

skills in each domain are tapped by just a single item, rather than on multiple

measures and therefore are likely to contain a higher proportion of measurement

error.

Highest grade (year), marks, and program (track)

Three aspects of performance are central to the analyses presented here: the

highest grade at which classes in language and mathematics were taken, the

program or track (such as university preparatory) of these classes, and the marks

obtained in them. Since education falls under provincial jurisdiction in Canada,

the types of programs (and the class numbers and names by which they are

known) differ by province. For this reason, respondents were first asked in

which province they took their final year of mathematics and language classes.

They then were asked the highest grade they completed in these two subjects,

and the level (such as university preparatory) at which they were taken. The




grade, level names, and class numbers corresponded to the provincial lexicon in which a student had taken the class. In the analyses reported here, the grade

at which a class was taken is dichotomized into whether the class was taken in

the final year of high school, which normally is Grade 12 or its equivalent.

Program or track was also dichotomized into whether the class taken was

university-preparatory or not. Grade and program are combined into a single

measure consisting of the cross-classification of the grade and program

dichotomies. High school performance in math and language is captured by the

marks young people reported in response to the following questions that referred to the highest math/language class taken: "What was your grade

average in that Math (Language) course?" The response options ranged from the

numeric ranges for the equivalents of marks from F to A+. Marks from official

transcripts would have been more ideal, since an unknown amount of both

random and systematic measurement error likely characterizes self-reported marks. Evidence from the US "High School and Beyond" (HS&B) survey

suggests that self-reported marks may be quite reliable, since among Grade 12

students, the correlation between self-reported average marks with those

obtained from official transcripts was 0.77 (Fetters, Stowe, and Owings 1984). Nonnamaker (2000) reports an almost identical correlation of 0.76 for university

students. Kurman and Sriram (1997:429) report correlations of .71 and .93 in

two different samples of Grade 8 students. With respect to systematic

measurement error, all three studies uncovered a self-enhancement bias in the

self-reports; in the HS&B survey, the magnitude of such self enhancement was

approximately a quarter of a grade letter. However, as long as the self

enhancement bias is not greater among females, this bias will not compromise

the patterns described below. Fortunately, Kurman and Sriram (1997:429) found

just the opposite: over-reporting of marks was significantly higher among males

rather than females.

Findings

Skill Profiles

To what extent do young men and women consider themselves to have different

skill sets? Table 1 contains few surprises. It shows that young men are more

likely than young women to rate their computer, problem-solving, and mathe

matical skills as excellent. Conversely, young women are more likely than their

male counterparts to judge themselves to be excellent in writing and reading. On

oral communication abilities there is no substantial gender difference. Note that

respondents in general were substantially more likely to rate themselves as

excellent than as poor on all skills. The relatively low ratings in math are con

gruent with other findings concerning Canadian youth in math achievement.




Table 1. Distribution of skill ratings, by gender

Oral Using a Solve new Reading Writing communication computer problems Mathematics

A) Men

Poor 2 5 4 12 2 9 Fair 10 16 13 17 9 19 Good 38 41 39 31 44 36 Very Good 30 26 29 23 32 22 Excellent 19 12 16 16 13 14

Total 100 100 100 100 100 100

B) Women Poor 1 2 3 11 2 15 Fair 4 8 9 20 11 22 Good 30 38 37 38 50 36 Very Good 39 37 33 23 30 20 Excellent 25 16 17 8 8 7

Total 100 100 100 100 100 100

Willms (1999) found that after adjusting for parental education, Canadian young

people were almost two years of schooling behind their European counterparts

on math achievement.

Relative Skills

A further step to understanding gender differences in human capital self

assessments is to examine perceived skill attainment in one domain relative to

other domains. This can be done by simply subtracting each person's ratings on

math, for example, from each of their ratings on the other skill domains. The

range of the resulting relative measure is from -4 to +4, with a zero indicating

the same level of skill. This relative measure makes each person their own

comparison point, thereby minimizing any effects due to individual differences

in self presentation or response styles. Table 2 shows the results. Several gender

similarities are worth noting. On average both genders rate their math skills the

lowest of the six skill domains, as evidenced by the fact that all means are

negative. Likewise both genders rate their reading abilities as the best, with

young women being particularly more likely to do so, at least relative to their

math skills; on the five-point scale, young women rate their math skills to be a

full point lower than their reading skills, while young men place themselves

0.40 points lower. The main gender difference is that young women differentiate

among their various skills substantially more than young men do. This can be

seen by the fact that among the young women, the mean relative scores range




Table 2. Mean math skills relative to other skill domains, by gender

Math skills relative to... Males Females

computer abilities -0.01 -0.14 writing abilities -0.11 -0.75 reading abilities -0.40 -1.00 oral communication abilities -0.26 -0.69 problem solving abilities -0.32 -0.48

from -1.00 to -0.14, whereas the range is less than half that for the young men - from -0.40 to -0.01. It appears then, that women are more discerning in their

judgements. Whether they are also more modest cannot be determined from

these patterns, since the answer to that hinges on how self-assessments relate to

marks. That is, it depends on whether women with identical marks as males,

taken at identical levels, nevertheless perceive themselves to have less human

capital skills than their male counterparts.

The Gender Divide

Having documented that a gender divide remains among young people in their

language and numeric skills, the next task is to establish that these differences

cannot be attributed to gender differences in taking math and language classes.

Some students fail to take these courses in Grade 12, and among those who do,

they can take them at different levels. With respect to levels, whether a given

course is taken at a university preparatory level is especially important. Clearly,

obtaining a good mark in a university preparatory class may be substantially

more difficult than obtaining the equivalent mark in a general program. Hence

the relationship between marks, skill assessment and gender needs to be

explored with these distinctions in mind. Thus, for example, it may be that

young women rate their mathematical skills lower than their male counterparts

because they failed to take advanced classes in mathematical subjects, or they

took them at advanced levels but failed to achieve marks comparable to those

of young men. In recent years, young women are more likely than their male

counterparts to take university preparatory classes/programmes (OECD 2001),

but these trends may mask subject matter differences.

The next table shows that women are indeed more likely than men to take a

language (English or French) class in the final year of high school. Not only

that, they are substantially more likely to take such a class at a university

preparatory level: 54% of female students but only 45% of their male counter

parts took a university-preparatory language class in the final year of high

school. These gender differences in language courses lead one to speculate that

the higher ratings young women provide for their writing and reading skills are




Table 3. Highest grade and level of high school math and language classes, by gender (%)

Highest grade and level of...

language math Grade and level Male Female Male Female

Li: < Grade 12, not university preparatory 35 31 30 26 L2: < Grade 12, university preparatory 6 4 23 24 L3: Grade 12, not university preparatory 15 11 13 12 L4: Grade 12, university preparatory 45 54 35 37

Total 100 100 100 100

predicated on their greater propensity to take advanced language courses in their

final year of high school.

Turning to math classes, the same table shows that women are at least as

likely as men to take mathematics courses in their final year of high school and

at least as likely to take them at the advanced university preparatory level (37%

versus 35%, respectively). Given the speculation in the previous paragraph, we

would have expected young men to be more likely than young women to take

an advanced math course in their final year of high school. The evidence from

this table is not at all consistent with the argument that women rate their mathe

matical skills lower than men because they have shied away from advanced

mathematics classes. A parsimonious argument would require that classes taken in language and mathematics, respectively, constitute the bases on which young

men and women rate their respective language and mathematical skills, or that

they are not the bases for either of their language and numeric skills ratings. It

would be awkward to argue that marks are a basis for one gender for one of the

skills, but not for either the other gender or the other skill. So we must conclude

that the gender differences in human capital skills self-assessments are not a

function of gender differences in the relevant prior courses taken.

More crucial than whether a student attempted advanced classes is the mark

obtained in conjunction with the type of class taken. Perhaps young men obtain

better marks than their female counterparts in the advanced math classes, for

example. The next table shows the average mark (on a GPA scale where F = 0

and A+ = 5) of men and women at each of the grade/program combinations for

language and mathematics.

This table reveals that young women's language marks are consistently and

substantially higher than those of young men in each of the grade/program combinations. On the other hand, gender differences in math marks are

negligible in all four grade/program combinations, with average female marks

being at least as high as those reported by males. This establishes that our puzzle

is genuine: Young women rate themselves lower on numeric skills despite

having taken equally advanced classes and performed equally as well, if not

better than, young men in both language and math classes.




Table 4. Mean marks in language and mathematics, by highest grade and level of mathemat

ics and language, and gender

Language mark Math mark Highest grade and level Male Female Male Female

LI: < Grade 12, not university preparatory 2.76 3.23 2.69 2.72 L2: < Grade 12, university preparatory 2.52 2.97 2.90 2.96 L3: Grade 12, not university preparatory 2.71 3.04 2.84 2.91 L4: Grade 12, university preparatory 3.11 3.40 3.03 3.04

For descriptive purposes, Table 5 provides information on two self-assessed skills (writing and mathematical) in relationship to mark combinations in lan

guage and math courses. Three patterns emerge. First, for identical combina

tions of marks, men rate their mathematical skills higher than do women, while

women rate their writing skills higher than do men, with only minor exceptions

(FF, FD, BF, and A+D for writing; FD and A+F for math). This suggests that

both men and women utilize gender-specific cues, such as cultural beliefs, in

addition to their marks when assessing their skills. Second, with trivial

exceptions, the higher the mark in a given subject, the higher is the self

assessment in the corresponding skill domain among both women and men.

Third, women seem to discriminate more than men between their mathematical

and writing abilities. One illustration of this is that the lowest math rating

among women occurs when their math performance is most discrepant with

their language performance (FA+); this is not the case for men. At a more global

level, the final row of Table 5 shows that the difference between the mean

writing versus math skill assessments is substantially larger among women than

men (3.58-2.84=0.74; 3.26-3.17=0.09, respectively). I turn now to analyzing the underlying structure of the six skill domains,

followed by a detailed examination of the relationships between this structure

and the levels and marks obtained in math and language courses.

The Structure of Skills

What are the relationships of the six skill domains to each other? All of the

intercorrelations are positive (not shown), but this can be due to a variety of

things, from methodological artefacts (common method variance) to common skill acquisition processes, such as parental social or cultural capital. The usual

procedure for finding the structure of a set of items is through principal com

ponents analysis (PCA). Since the psychometric properties of the self-assessed

skill items are unknown, nonlinear principal components analysis (NLPCA -

also known as categorical principal components analysis) is employed. As in

PCA, NLPCA defines a lower-dimensional latent space for the items entered

into the analysis. As in PCA, this space is defined in terms of orthogonal




Table 5: Mean self-assed writing and mathematical skills by mark combination and gender

Writing Mathematical Math/language mark Male Female Male Female Male Female

combination N N Mean Mean Mean Mean

FF 36 16 2.61 2.56 2.69 2.13 FD 30 25 2.80 2.71 2.13 2.33 FC 138 82 2.83 3.33 2.20 1.82 FB 140 190 3.12 3.54 2.25 1.86 FA 61 115 3.68 4.02 2.20 1.92 FA+ 9 25 4.00 4.32 2.44 1.40 DF 22 9 2.50 3.11 2.52 2.22 DD 61 33 2.67 2.88 2.38 2.22 DC 211 136 2.94 3.09 2.45 2.10 DB 187 180 3.19 3.51 2.39 2.02 DA 76 120 3.60 3.73 2.35 1.91 DA+ 8 18 3.63 4.17 2.25 1.72 CF 97 31 2.66 2.90 2.77 2.29 CD 166 54 2.75 3.02 2.75 2.22 CC 897 412 2.95 3.11 2.76 2.38 CB 1,030 898 3.24 3.43 2.68 2.39 CA 414 751 3.59 3.78 2.57 2.31 CA+ 59 122 3.81 4.10 2.29 2.07 BF 71 37 2.83 2.78 3.42 2.76 BD 114 38 2.86 3.32 3.18 3.05 BC 901 458 2.94 3.18 3.14 2.95 BB 1,296 1,161 3.30 3.41 3.21 2.84 BA 831 1,357 3.63 3.76 3.06 2.74 BA+ 119 313 3.88 4.07 2.96 2.60 AF 41 13 2.44 2.85 3.41 3.08 AD 59 24 2.73 3.04 3.64 3.08 AC 475 251 2.83 3.21 3.61 3.08 AB 966 801 3.25 3.45 3.66 3.24 AA 801 1,206 3.61 3.71 3.55 3.29 AA+ 172 462 3.94 4.04 3.48 3.19 A+F 11 5 2.55 2.80 3.45 4.20 A+D 27 8 2.89 2.38 3.70 3.50 A+C 126 56 2.83 3.02 3.98 3.46 A+B 287 206 3.14 3.35 3.94 3.50 A+A 459 507 3.64 3.70 4.24 3.79 A+A+ 210 381 4.00 4.01 4.20 3.92

Total 10,808 10,431 3.26 3.58 3.17 2.84

Key: The first letter refers to the mark in mathematics; the second to the language mark. Both

marks are for the last mark obtained in high school.

dimensions where the first dimension accounts for the greatest amount of item

variance, and each additional dimension accounts for successively less variance.

In contrast to PCA, its categorical counterpart does not assume that the item

response categories are metric or linearly related to the underlying dimensions.




NLPCA facilitates visualizing the human capital skill domain items in a lower

dimensional latent space, which permits one to see the location of each of the

response categories of all of the skill items and their relationships to each other.

In NLPCA the category values (here "1" to "5") are replaced by optimal

scores on each dimension (for details see Gifi 1990; Heiser and Meulman 1994).

The optimal scoring algorithm allows ordinal constraints to be imposed so that

ordered categorical variables result in increasing, or at least non-decreasing, quantifications within the r-dimensional space (with r most often 2). Response categories inconsistent with the implied ordering in r dimensions are manifested in tied optimal quantifications for two or more categories. Since no tied quan

tifications were found for any of the human capital skill items, we can conclude

that the original response categories can justifiably be assumed to be ordinal. At

the same time, the quantifications indicate that the difference between a 1 (poor)

and a 2 (fair) is not nearly as large as the difference between a 4 (very good) and

a 5 (excellent). In fact, without exception for all of the skill items, there is a

monotonically increasing difference in the quantifications between successive response categories as one moves from "poor" to "excellent."3

All of the human capital skills have positive, and relatively large, loadings

on the first, or primary, dimension. This dimension captures 44% of the

variation in the human capital items; the second dimension an additional 19%,

for a total of 63%. The second dimension has positive loadings on mathematics,

computer, and problem-solving skills, with negative loadings on the remainder (reading, writing, and oral communication).4

Figure 1 provides the two-dimensional "cognitive map" of the self-assessed

skills among eighteen to twenty year old Canadian youth. On the primary

(horizontal) axis, responses of "poor," "fair," and "good" are to the left of the

origin for all items, with all responses of "very good" and "excellent" on the

right side. This suggests that the first axis can be interpreted as the volume of

human capital skills. To interpret the vertical axis, it is perhaps simplest to first

describe the points in each of the quadrants. In the top left quadrant we find the

response categories of "poor" through "good" for reading, writing, and oral

communication skills. Note the cluster of points representing low assessment of

writing and reading skills (rl, r2, wl, and w2). Since proximities of points

translate to strength of association between response categories, it follows that

respondents who rated themselves as "poor" or "fair" on one of these skills are

particularly likely to describe themselves as "poor" or "fair" on the other.

3. The optimal quantifications are not shown, but are available from the author. If the original

response categories (1 to 5) were recoded to their optimal quantifications, the unrotated PC A

solution would be identical to that of NLPCA.

4. Mathematical and writing skills enjoy the highest communalities, while computer skills are the

least well represented in the two-dimensional cognitive map, indicating that the former two

skills are the most critical ingredients in young people's cognitive map of their skills.




The bottom left quadrant contains the same response categories for mathe

matics, problem solving, and computer skills. In the top right quadrant we find

the response categories of "very good" and "excellent" for the same three skills,

while the bottom right quadrant contains the same response categories for the

writing, reading, and oral communication skills. Within this map, the longest

distance is between poor problem solving skills (p 1) and excellent mathematics

skills assessments (m5). That is, not surprisingly, a strong negative association

exists between these two responses, with respondents who describe themselves

as poor in problem solving skills being particularly unlikely to describe their

math skills as excellent. But note also the relatively large distance between p5

and w5. This means that respondents who rate their math skills as excellent are

quite dissimilar from those who rate their writing skills that way.

Figure 1. Map of human capital skills

m5

p5

r2 w2 m4 C5

r3

l l l l l l ll lllw 3

03 c4p4

Ir OS (5'A3 r4 o4

wS

rl

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Key: c = computer, m = math, o = oral communication, p = problem solving r = reading, w =

writing; 1 = poor, 2 = fair, 3 = good, 4 = very good, 5 = excellent. Example: pl represents the

location of respondents who rated their problem-solving skills as poor.




This diagram is reminiscent of Bourdieu' s (1984) conception on the relationship between cultural and economic capital. In this diagram, the horizontal line pass

ing through the origin or centroid represents the volume of capital. That is, the

amount or volume of human capital for any point is conceptually quantified by

its perpendicular position on this line. The vertical axis captures variation in the

composition of human capital skills. Points above or below the horizontal axis

represent different compositions of human capital, with numeric skills exceeding language skills in the top half, and vice versa, language skills

exceeding numeric skills in the bottom half.

Looked at somewhat differently, we can see that the writing, reading, and

oral communication skills form paths from the top left to the bottom right. The

lowest assessments on these three skills are closest to the top left corner and the

highest in the bottom right, with the in between response categories tending to be on a continuum between these end points. Likewise, the mathematical, prob

lem solving, and computer skills are on pathways from the bottom left to the top

right quadrant. Note again that the response categories in between these two

extremes are in a correct ordinal position, and come close to forming straight

lines. As a result, it is possible with minimal loss of information to represent

each of the skills as a continuum on a straight line. An angle of approximately

90 degrees separates the location of points representing writing skills from that

for mathematical skills. This indicates that variation in self-assessed writing

skills is essentially independent of variation in mathematical skills. The remain

ing skills are mixtures in different proportions of numeric and language skills.

Since gender gaps are the main focus of the analysis, it is important to

ascertain that the underlying structure of self-assessed skills is comparable

between the genders. To test this, NLPCA was run separately for men and

women. The results indicated that the underlying structure was indeed

remarkably similar: for both genders, two dimensions with eigenvalues

exceeding 1.0 were extracted, the proportion of variance explained by each

factor was approximately the same, the rank order of the loadings on the two

dimensions was identical, and in general the loadings differed only at the second

decimal point.5 The next section explores how combinations of marks and levels in math and

language respectively affect young people's human capital skills ratings. NLPCA permits one to project other variables (known as passive variables) into

the space defined by the skill items. In the application here, the location of

various sub-groups - defined on the basis of combinations of gender, math and

5. Parallel analyses were conducted on the PISA 2000 follow-up survey. The overall results, as

well as the separate analyses by gender, were again similar. This suggests that the two

dimensional cognitive map is robust and gender invariant.




language marks, and levels/program - are portrayed visually. They are called

passive variables since they do not affect the structure of the underlying space.

The various sub-groups are located at their average score in the lower

dimensional space. If school performance in math or language is the basis of

young people's ratings, no appreciable gender differences in the relative

locations of males and females for any of the level and mark combinations

should occur. That is, to the extent that young people judge their skills on the

basis of the mark they obtained in a specific level of a subject that they enrolled

in, there is little ground to expect systematic gender differences in their skill

ratings.

Language Marks

Figure 2 shows the relationship between the volume and composition of human

capital skills on the one hand, and language marks and levels on the other,

separately for each gender. Six patterns emerge. First, marks obtained in lan

guage are, as expected, increasing more or less monotonically on the first

dimension from Fs at the left to A+ at the right. That is, language marks predict

volume of human capital skills, with the following inequalities generally

holding among both men and women:

F < D < C < B < A < A+

Several glaring exceptions to this pattern occur, and all exceptions involve a

failing mark in language. Note for example, the location of students who have

taken but failed a university preparatory language class in Grade 12 (g4F and

b4F). For both genders, their location is substantially further to the right than

expected - for the males exceeding even that of some groups that obtained an

A, and for the females exceeding some groups that obtained a C. Likewise

males who previously attempted a university preparatory class but failed (b2F)

are situated too far to the right. These exceptions suggest that students discount

failing marks. That is, obtaining a failing mark in language, especially if the

class was a university-preparatory one, fails to translate into especially low self

assessments of their volume of human capital skills. It is as though by having

attempted a language class at a university preparatory level, the fact of a failing

grade is partially excused. On the other hand, the number of cases involved in

these exceptions is comparatively small, and the anomalous locations may

represent nothing more than chance fluctuation. In any event, the tendency for

low marks, especially failing marks, to be anomalously located constitutes the

second pattern, one that will be manifested in other analyses that follow.

The third pattern is that the vertical dimension almost perfectly separates the

genders, with the top half populated by males and the bottom half by females.




Figure 2. Human capital skills in relation to language marks and levels, by gender

b4A b2F

0.4 blC g4F b4D b3F b2C WC b1B

b3D b4B b3A -

b3B g3D b3A b2A -

b4A

b2D b2t b3A bA h4A+

? ?A -A - 3 blF a,3C g4D g2D b2A 0.0 g3g

o glF gqiD gI a E

C) g2A, gA 3A g4B WAg

g4A

-0.4 g_IA g2A+ A

g4A+ glA+

g2F

-0.8 I l l

-1.0 -0.5 0.0 0.5 1.0

Volume

Key: The first character refers to gender (b=males, g=females); the second to the course level; the

third to the mark obtained. For example, g4A refers to females who received a mark of A in a

Grade 12 university-preparatory language course.

This is strong evidence that women who have taken equally advanced language

classes and performed equally as well as men in them, nevertheless are dis

proportionately represented in the lower region of numeric skill dominance and

vice versa, disproportionately unlikely to appear in the upper region. That is,

Females < Males on numeric dominance regardless of language mark or level.

Several exceptions to the third pattern occur that involve low language marks

(g3D, g4F, and b IF). These anomalies are perhaps a second form of discounting

unfavourable marks.

A fourth pattern takes the form of a gender by language mark interaction

effect on the composition of human capital skills. Among males, increasingly

high language marks have no discernable effect on the composition of their

human capital skills. This is deduced from the fact that no systematic tendency

is found for their position on the second dimension to either increase or decrease

as one moves from left to right on the first dimension. Stated differently, young

men who obtain a high mark in language are neither more nor less likely to

assess their numeric skills to be better or worse. The situation is quite different

among young women: the higher the mark they received in language, the lower




they are on the second dimension. This is an important interaction effect,

indicating that among males the mark obtained in a language class has no

bearing on their numeric skill ratings, but among females it has a relatively

strong negative effect on their numeric skill assessment.

The effect of level at which a language class is taken comprises the fifth

pattern: level has a modest effect on the volume of human capital skill ratings

among both genders. Specifically, there is a fairly consistent tendency for

students who have taken a Grade 12 university preparatory language class to be

located to the right of all other grade/level groups who have obtained an

identical mark. For example, males who have taken a Grade 12 university

preparatory language class and obtained an A+ are located to the right of males

in all other language classes who have also obtained an A+; the same generally

holds true among young men who have received other marks. Among the

remaining grade/level groups, there does not appear to be any systematic

difference. The same general pattern is present among young women, namely:

L4 > LI, L2, L3

From these patterns it appears that the most important factor is the absolute

mark obtained, with level of minor significance, except for a clear tendency for

those who have taken a Grade 12 university preparatory class and obtained a

specific mark to have a higher volume of human capital skills than other

students who have obtained an identical mark in language.

The sixth and final pattern provides some evidence for what might be

labelled a gendered self-confidence effect. This is especially noticeable at the

Grade 12 university preparatory classes. Among these, males score higher than

females on volume of human capital skills when marks are held constant. That

is, for any given mark, males are located further to the right than females. This

modesty effect is not apparent to the same extent in the other grade/level groups.

Hence the gender modesty effect seems to characterize primarily young adults

who are in all likelihood well on their way to post-secondary university

education.

Math Marks

Figure 3 provides parallel information as the preceding one, except that it

provides the locations of young men and women on the basis of marks and

grade/level combinations of math classes. Even a cursory glance at this map

shows that performance in mathematics plays a quite different role in some

respects from that of language in human capital skill self-assessments.

Remember from the previous map that a horizontal line drawn near the

origin of the y-axis almost perfectly separated the genders. In the map for math




Figure 3. Human capital skills in relation to math marks and levels

b4A t 1 .0

b2A+ b3A+

blA+ b4A b2A

0.5 g4A+ b4B

.bA b3A

._ b3LBb2 0 OL b3D blB bAC g4A E 0.0 bAC b4D glA+ C) glA 0 3A+ B2A

biB g3A b,C g3B g4B

b3F: b1 F: gIB g2B

-0.5 g3C gAb

g3D g4 'y2C g lD g D B gF

gAB

-1.0 - I I

-1.0 -0.5 0.0 0.5 1.0

Volume

Key: The first character refers to gender (b=males, g=females); the second to the course level; the

third to the mark obtained. For example, g4A refers to females who received a mark of A in a

Grade 12 university-preparatory math course.

marks, a line drawn from the lower left to approximately the upper right vertex

is the one that separates males from females. That is, young men appear in the

upper left triangle and young women in the lower right one, with only minor

exceptions (g4A+ is a little too high; b4D a little too low). Within each gender,

mathematics marks tend to be lowest near the bottom left and to increase as one

moves towards the upper right region of the map. The implication is that for

both genders, the higher the math mark, the higher the volume of human capital

skills and the more prominent the numeric skills relative to the language skills.

Stated differently, math marks crucially affect both the volume and composition

of human capital self-assessments and they appear to do this equally for males

and females. At the same time, the fact that at any point along the diagonal,

females are below the diagonal and males above, indicates a consistent tendency

for the composition of human capital skills to be weighted more towards the

numeric for young men than is the case for young women. Thus, although it is

true that low math marks function to make both males and females judge their

numeric skills to be low, females judge them to be even lower than males.




Likewise high marks produce high assessment of numeric literacy (in addition

to high volume), but the structure of skill composition is weighted even more

highly towards the numeric among young men than among young women. This

is quite different from the role of language marks, where among males the lan

guage mark affected only the volume and not the composition of human capital

skills. A second difference is that there is evidence that both track (university

preparatory versus other) and year (Grade 12 versus less than Grade 12 math)

are significant factors in addition to marks obtained in math for the volume and

composition of human capital skills. The patterns are stronger for young men

than for young women. Among men, the pattern typically is L4 > L2 > L3 > LI.

Thus among men who took a university preparatory math class in Grade 12 and

obtained a given mark hold higher self ratings in both the volume of human

skills and the numeric dominance of such skills than those who obtained an

identical mark in any of the other levels. Next most important for volume and

composition is having taken such a class at a university preparatory level in a

lower grade, followed by taking a non-university math class in Grade 12, and

finally not having taken any math class at the Grade 12 level.

Among young women, the patterns are somewhat less clear and conse

quently more complex. For example, at the upper range of marks (B to A+)

Level 2 females score higher than their level 4 counterparts with respect to

volume of human capital skills. At the lower range of marks (F to C), the pattern is the same as for males. In general L3 > LI on dominance of numeric skills.

There is stronger evidence of a possible gender modesty effect here than

found for language performance. At the C or higher mark, males exceed females

on both the volume and the numeric dominance of their skills: the location for

males at these mark levels is always to the right and higher than that of females

with identical mark and grade/level. At all levels and grades, young men exceed

their female counterparts on the relative dominance of numeric skills. The

gender modesty effect is especially evident among those in university pre

paratory math classes who get A+ in their final year; among them, young men

are located especially high relative to young women with equal math perfor

mance on both volume and numeric preponderance of skills.6

Relative Marks

The analyses so far has revealed distinct gender differences as well as simi

larities, in the relationships between performance and perception. Yet the key

6. Although this could be due to gender modesty, it could also be a reflection of the fact that the

gender gap in math tests has generally been found to increase at the very top end of the distri

bution (Benbow and Stanley 1980; 1983). Hence among this group of males, their math skills

may indeed be superior to that of females with comparable marks in the advanced math classes.




puzzle - why young women with identical marks taken at the same level as

their male counterparts nevertheless rate their numeric skills to be lower than their male counterparts - remains. It is possible that young women simply have

less confidence than young men in their numeric abilities at every comparable level of performance. But there is another possibility, a clue to which is found

in the gender-language performance interaction effect documented earlier. This interaction effect took the form that among females but not among males,

language performance affected the composition of their skills in a systematic manner, namely the better their language mark, the lower the preponderance of

their numeric ability. Recalling that female students perform substantially better than male students in language classes, but that there is at best a minor gender

difference (also in favour of females) in math performance, suggests that the key

to solving the puzzle may reside in how a student's performance in math

compares to that of language. To explore this possibility, it is necessary to

examine marks in math and language simultaneously. Since this analysis

contains even more data points than the previous ones, it will be necessary to

examine various subsets of them at a time, in isolation of the other points.

Starting with the situation where the math mark is identical to the language

mark, it should be the case that: a) the volume of human capital skills should

increase with increasing marks, b) the composition of human capital skills should be unaffected by increasing marks, since respondents performed the same in math as in language, and c) no gender difference in either volume or

composition of human capital skills should emerge, since males and females

performed equally well in both subjects. With these expectations in mind, let us

examine the evidence (see Figure 4). With respect to volume of human capital

skills, for both genders there is a clear correspondence between their marks and

their location on the first dimension, with FF being farthest to the left, and

A+A+ farthest to the right; the sole exception is among boys, where DD is

slightly to the right of CC. This pattern is congruent with the first expectation.

With respect to the composition of human capital skills, there appears to be

a positive relationship between increasing (but equal) marks in math and

language and increasingly higher concentrations of self-assessed numeric skills7 Stated differently, having increasingly high but equal marks in math and English

is associated with increasingly thinking of oneself as being more skilled num

erically than linguistically. Perhaps young people consider it more difficult to

obtain a good mark in math than in language, and hence consider equal marks

7. For both genders, the lowest point on the second dimension is actually at DD. As suggested

previously, students who receive failing marks may be partially discounting the relevance of

their marks for their self-assessments. We should keep in mind, however, that the number of

cases with failing marks in both subjects is quite small (N < 20 for females) and sampling fluctuation constitutes an equally plausible alternative interpretation.




to indicate having better numeric than language skills. In any event, this pattern

is incongruent with the second expectation.

Figure 4 also shows a clear gender effect: For all six mark combinations,

young men are located further to the right than their female counterparts on the

volume of human capital skills. Likewise, and equally without exception, young

men are located higher than young women on the vertical axis, indicating that

males at each of these mark combinations see the composition of their skills to

be weighted more towards the numeric than the equivalent group of females.

These patterns are in direct contradiction to the third expectation and support

instead a gender modesty and a gender stereotype dynamic. The gender modesty

effect is inferred from the fact that females who have obtained identical marks

as males nevertheless rate themselves as having less human capital skills.

Additionally, the pattern with respect to the composition of human capital skills

is consistent with a gender stereotype dynamic. Both genders are aware of the

common perception that men's mathematical abilities are superior to that of

women's. Even when their marks do not conform to this stereotype, on average

their self-assessments reproduce the gender difference in their self-assessed

composition of human capital skills.

Figure 4. Human capital skills for equal math and language marks, by gender

Math=Language

_.. -A+

uz ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.. ,........

o

Volume

N _m

Noe:Dselieconcthloainofmlssoiliethsoffml.




Figure 5. Human capital skills and mark combinations in math and language, by gender

Math grade F Math grade D Math grade C

-1. 0. 0. . . . 10000 05 1. . 10 -. . . . .

E E~- -.~ A+ E

8 8 E

0+~~~~~~~~~~~~~~A

-1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 VWUm Voume Voume

Math grade B Math grade A Math grade A+

Dicontn 'alr.I lotalisacs nmlu oiinrv ale+b

F 'A~~~~~~~~~~~~~~~~~~~~~~~~~~~+ A+ 0~~~~~~~~~~~~~~~~~~~~~0

A+~~~~~~~~~~~0 R~~~~~~~~~~~

-1.0 -0.5 0.0 0.5 1.0 1.0 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Volume Voume Volum

Note: Dashed lines connect the locations of males, solid lines those of females.

The six panels of figure 5 are formed on the basis of the six possible math

marks, thereby holding math marks physically constant. An examination of the

six panels collectively reveals four patterns:

Discounting failure. In almost all instances, anomalous positions (revealed by a zig-zag pattern in either dimension) involve a failing mark. These "anomalies"

are congruent with the discounting failure hypothesis.

Male appropriation of numeric skills. At all combinations of marks, young men generally consider themselves to possess a higher proportion of numeric

skills than do their female counterparts. This is revealed by the fact that the

dashed lines (representing positions of males) typically are higher than the solid

lines (representing females).

Accelerating self-enhancement bias among males. The better young men's

math marks, the more the volume of their self-assessed skills exceeds those of

comparably-performing young women. Compare the lower three panels with the

upper three. In the three lower panels of figure 5 (representing math marks of

B or better), males, with few exceptions, are located to the right of females with

identical language marks. This tendency is visible particularly in the upper




ranges of language marks as well. However, this pattern is not nearly as clear

or consistent in the top panels of figure 5. Is the underlying dynamic male self

enhancement or female modesty? Taking females as the focal group, what we

see is that young women who obtain good math marks are more modest than

their male counterparts with respect to the total volume of their human capital

skills. Male self-enhancement is just the opposite side of the female modesty

coin. What appears for the first time in this figure, however, is that the extent of

enhancement/modesty appears to be a function of performance in math. It is as

though when men's math performance is congruent with the cultural cues, they

view this as an indication of general competence.

Gendered importance of relative marks. Among males there often is no

discernable downward trend on the vertical axis except when their language

marks are B or better. Among women, the negative slope is somewhat clearer

throughout the whole range of language marks. This suggests again the greater

importance of relative marks for women than for men.

Conclusion

In this paper I have argued that it is fruitful to conceptualize self-assessed skills

on the bases of their total volume and their composition, rather than on

individual types of skills, such as language or mathematical. Empirically this

was implemented by constructing an underlying cognitive map of six self

assessed skills. By projecting combinations of levels and marks in language and

math courses onto this map, it was possible to assess in greater detail the

relationships between performance and perception, as well as gender differences

in these relationships. The analyses in this paper permit the following general

izations to be made:

On the six human capital skills which are arguably the most important in

knowledge-based economies, females rate their reading and writing skills higher than males. Conversely, males rate their math, problem-solving and computer

skills higher than females (and there is essentially no gender difference on oral

communication skills). These six human capital skills can be parsimoniously presented in a two-dimensional underlying space that differentiates their volume from their composition. Within that space, numeric (math) skills are independ ent of language (reading and writing) skills, since these are orthogonal to each

other. In between these skills are problem solving and computer skills (which

are intimately related to each other and closer to numeric than the language

skills). In virtually all comparisons, men rate the numeric component of their skills

higher than do women with comparable performance. The male superiority in

numeric skill ratings cannot be attributed to their obtaining either higher marks




or taking more advanced classes than females in math course, since females are

as likely as males to take the more advanced classes and to obtain marks that are

equal to those of males in these classes. This finding suggests a pervasive

gender stereotyping effect. In most relevant comparisons, young women rate their volume of human

capital skills as less than their male counterparts whose performance is com

parable. This suggests the operation of a gender modesty, or self-confidence, dynamic.

Absolute marks obtained in both language and math classes have large

effects on the volume of human capital skills. Clearly, marks obtained are a key

basis on which self-assessments are made. Likewise, having taken university

preparatory classes in the final year of high school boosts human capital assess

ments, with students in such classes exhibiting a greater volume of human

capital skills than others who obtained identical marks but at lower levels. This

program effect is not nearly as strong as either absolute or relative marks.

Marks obtained in language appreciably affect the composition of human

capital skills among young women but not among their male counterparts.

Among females, the better the language marks, the lower their relative ratings

on numeric skills. This gender interaction effect suggests that the process by

which young women assess their human skills is in some fundamental respects

different from that of young men.

Marks obtained in math affect both the volume and composition of human

capital skill self-assessments, with higher marks resulting in greater volume and

greater preponderance of numeric skills. These effects are similar in nature for

both genders. The relation of math to language marks vitally influences young people's

perception of their human capital skills. The better their mark in one subject

compared to the other, the more their self-ratings are pulled toward the skill in

which they performed better. This pattern indicates that young people's assessments are made to a large extent on the basis of their relative performance in math and language. Relative marks appear to be a stronger base for skill

assessments among young women than among young men.

Young people with especially low performance in either math or language

are disproportionately frequently located anomalously, suggesting the presence

of a discounting failure attribution dynamic.

I started with the puzzle of why young women on average rate their numeric

skills as lower than boys, despite the documented fact that they are no less likely

than their male counterparts a) to take math classes, b) to take less advanced

math classes, or c) to obtain lower marks in these classes. The paradox uncov

ered in the analyses suggests that it is precisely because on average girls have

greater human capital skills that they rate their numeric skills as lower. That is, since young women's math performance is at a level comparable to that of




young men, but their language performance exceeds their math performance

(46% of females versus 33% of males obtained a higher mark in language than

in math), young women devalue their numeric skills because their linguistic

skills are better.

Yet there is more to the puzzle. Although both genders employ a self

comparison strategy to assess their cognitive skills, the evidence indicates that

young women differentiate amongst their various skills more than young men.

It appears young men's skill assessments are more influenced by their highest

mark whereas their female counterparts are more influenced by their relative

marks. There is some evidence of a gendered modesty effect. This effect is inferred

from the tendency of young men to be located to the right of young women with

identical combinations of marks (i.e., to be located in regions indicating a

greater volume of skills). The modesty effect is quite modest, and is therefore

a relatively minor component in the overall gender differences in skill

assessments documented here.

The fact that at almost all combinations of marks women are located lower

than men on the numeric component of their skills suggests the presence of a

pervasive gender stereotype. Male dominance in things numeric/technological

is part of the culture, and this view seems to be accepted and reproduced in the

cognitive maps of young people, both male and female.

What implications do the findings presented here have for the future of

young people? Here it is useful to remember Thomas' (1931) dictum (that

which is perceived as real is real in its consequences). With respect to admission

to post-secondary education, the consequences should be minimal, since

admission is predicated primarily on marks obtained, rather than on self

assessed human capital skills, and it is likely that young men and women are

equally aware of that. Although it is possible that young women whose marks

are equal to those of young men may be less likely to apply for admission

because they lack the confidence that they can do well, it is more likely that it

will affect in the first instance the types of programs that they will select in post

secondary institutions, and the types of occupations to which they will aspire

and for which they will prepare themselves. The argument here is simple: young

people, I suggest, will choose a program of study that maximizes their self

perceived strengths and avoids their weaknesses. Since young women perceive

themselves to be inferior in mathematical, problem-solving, and computer skills,

they will choose programs that do not require excellence in these. Likewise,

when thinking about their career, they will select among those that emphasize

language rather than numeric skills. Of course, these are just possibilities. Yet

the available evidence strongly supports such dynamics. For example, in a study

of high school students Chan et al. (2000) found virtually identical gender

differences in expressed interests in a variety of subject areas and perceived




ability in these subject areas. For example, the largest gender differences in

perceived ability is in engineering and computer science and these are also the

two subject areas with the largest gender difference in expressed interest. This may very well be the reason that computing science is unique as the only

discipline in which there has been a pronounced decline in female undergradu

ates over the past few decades (Camp 1997). And among undergraduates,

almost twice as many men as women cited their abilities in math and/or science

in high school as a reason for choosing a science, math, or engineering major.

Future research needs to assess to what extent differential skill assessments underlie the known gender differences in post-secondary programs of study, and the ultimate sex segregation of occupational distributions.

The findings also have implications for school counsellors: they need to rely

less on self-assessments and more on actual marks in math and language. The

same holds true for career counsellors. The reliance in some quarters on

"interests" and self-assessed skills is basically wrong if we wish to have a less

segregated post-secondary program and occupational distributions. Occupa tional guidance clearly should not be based on inventories of self-assessed skills

and aptitudes.

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Documents

Performance and Perception: Exploring Gender Gaps in Human Capital Skills