Trends in Gender Disparities Among High-Achieving Students in Mathematics: An Analysis of the American Mathematics Competition (AMC)

Abstract

Using the test scores of more than 2,250,000 students who participated in the American Mathematics Competitions (AMC) from 2009 to 2019, this study examined the direction and magnitude of the trends in gender disparity in participation and high achievement in self-select mathematics exams. The results of this study indicated that the male to female ratio among the AMC participants increased significantly from 2009 to 2019. The findings also showed an established disparity that favored males for each year and for all competitions in both the top 1% and 5% levels, while the trend in the male to female ratios over a decade was stable, except for the top 1% of the population in the AMC 8, in which there was a significant increasing trend that favored males. The possible impacts of these findings within the context of the underrepresentation of women in STEM (science, technology, engineering, and mathematics) fields are discussed.

Keywords

Mann–Kendall trend test gender gap STEM mathematical ability AMC contest

Closing gender disparities in occupational and educational outcomes has been a major endeavor in many developed countries, including the United States (Organisation for Economic Co-operation and Development [OECD], 2011). Many researchers from diverse fields have agreed that the problem is quite evident in certain areas, in particular in science, technology, engineering, and mathematics (STEM) careers (Bahar & Maker, 2015; Ceci & Williams, 2007; Dweck, 2007; Halpern, 2007; Hyde, 2007; Lubinski & Benbow, 2007). A recent federal study also confirmed that women are concentrated in different occupations than are men, with relatively high numbers in the social (60%) and life sciences (48%) and relatively low numbers in computer and mathematical sciences (26%), and engineering (15%; National Science Board, 2018).

Research that has paid attention to the gender disparities in the STEM pipeline have examined many psychosocial and cognitive factors that were thought to account for the problem, including, but not limited to, students’ personal attitudes, low self-efficacy in STEM, lack of ability, their perceptions of their ability, self-confidence, teacher attitudes, educational opportunities, gender stereotyping, and parental influence (e.g., Bahar & Maker, 2020; Ceci & Williams, 2007; Dweck, 2007; Feingold, 1988; Fennema, 1990; Fennema et al., 1990; Gavin, 1996; Halpern, 2007; Hyde, 2007; Lubinski & Benbow, 2007, 2021; Reis & Callahan, 1989; Reis & Park, 2001; Stumpf & Stanley, 1996; Swiatek & Lupkowski-Shoplik, 2000). The influence of these factors in gender disparities was found to be more apparent and even greater in mathematically or spatially intense tasks (Fennema & Carpenter, 1981; Gallagher & De Lisi, 1994; Maccoby, 1966). Furthermore, differences in higher levels of mathematics achievement have been identified as a major factor in contributing to the explanation of the underrepresentation of females in later STEM careers (Ellison & Swanson, 2010; Hedges & Nowell, 1995; Makel et al., 2016; Niederle & Vesterlund, 2007, 2010; Wai, Cacchio, et al., 2010; Wai et al., 2018; Wise et al., 1979). Additionally, disparities in high levels of ability were associated with later differences in representation in high-paying jobs (Lazear & Rosen, 1990) and in high-level STEM achievements such as earning higher degrees, publications, and patents (Makel et al., 2016; Wai, Lubinski, et al., 2010).

Gender Disparities Among High-Achieving Students in Mathematics

Researchers have presented mathematics proficiency as a major gatekeeper for many STEM careers (Ceci & Williams, 2010) as they traced gender-related differences in occupational outcomes, particularly in mathematically intensive programs and occupations, to disparities in school mathematics achievement (Ellison & Swanson, 2010; Hyde et al., 1990; Hyde et al., 2008; Lindberg et al., 2010; Olszewski-Kubilius & Lee, 2011; Robinson & Lubienski, 2011). Earlier studies that investigated the gender differences in school mathematics performance among the general population found well-established disparity in which males scored higher than did females (Fennema & Carpenter, 1981; Fennema & Sherman, 1977; Maccoby, 1966; Maccoby & Jacklin, 1974). However, it is widely agreed that gender-related disparities in overall K-12 mathematics achievement have gradually died down over decades (Hyde, 2005; Hyde et al., 2008; Hyde & Linn, 2006; Lindberg et al., 2010; Robinson & Lubienski, 2011).

In one meta-analysis, Hyde et al. (1990) analyzed the independent effect sizes of 100 studies published before 1990, which represented tests of 3,985,682 subjects (2,016,836 females and 1,968,846 males) and found that males scored higher in mathematics performance with a small effect size of d = 0.14. The findings of the study also documented that the magnitude of gender differences has declined since the 1960s and that the effect sizes have narrowed from 0.31 to 0.14 over the past three decades. In a later meta-analysis, Lindberg et al. (2010) analyzed data from 242 studies published between 1990 and 2007, which represented tests of 1,286,350 students (654,232 females and 632,118 males). Similar to Hyde et al.’s (1990) findings, these authors confirmed small effect sizes in mathematics performance among the general population and found no greater decline in the magnitude of gender differences in mathematics performance after the 1990s. They commented that these results might be because gender differences were already small in 1990 and left little room for further decline. In general, researchers have associated the decline in the gender disparity in general mathematics achievement to various sociocultural factors. These include, but are not limited to, the increased number of female role models, particularly in STEM fields (OECD, 2011), availability of advanced and accelerated courses for girls (Ceci et al., 2014; Stanley, 1994; Wai, Lubinski, et al., 2010), more equitable mentoring options (Halpern, 2007), and increased emphasis on equity and access to teacher preparation programs that provide teachers with more equitable instructional strategies (Hyde et al., 2008).

Findings from these large-scale studies have also helped us understand different aspects of the gender disparity (Else-Quest et al., 2010; Hyde et al. 1990; Lindberg et al., 2010; McGraw et al., 2006). Although the gender differences in school mathematics performance among the general population were found to diminish to the point of nonexistence over years, particularly among younger students, they increased gradually as students got older, and eventually, a small to moderate effect size was found that favored males, particularly in the high school and college years (Hyde et al. 1990; Lindberg et al., 2010). Furthermore, studies that have investigated gender disparities in mathematics among high-achieving students have suggested that the gender disparity is not stable throughout the achievement distribution. As researchers have documented that the ratios of males to females in the highest score ranges favored males across grades and such ratios increased in the upper tail of the distribution (Andreescu et al., 2008; Benbow & Stanley, 1980, 1983; Desjarlais, 2009; Ellison & Swanson, 2010; Hedges & Nowell, 1995; Hyde et al., 1990; Linn, 2010; Makel et al., 2016; Niederle & Vesterlund, 2010; Olszewski-Kubilius & Lee, 2011; Reis & Park, 2001; Wai et al., 2010; Wai et al., 2018; Xie & Shauman, 2003), the disparity has been consistent in a series of mathematics test scores, including the ACT/SAT, AP exams, GRE (Graduate Record Exam), American Mathematics Competitions (AMC), and National Assessment of Educational Progress (NAEP; Niederle & Vesterlund, 2010). Table 1 summarizes the findings of major studies that reported male to female ratios (MFR) among high-achieving students in mathematics examinations.

Table 1.

Summary of Studies and Reports Examining Gender Differences in Top Achievement Throughout the Distribution.

Study	Examination instrument	Data year	Sample size	Participants’ grade/age	MFR values in top percentiles
Study	Examination instrument	Data year	Sample size	Participants’ grade/age	Score of 5	10%	6%	5%	3%	1%	0.1%	0.01%
Wai, Cacchio, et al. (2010)	SAT	1981-1985	83,701	Grade 7				0.93		1.43		13.50
Wai, Cacchio, et al. (2010)	SAT	1986-1990	154,075	Grade 7				0.94		1.31		7.60
Wai, Cacchio, et al. (2010)	SAT	1991-1995	187,449	Grade 7				1.00		1.26		3.87
Wai, Cacchio, et al. (2010)	SAT	1996-2000	261,358	Grade 7				1.05		1.14		4.13
Olszewski-Kubilius and Lee (2011)	SAT	2000	109,191	Grade 7 & 8								3.70
Wai, Cacchio, et al. (2010)	SAT	2001-2005	279,540	Grade 7				1.03		1.13		3.55
Olszewski-Kubilius and Lee (2011)	SAT	2008	109,191	Grade 7 & 8								3.20
Wai, Cacchio, et al. (2010)	SAT	2006-2010	207,227	Grade 7				1.00		1.10		3.83
Makel et al. (2016)	SAT	2011-2015	172,377	Grade 7				0.94		0.94		2.53
McGraw et al. (2006)	NAEP	2003	469	Grade 4				1.66
McGraw et al. (2006)	NAEP	2003	565	Grade 8			1.20
McGraw et al. (2006)	NAEP	2000	601	Grade 12					3.00
Hedges and Nowell (1995)	Project Talent	1960	73,425	15 Years old		1.33		1.50	2.10	7.00
Hedges and Nowell (1995)	HS&B	1980	25,069	Grade 11 & 12		1.67		2.06
Hedges and Nowell (1995)	NELS:88	1992	24,599	Grade 12		1.34		1.64
Ellison and Swanson (2010)	AMC 12	2007	118,964	Grade 11 & 12			4.20			6.14	9.00
College Board (2009)	AP Calc AB	2009	211,009	Grade 9-12	1.45
College Board (2019a)	AP Calc AB	2019	269,004	Grade 9-12	1.27
College Board (2009)	AP Calc BC	2009	70,088	Grade 9-12	1.87
College Board (2019a)	AP Calc BC	2019	125,267	Grade 9-12	1.71
College Board (2009)	AP Statistics	2009	114,498	Grade 9-12	1.53
College Board (2019a)	AP Statistics	2019	209,569	Grade 9-12	1.36

Note. MFR = male to female ratios; AMC = American Mathematics Competitions; NAEP = National Assessment of Educational Progress; NELS = National Educational Longitudinal Study.

In one of the most comprehensive studies in the field, Hedges and Nowell (1995) performed secondary analyses of six large data sets, including the National Educational Longitudinal Study, the National Longitudinal Study of Youth, and NAEP, to investigate the gender differences in test scores of over hundreds of thousands of high scoring individuals between 1960 and 1992. The study found high ratios of male to female participants (5 to 1 among the top 3% and 7 to 1 among the top 1%) in the upper tails of the ability distributions of unselected, nationally representative samples. Although they were unable to provide an explanation for the differences found in the high levels of ability, the authors recommended future researchers to seek answers in differences in social factors such as socialization.

Examining roughly 120,000 students’ performance in the 2007 AMC, Ellison and Swanson (2010) looked for gender differences in the very high achievement levels among high school students. The findings indicated a MFR of 4 to 1 among the participants who scored at least 100 points (top 6%). Furthermore, they found that the gender gap widened dramatically as they moved beyond the top 1 percentile and reached a ratio of more than 10 to 1 (Ellison & Swanson, 2010).

According to the reports published by College Board (2009, 2019a), female students were found to be underrepresented among the highest scoring participants in all AP mathematics exams: AP Calculus AB, Calculus BC, and Statistics. AP exams are criterion referenced tests, and students’ exam scores are reported on a 1 to 5 scale, with a score of 5 representing the highest score (Shaw et al., 2013). Among the students who scored a 5 on the AP Calculus AB, Calculus BC, and Statistics exams in 2009, 40%, 35%, and 40% were females, respectively. The representation of the females among the participants who scored a 5 increased to 44%, 37%, and 42%, respectively, in 2019.

Major university-based talent identification programs, such as the Duke University Talent Identification Program (Duke TIP), Johns Hopkins Center for Talented Youth (CTY), and Northwestern University’s Center for Talent Development (CTD) traditionally have used SAT, PSAT, and ACT scores as measures of program admission criteria. Thousands of students have taken these tests to be able to participate in these talent search programs. Studies that have investigated the gender disparity among the participants have documented consistently that greater numbers of males than females were found in the highest score ranges (Benbow & Stanley, 1980; Ceci & Williams, 2010; Makel et al., 2016; Olszewski-Kubilius & Lee, 2011; Wai, Lubinski, et al., 2010, 2012). In one of the earliest studies on talent search participants, Benbow and Stanley (1980) investigated the SAT scores of more than 40,000 students (younger than 13 years old) and reported that the male to female ratio (MFR) on the SAT—Mathematics was approximately 13 to 1 for students scoring in the top 0.01% (score range 700-800). Later, Wai, Cacchio, et al. (2010) replicated Benbow and Stanley’s study with over 1.6 million seventh grade students in the right tail (top 5% in ability) over 30 years (1981-2010) using SAT and ACT mathematics scores and reported that this ratio dropped to 4 to 1 in the 1990s and then remained stagnant for the next two decades.

Using the test scores of more than several hundred thousand students who participated in talent search assessments between 2000 and 2008, Olszewski-Kubilius and Lee (2011) examined whether gender differences reported previously for specific scoring levels still existed over years. They found a steady and consistent MFR in the highest tail in mathematics (score range 700-800) of 3.7 in 2000 and 3.2 in 2008. In an update that studied the MFR in talent search participants, Makel et al. (2016) investigated 320,000 seventh grade students in the right tail (top 5%) through the extreme right tail (top 0.01%) and found that there were approximately 2.5 males for every female in the top 0.01% in mathematical ability on the SAT and ACT (Makel et al., 2016). This finding indicates that the MFR in the extreme right tail of mathematical ability in the U.S. had shrunk from 13.5 to 2.5 between 1980 and 2015.

Gender Disparities in Participation in Mathematical Tasks

Gender-related social cognitive variables such as self-concept, mind-set, differential aptitudes, self-confidence, gender roles, and stereotypes might influence participation and engagement in activities as well as subsequent performance (Bandura, 1994; Dweck, 1986; Eccles et al., 2006; Halpern, 2012). Underlining the drive for choosing to participate in a mathematical task is beyond the goal of this study. However, given that the gender differences in representation can inform the disparities in the upper end of the achievement distribution, it is vital to explore whether such disparities in participation preferences exist for any particular group. Although the literature on the differences in participation in mathematical tasks is very limited, some studies and reports that investigated the gender gap in STEM have also noted about parities/disparities between females’ and males’ participation in self-selected mathematics tasks (College Board, 2019a, 2019b; Desjarlais, 2009; Dreber et al., 2014; Ellison & Swanson, 2010; Datta Gupta et al., 2013; Iriberri & Rey-Biel, 2020; Mayr et al., 2012; Niederle & Vesterlund, 2007). Table 2 summarizes the findings of these studies that reported MFR in participation in mathematical tasks.

Table 2.

Summary of Studies and Reports Examining Gender Differences in Participation in Math Tasks.

Study	Task/examination	N			Participants’ age/grade	Gender representation		MFR
Study	Task/examination	F	M	T	Participants’ age/grade	F	M	MFR
Niederle and Vesterlund (2007)	Mental arithmetic task	14	29	80	Adults	35.00%	73.00%	2.09
Mayr et al. (2012)	Mental arithmetic task	262	281	543	25-75	36.00%	56.00%	1.56
Ellison and Swanson (2010)	AMC 10	41,697	48,290	89,987	Grades 9-10	46.34%	53.66%	1.16
Dreber et al. (2014)	Numerical exercises	109	107	216	16-18	16.00%	35.00%	2.19
Ellison and Swanson (2010)	AMC 12	50,979	67,985	118,964	Grades 11-12	42.85%	57.15%	1.33
Iriberri and Rey-Biel (2020)	Math contest	9,310	12,140	21,450	Grades 6 to 8	43.40%	56.60%	1.30
Datta Gupta et al. (2013)	Maze-solving task	141	139	280	Adults	34.00%	60.00%	1.76
College Board (2009)	AP Calculus AB (2009)	102,711	108,298	211,009	Grades 9-12	48.68%	51.32%	1.05
College Board (2019a)	AP Calculus AB (2019)	132,848	136,156	269,004	Grades 9-12	49.39%	50.61%	1.02
College Board (2009)	AP Calculus BC (2009)	28,974	41,114	70,088	Grades 9-12	41.34%	58.66%	1.42
College Board (2019a)	AP Calculus BC (2019)	52,581	72,686	125,267	Grades 9-12	41.98%	58.02%	1.38
College Board (2009)	AP Statistics (2009)	57,763	56,735	114,498	Grades 9-12	50.45%	49.55%	0.98
College Board (2019a)	AP Statistics (2019)	110,381	99,188	209,569	Grades 9-12	52.67%	47.33%	0.90
Wai, Cacchio, et al. (2010)	SAT (1981-1985)	43,367	40,334	83,701	Grade 7	51.81%	48.19%	0.93
Wai, Cacchio, et al. (2010)	SAT (1986-1990)	79,544	74,531	154,075	Grade 7	51.63%	48.37%	0.94
Wai, Cacchio, et al. (2010)	SAT (1991-1995)	93,787	93,662	187,449	Grade 7	50.03%	49.97%	1.00
Wai, Cacchio, et al. (2010)	SAT (1996-2000)	127,788	133,570	261,358	Grade 7	48.89%	51.11%	1.05
Wai, Cacchio, et al. (2010)	SAT (2001-2005)	137,673	141,867	279,540	Grade 7	49.25%	50.75%	1.03
Wai, Cacchio, et al. (2010)	SAT (2006-2010)	103,359	103,868	207,227	Grade 7	49.88%	50.12%	1.00
Makel et al. (2016)	SAT (2011-2015)	88,891	83,486	172,377	Grade 7	51.57%	48.43%	0.94
Desjarlais (2009)	AMC 8	178,857	183,857	362,714	Grades 6 to 8	49.31%	50.69%	1.03

Note. AMC = American Mathematics Competitions; MFR = male to female ratios.

Large-scale studies that investigated the disparities in the highest score ranges among the participants of talent identification programs have also informed the literature about the gender gaps in program participation (Benbow & Stanley, 1980; Makel et al., 2016; Olszewski-Kubilius & Lee, 2011; Wai, Cacchio, et al., 2010). According to these reports, the number of males and females were roughly equal across the years as the MFR values ranged from 0.93 to 1.05 over the past four decades (see Table 2). Given that the participants invited to these programs were the students who had previously scored in the top 5% of achievement for their grade on standardized tests (Wai, Cacchio, et al., 2010), the MFR values suggested gender parity in participation among the high-achieving students who chose to participate in talent search programs. Together with this fact, these findings show that the parity in participation among the invited students did not reflect on high performance, as the studies reported large disparities in the upper end of the achievement distribution.

The reports published by College Board (2009, 2019a) presented vital information with regard to gender disparities in participation across AP mathematics exams. As seen in Table 2, the MFR among the participants in the 2019 AP Statistics exam was 0.90 to 1.00, while it was 1.02 to 1.00 for AP Calculus AB, and 1.38 to 1.00 for AP Calculus BC exams. This means that the majority of the participants were female in the AP Statistics exam while males dominated the AP Calculus BC exam in 2019. Different from these two AP programs, the number of female and male participants were in parity for the AP Calculus AB exam. In addition, when the 2019 MFR values are compared with the ones reported in 2009, we can see that females’ representation increased across the years for all three AP mathematics courses. However, the reports did not present whether the changes were statistically significant.

In a study that examined gender differences in the AMC, Desjarlais (2009) compared the performances of 183,857 male and 178,857 female eighth graders in the United States from 2003 to 2007. Although the findings suggested that the male mean score was statistically greater than the female mean score for each year (p < .001), the number of the female and male participants were almost in parity with a 1.03 to 1.00 MFR value. Later, in a study investigating the gender differences in the very high-achievement levels among the AMC participants, Ellison and Swanson (2010) reported that 47% of the participants among 10th graders (AMC 10) were female but this percentage declined to 43% for participants who were in Grades 11 and 12 (AMC 12).

A new line of research, particularly in behavioral economics, have identified the gender differences in competition preferences as a possible factor that could explain the observed gender gap in labor market outcomes (Ellison & Swanson, 2010; Gneezy et al., 2003; Iriberri & Rey-Biel, 2020; Niederle & Vesterlund, 2007). Although none of these studies reported whether the differences in competition participation influenced the differences in the upper end of the achievement distribution, the reported disparities in competition participation might inform the findings of this study. In one of the most renowned studies on gender gaps in labor markets, Niederle and Vesterlund (2007) compared 40 men’s and 40 women’s competition preferences in mathematical tasks in laboratory settings. Controlling for differences in ability, the researchers examined whether gender differences appeared in the preference to perform under a fixed rate payment per item solved or a tournament payment schedule. The findings indicated men and women differed in their attitudes toward competition participation; while 73% of the men chose to compete in a tournament, only 35% of the women decide to do so. Several follow-up studies (Niederle & Vesterlund, 2008, 2010) that compared males’ and females’ performances and preferences in competitive and noncompetitive mathematical activities have found that females were less likely to choose competitive tasks over noncompetitive ones than were males too (Flory et al., 2015; Niederle & Vesterlund, 2007, 2008). In the first systematic attempt to characterize age dependent gender differences in competitive behavior over the life span, Mayr et al. (2012) examined the preferences of 543 adults aged 25 to 75 years in the United States and explored whether participants chose to perform a simple mental arithmetic problem under a mastery or competitive schedule. Overall, 56% of men and only 36% of women chose to compete and the difference gradually increased across the life span until age 50 and started to drop thereafter (Mayr et al., 2012).

Contrary to the studies that found gender differences in participation in competitive mathematical tasks, some economics studies did not find similar gender disparities across other domains. For example, in 2014, Dreber et al. replicated Niederle and Vesterlund’s (2007) study and examined gender differences among 216 Swedish high school adolescents’ preferences for competition, altruism, and risk in verbal and mathematical tasks. The authors found that 35% of the boys and only 16% of the girls chose to compete in a mathematical task, while boys and girls are equally likely to self-select into competition in a verbal task. In a similar economics study, Comeig et al. (2016) investigated 102 undergraduate students’ gender differences in the willingness to compete in sports. The findings indicated varying but small differences between females and males’ competition preferences across tasks. The authors concluded that differences in preferences for competition do not come from the gender alone but from several combinations of domain-specific factors including self-confidence and many other psychosocial factors.

Although the research findings do not agree on whether the labor gaps in STEM outcomes are due to the gender differences in competition preferences or domain-specific self-confidence, there is agreement in the literature that females being less likely to choose to participate in these tasks will not only reduce the number of females who engage with them but also the number of those who places among high achievers (Niederle & Vesterlund, 2007).

What Is the American Mathematics Competition (AMC) and Does It Really Matter?

The AMC has always been the most prestigious mathematics competition in the United States. The Mathematical Association of America (MAA), which consists of the world’s largest community of mathematicians (MAA, 2020), sponsors the contests. The MAA’s goal is to strengthen the mathematical abilities of students and help them develop their problem-solving skills through these competitions (MAA, 2020). Furthermore, according to the MAA, “The AMC program helps America’s educators identify talent and foster a love of mathematics through classroom resources and friendly competition” (MAA, 2020, para. 1).

The AMC competitions include a series of examinations that eventually lead all the way to the International Mathematical Olympiad (MAA, 2020). Figure 1 shows the order of these examinations. Each year, over 300,000 students at more than 3,000 high schools and 2,000 middle and elementary schools across the U.S. participate in the first step of the AMC competitions: AMC 8, for students in Grade 8 or below; AMC 10, for students in Grade 10 or below, and AMC 12 for students in Grade 12 or lower. The AMC 8, 10, and 12, are self-select competitions in which any student can participate, and students who perform well on the AMC 10 or 12 are invited to participate in the next round. Figure 1 shows the approximate number of participants and qualifiers for each of the contests’ levels. After several challenging rounds of examinations that take place over months, six students are selected to form the United States International Mathematics Olympiad Team and compete at the International Mathematical Olympiads. Different from AMC 10 and 12, there is no next round for AMC 8 participants. However, there are several awards for participants who do well on the exam. Certificate of Distinction (given to perfect scorers), Distinguished Honor Roll (given to students who scores in top 1% ), Honor Roll (given to students who scores in top 5%), Merit Certificate (given to high scoring students who are in 6th grade or below), and Certificate for Outstanding Achievement (given to top three students for each school) are awarded to high-achieving students.

Figure 1.

Steps of American Mathematics Competitions.

Participation in the AMC contests offer opportunities and challenges to the participants. For many mathematically competent students, the AMC contests serve as a talent development platform (Campbell & Walberg, 2011). The contests include many nonstandard problems and tasks that provide talented students with a rigorous curriculum and resources that are needed to stimulate extraordinary students who are motivated to achieve in mathematics. In Campbell and Walberg’s (2011) study, which investigated competitions’ effects on talented students, the authors analyzed data from 345 adults who participated formerly in prestigious competitions, such as the International Mathematics Olympiads. Their findings indicated that these competitions served as alternative talent development programs and related to these students’ postsecondary achievement. Furthermore, most competitors (76%) and their parents (83%) reported that these competition programs helped increase their awareness of educational opportunities (Campbell & Walberg, 2011).

High performance in the AMC contests, particularly at later levels, requires a firm commitment in time and effort, which leads students to develop certain academic and nonacademic skills. In an earlier study, Campbell (1996) interviewed former “Mathematics Olympians” and noted that the participants reported that these competitions were significant programs that had helped them develop essential skills, attitudes, and orientations, including time management, organizational skills that helped them study for challenging examinations, and the opportunity to socialize with like-minded peers. According to Andreescu et al. (2008), these competitions also serve as a tool to identify mathematically gifted students. The problems in the AMC examinations require creative thinking and insight into higher level mathematical concepts that can differentiate between children who are moderately and profoundly gifted in mathematics (Andreescu et al., 2008).

A successful competitor attracts the attention of many prestigious universities. Some elite universities, including MIT, Yale, and Cal Tech, consider a high AMC score a significant indicator of strong mathematical ability and ask applicants to report their AMC scores specifically in their college applications (Ellison & Swanson, 2010). This may motivate students extrinsically to qualify for the next levels of the contests and eventually lead participants to study harder to achieve their goals. However, a high score in the AMC is a challenging task that requires strong commitment and preparation. Although hundreds of thousands of students enter the first round of the exams, only a few thousand students (2% to 5%) score high enough to qualify to the second round.

Present Study

This study aimed to contribute to the literature in several ways. First and foremost, using a specific trend analysis technique, I investigated the direction and magnitude of the trend in gender disparity among high-achieving students in mathematics. Although there exists a well-established literature on this topic, prior studies only reported the magnitude of the change numerically and compared the numbers over years and did not assess the significance of the trend statistically. This study will not only extend the literature on gender disparities among high-achieving students in mathematics but also will serve as a guide for future researchers who want to test for the presence of a trend through scientifically and statistically sound analysis techniques.

Second, in addition to examining gender differences at very high-achievement levels using a specific trend analysis method, this study investigated the gender disparity in participation in a large-scale mathematics competition. Although several studies reported MFR among participants in competitions and tournaments in mathematical tasks, no prior study has investigated such a trend across years. Considering many studies noted that gender differences within groups have been gradually evolving over time, this study will fill a gap in the literature, and the findings may have significant implications for educators and researchers. Moreover, the findings related to the gender disparity in participation in competition can inform the overall literature on gender differences in the right-tail of the achievement distribution, too. This study posed the following questions:

Research Question 1: What is the trend in the gender disparity in participation in the AMC?

Research Question 2: What is the trend in the gender disparity among high-achieving students who participated in the AMC?

Method

Participants and Testing

The data in this study were obtained from the MAA’s online public database. Table 3 provides the number of students who participated in the contests from 2009 to 2019. The data did not include the AMC 8 participants from 2019 because they are not available yet.

Table 3.

Number of American Mathematics Competition (AMC) Participants.

Contest		2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
AMC 8^a	Female	68,149	56,952	54,231	51,212	52,581	50,896	50,594	46,674	43,088	40,531	NA^b
	Male	79,138	63,541	61,764	58,985	61,388	60,833	60,909	57,029	54,119	52,120	NA
	Total	150,733	123,108	118,767	113,196	116,724	114,221	114,066	106,019	100,211	95,841	NA
AMC 10^c	Female	23,695	18,996	21,254	21,564	20,624	18,775	16,628	15,299	18,011	13,062	13,278
	Male	28,113	22,469	26,407	27,109	26,862	23,826	21,716	21,406	23,598	17,872	18,618
	Total	61,723	51,205	59,218	60,394	56,717	51,659	46,302	44,399	51,508	39,400	40,703
AMC 12^d	Female	26,404	20,877	22,831	20,927	19,218	16,546	14,861	15,299	14,840	10,162	10,648
	Male	34,915	28,086	31,333	29,330	27,930	23,271	20,647	21,406	21,325	15,195	15,813
	Total	71,305	57,771	63,676	60,152	54,930	46,765	41,898	44,399	43,652	31,482	33,461

Participants included students who were in Grade 8 or below. ^bCompetition data belonged to the AMC 8 participants for 2019 testing were not available yet. ^cParticipants included students who were in Grade 10 or below. ^dParticipants included students who were in Grade 12 or below.

These competitions are administered around the country on a weekday the MAA designates. Students can take the test at their own school or a neighboring institute that offers the test. The AMC 8 is administered once, while the AMC 10 and 12 are held twice annually and referred to as the AMC 10A/12A and AMC 10B/12B. The A and B versions of the tests are given within a week or two, and students are allowed to take both versions. Historically, students’ interest in the A versions has been higher than in the B. Given the greater number of students who participate in the A versions, only the AMC 10A and 12A participants’ data were included in this study. Each of these three competitions consists of 25 multiple-choice questions, and the test items are designed to promote the development and enhancement of problem-solving skills (MAA, 2020). They also are designed explicitly to test the depth of knowledge and advanced problem-solving skills (Ellison & Swanson, 2010).

Desjarlais’ (2009) study examined reliability and validity evidence of the AMC 8 contests. Both the Cronbach’s α and Spearman–Brown split-half coefficients were found to be approximately .70, which indicated adequate internal consistency. She also reported that a committee of in-service and preservice middle school teachers assessed each item’s content validity continuously, and only those items the committee found to be appropriate were selected as test items.

Data Analysis

In this study, the Mann–Kendall (MK) trend test was employed to answer the research questions. The MK is a nonparametric method used to test the presence of a trend over time (Kendall, 1975; Mann, 1945). The test is viewed best as an exploratory analysis and is used most appropriately to identify stations where changes are significant or of large magnitude and to quantify these findings (Hirsch et al., 1982). The MK test involves the following assumptions: (1) in the absence of a trend, the data are distributed independently and identically, (2) the measurements represent the true states of the observations at the times of measurement, and (3) the methods used for sample collection, instrumental measurements, and data analysis are unbiased.

After these three assumptions were assessed to ensure that none of them was violated, the test was performed using XLSTAT software. Because the MK test does not indicate the magnitude of the slope or estimate the slope of trend over time even when a trend is present (Environmental Protection Agency, 2009), I used Sen’s nonparametric procedures and calculated Sen’s (1968) slope. Sen’s slope is a robust estimate of a trend’s magnitude and has been used widely to identify the slope of trend lines (Yu et al., 2002).

Many prior studies have used the MFR to examine gender disparity at any specific achievement level (Benbow & Stanley, 1983; Makel et al., 2016; Wai, Cacchio, et al., 2010; Wai et al., 2018). In this study, a simple MFR among participants was reported as a measure of gender disparity and denoted with the $γ (θ)$ function. The function is calculated as follows:

γ (θ) = \frac{m (θ)}{f (θ)}

The function $γ (θ)$ basically denotes the MFR above a specific percentile $(θ)$ , as $m (θ)$ represents the number of males and $f (θ)$ represents the number of female students in the distribution overall. For example, $γ (99)$ = 4 means that the MFR in the 99th percentile (top 1%) is 4, that is, the top 1% of the student population is composed of 80% males and 20% females. When the number of male and female students in a specific percentile are equal, the value of the function is 1, which indicates that there is no disparity. As the number of female students exceeds that of males, the value of the function becomes less than 1 and the disparity favors female students; alternatively, as the number of male students exceeds that of females, the value of the function becomes greater than 1 and disparity favors male students.

In prior studies, the gender disparities among high-achieving students have been examined at various performance levels, including the top 0.01%, 0.1%, 1%, and 5%. In this study, because very few females were found in these top levels, the disparities were examined only in the 99th and 95th percentiles (top 1% and 5%, respectively). For example, in 2014, no female students scored in the top 0.1% on the AMC 12A contest, while 36 males scored at this level. After each $γ (θ)$ value was calculated for each competition over years, the analysis was conducted.

In the MK test for n data collected over time { $γ_{1}$ , $γ_{2}$ ,. . ., $γ_{n}}$ , the first step is to calculate the sign function, as follows:

sgn (γ_{j} - γ_{i}) = {\begin{matrix} 1, γ_{j} - γ_{i} > 0 \\ 0, γ_{j} - γ_{i} = 0 \\ - 1, γ_{j} - γ_{i} < 0 \end{matrix}

This function indicates simply whether the differences between the data from consecutive years are positive, negative, or zero. Calculation of the sign function allows us to compute the MK test statistic, S, which is calculated as follows:

S = \sum_{i = 1}^{n - 1} \sum_{j = i + 1}^{n} sgn (γ_{j} - γ_{i})

A negative S value represents a decreasing trend, while a positive value indicates an increasing trend over time. To test the significance of this value, the mean and variance of the S are computed, the Z score is obtained subsequently, and finally, the null and alternative hypotheses are tested to determine the significance of the trend.

Results

Research Question 1

Table 3 presents basic descriptive data about the participants in the AMC 8, 10, and 12 contests from 2009 to 2019. As seen in the table, the number of male and female participants in each competition decreased consistently from 2009 to 2019. For example, 150,733 students participated in the AMC 8 contest in 2009 and a decade later, this number had dropped to just under 100,000. Although the declines for both the female and male participants were consistent, the rates of the drops differed across genders. Each year, the number of male participants was greater than that of female participants in all three contests (Table 3).

The MFR for all participants, as denoted with the gender disparity function of $θ$ = 0, $γ (0) = m (0) / f (0)$ , was calculated for each competition from 2009 to 2019 (Table 4). The MFR values for the AMC 8 showed an upward trend over a decade and increased from 1.16 to 1.29. The MK test indicated that the upward trend was statistically significant and favored males (p = .001). This finding suggests that, regardless of the total number of participants, the MFR increased continuously from 2009 to 2018 (Table 4). As seen in Figure 2 and Table 4, the magnitude of the increase in the MFR, computed by Sen’s slope, was roughly 0.02 units per year. Similar to the AMC 8, the MFR values for the AMC 10 participants showed an upward trend over years and increased from 1.19 to 1.50. Sen’s slope estimated the magnitude of the change as 0.022 units per year. The MK test result confirmed the upward trend, which was statistically significant and favored males (p = .002). The MFR for the AMC 12 also increased from 1.32 to 1.49 over a decade. The MK test confirmed the upward trend, which favored males and was statistically significant (p = .003). Sen’s slope indicated a 0.016-unit change per year for the exam (Figure 2).

Table 4.

Male to Female Ratios at Top Ability Levels Over Years.

Contest	Percentile	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
AMC 8	Top 1%	3.07	3.76	3.39	3.28	3.83	3.93	3.69	3.86	3.89	4.27	NA
	Top 5%	2.80	2.72	2.50	2.67	2.63	2.80	2.72	2.98	2.79	3.03	NA
	TMFR	1.16	1.12	1.14	1.15	1.17	1.20	1.20	1.22	1.26	1.29	NA
AMC 10	Top 1%	5.48	5.80	5.36	5.10	5.62	5.46	3.92	5.82	6.85	5.46	6.97
	Top 5%	3.70	3.84	3.49	3.57	3.52	3.92	3.24	3.72	4.56	4.34	4.71
	TMFR	1.19	1.18	1.24	1.01	1.30	1.27	1.31	1.29	1.31	1.37	1.5
AMC 12	Top 1%	5.58	6.32	6.73	7.94	7.38	7.62	7.45	6.89	6.75	6.97	10.15
	Top 5%	3.76	4.45	4.85	4.53	4.37	4.87	4.59	4.27	5.88	4.71	5.50
	TMFR	1.32	1.35	1.37	1.40	1.45	1.41	1.39	1.45	1.44	1.50	1.49

Note. AMC = American Mathematics Competitions; TMFR = total male to female ratio among all participants of the competition.

Figure 2.

Trend of male to female ratios among all participants and Sen’s slope from 2009 to 2018.

Research Question 2

Trend in Top 1% Performance Level

The MFR for all three competitions showed fluctuating trends in the top 1%, γ(99) performance level over years (Figure 3). For the AMC 8 participants, the MFR increased from 3.07 to 4.27, with a 3.70 mean, from 2009 to 2018. As seen in Table 5, the MK test confirmed that the direction of the trend was upward, favored males, and was statistically significant (p = .012). As Figure 3 shows, the estimation of the magnitude of the trend, as computed by Sen’s slope, was 0.098 (Table 6). The MFR values for the AMC 10 contest increased from 5.48 to 6.97 between 2009 and 2019, with a mean of 5.62 (Table 7). Although this increment favored males, it was not significant (p = .276). For the AMC 12 contest, the MFR values increased from 5.58 to 10.15 over years, with a mean of 7.25 (Table 5). Similar to the AMC 10 contest, the increase of the mean favored males but also was not statistically significant (p = .119).

Figure 3.

Trend of male to female ratios at the top 1% of overall distribution and Sen’s slope from 2009 to 2018.

Table 5.

Mann–Kendall Two-Tailed Trend Test Values for the Male to Female Ratios.

Contest	Percentile	Min	Max	M	SD	Kendall’s tau	S	Var(S)	p
AMC 8	Top 1%	3.068	4.270	3.697	0.355	.644	29	125	.012
	Top 5%	2.497	3.026	2.763	0.157	.333	15	125	.210
	TMFR	1.116	1.286	1.190	0.053	.867	39	125	.001
AMC 10	Top 1%	3.916	6.970	5.620	0.821	.273	15	165	.276
	Top 5%	3.235	4.710	3.874	0.470	.418	23	165	.087
	TMFR	1.011	1.500	1.270	0.122	.745	41	165	.002
AMC 12	Top 1%	5.582	10.148	7.252	1.159	.382	21	165	.119
	Top 5%	3.758	5.878	4.707	0.580	.418	23	165	.087
	TMFR	1.320	1.495	1.414	0.056	.709	39	165	.003

Note. AMC = American Mathematics Competitions; TMFR = total male to female ratio among all participants of the competition.

Table 6.

Mann–Kendall Two-Tailed Trend Test Values for Total Number of Participants.

Contest		Min	Max	M	SD	Kendall’s tau	S	Var(S)	p
AMC 8	Female	52,120	79,138	60,983	7,320	−.822	−37	125	<.001
	Male	40,531	68,149	51,491	7,682	−.956	−43	125	<.001
	All	95,841	150,733	115,289	15,019	−.867	−39	125	<.001
AMC 10	Female	17,872	28,113	23,454	3,439	−.636	−35	165	.006
	Male	13,062	23,695	18,290	3,452	−.745	−41	165	.001
	All	39,400	61,723	51,203	7,810	−.673	−37	165	.003
AMC 12	Female	15,195	34,915	24,477	6,334	−.818	−45	165	<.001
	Male	10,162	26,404	17,510	5,044	−.855	−47	165	<.001
	All	31,482	71,305	49,954	12,621	−.818	−45	165	<.001

Note. AMC = American Mathematics Competitions; TMFR = total male to female ratio among all participants of the competition.

Table 7.

Sen’s Slope Values for the Male to Female Ratios (MFR).

Contest	Percentile		Value	Lower bound (95% CI)	Upper bound (95% CI)
AMC 8	Top 1%	Slope	0.098	0.018	0.162
		Intercept	−193.735	−257.821	−112.662
	Top 5%	Slope	0.038	−0.002	0.069
		Intercept	−74.353	−105.080	−34.004
	TMFR	Slope	0.018	0.014	0.021
		Intercept	−35.149	−38.404	−30.905
AMC 10	Top 1%	Slope	0.060	−0.062	0.225
		Intercept	−115.294	−447.836	130.869
	Top 5%	Slope	0.097	−0.043	0.164
		Intercept	−190.926	−327.015	90.814
	TMFR	Slope	0.022	0.013	0.039
		Intercept	−42.120	−77.851	−25.226
AMC 12	Top 1%	Slope	0.181	−0.158	0.407
		Intercept	−357.662	−811.505	325.107
	top 5%	Slope	0.107	−0.026	0.219
		Intercept	−211.175	−435.312	56.714
	TMFR	Slope	0.016	0.010	0.024
		Intercept	−30.057	−46.792	−19.104

Note. AMC = American Mathematics Competitions; TMFR = total male to female ratio among all participants of the competition; CI = confidence interval.

Trend in Top 5% Performance Level

The mean MFR values showed a growth in favor of males for all three competitions from 2009 to 2019 (Figure 4). However, none of these trends in the gender disparities were statistically significant for the students who placed in the top 5% performance level (Table 5). For the AMC 8 contest, the mean MFR value was 2.76 with a nonstatistically significant increase from 2.80 to 3.03 (p = .210) between 2009 and 2019 (Table 4). The MFR values for the AMC 10 contest had a nonstatistically significant increase from 3.70 to 4.71 (p = .087), with a 3.87 mean MFR over years. Similar to the AMC 8 and 10 contests, the MFR values showed a nonstatistically significant increase from 3.76 to 5.50 over years for the AMC 12 contest (p = .087), with a mean of 4.07.

Figure 4.

Trend of male to female ratios at the top 5% of overall distribution and Sen’s slope from 2009 to 2018.

Discussion

Trend in Gender Disparity in Participation in the American Mathematics Competition

Four elements of the findings with respect to gender disparity in participation in the AMC are worthy of note: (1) The number of females and males participating in the AMC has significantly and rapidly decreased across years (Table 3); (2) Each year, the number of male participants exceeded that of female participants in all three AMC exams; (3) Regardless of how many students participated in the contest, the ratios of the total number of male to female participants (TMFR) for all three contests increased significantly over a decade (Table 4); and (4) the disparity not only increased over the years but also increased consistently as the age of the participants increased.

Element 1

As the MK test results indicated (Table 6), a significant decline in participation existed in the AMC from 2009 to 2019. First, one might ask whether such a decline in participation is the result of reduced enrollment at secondary schools. However, federal data show that the total enrollment in secondary schools increased nearly 2% from 2009 to 2018 (U.S. Department of Education, National Center for Education Statistics, 2018). Thus, the decline in participation cannot be attributable to a reduced enrollment.

One possible explanation for this decline might be related to the growing availability of noncompetitive K-12 programs for students. Because people, in general, are less likely to choose competitive environments to noncompetitive ones unless there is a significant benefit from it (CITE). As seen in Table 2, prior studied noted that even in the environments in which incentives were offered, 35% to 73% of males and 16% to 49% of females chose to compete. Over the past two decades, especially with the support of developing internet and educational technologies, many noncompetitive programs such as summer camps, university-based programs, and other talent development platforms reached wider populations and attracted many students. Furthermore, schools have offered more advanced programs than ever, including AP and IB courses and dual-enrollment programs, which have been adequate options for many students who looked for opportunities to develop their talents. For example, according to a report from College Board (2019a), over 100,000 high school students took five or more AP exams in 2019, while this number was only about 10,000 in 1999, which shows how commitment to many AP courses have been the new norm among talented high school students. Although the growth in the number of the educational opportunities has been a positive educational advancement, students committed to these programs may not have had much extra time to prepare for programs that requires significant preparation time, like the AMC.

Elements 2 and 3

The median MFRs among AMC 8, 10, and 12 participants across years were found to be 1.20, 1.29, and 1.45, respectively, in this study. Although identifying each factor that is responsible for the gender differences in participation in mathematical tasks is beyond the scope of this study, it is critical to identify potential factors that might be accounted for.

These findings are consistent with those of prior studies that associated the gender disparities in participation in mathematical tasks with differences in competition preferences (Campbell, 2002; Dreber et al., 2014; Ellison & Swanson, 2010; Datta Gupta et al., 2013; Iriberri & Rey-Biel, 2020; Mayr et al., 2012; Niederle & Vesterlund, 2007). Research indicates that some personality traits might have decisive influences on self-select participation preferences. According to social dominance theory (Sidanius & Pratto, 1999), gender is one of the three elements of hierarchical relations in society that may influence individual beliefs and behaviors. Traditionally, men perceive competitions as platforms to establish social dominance, and Mayr et al. (2012) attributed such an increased interest in social dominance to an increased “taste for competition” (p. 282). Given that some fields, such as mathematics, have been perceived historically as masculine domains, boys might perceive mathematics competitions as a platform to prove their social dominance, and this might account for the gender disparities in the “taste” that Mayr suggested.

The gender differences in domain-specific self-confidence may be another potential explanation for why the number of male participants exceeded that of female participants for all three exams each year. Research has suggested that preferences develop in a social context with respect to the domain and often are predicted by self-confidence (Comeig et al., 2016). Although the AMC is a self-select contest, it takes place at students’ own schools, and mathematics teachers serve to advertise the competitions. Given that teachers were found to be less likely to nominate bright female students for advanced mathematics programs even though they had the ability to do well (Andreescu et al., 2008; Campbell & Walberg, 2011), established social expectations and teachers’ perceptions of students’ abilities might also contribute to the gender differences in confidence and eventually also result in gender differences in participation preferences (Dreber et al., 2014; Wozniak et al., 2010).

The findings not only show that the number of male participants exceeded that of female participants in all three contests but also indicate that females are “shying away from” the AMC competitions significantly faster than males. Considering that no prior studies have investigated the trend in gender disparity in the AMC participation or other mathematical exams, we have no criterion for the findings of this study. Besides, the current data and findings of the study would not allow for a complete explanation for this issue. However, the rapidly growing availability of other advanced programs might be the reason that can explain where females are heading to when they shy away from the AMC. For example, a recent report (College Board, 2019a) shows that the MFR in participation in three AP mathematics courses, Calculus AB, Calculus BC, and Statistics, decreased from 1.06 to 1.03, from 1.42 to 1.38, and from 0.98 to 0.90, respectively, between 2009 and 2019 while they increased significantly for the AMC competitions during the same time period. If this is the case and females have been choosing other advanced programs over the AMC, then there might be several more reasons contributing to this shift. A further investigation will be needed to document the complete picture of the story; the issue is beyond the capacity of this study.

Element 4

The median MFR values, 1.20, 1.29, and 1.45 found among AMC 8, 10, and 12 competition participants, respectively, would also suggest that the gender disparity in participation in the AMC increased consistently as the age of the participants increased. This finding is consistent with the finding that the gender difference in competition preference in mathematical tasks gradually increased across the life span until age 50 and started to drop thereafter (Mayr et al., 2012). Moreover, according to Roberts et al. (2006), social dominance is among the personality traits that is correlated positively with age and continues to develop from puberty to late adulthood. This may also imply that the disparity in interest in social dominance might also account for the increased disparity as the age groups among the AMC participants increase.

The findings related to participation, in general, have some worrisome implications that the gender gaps in postsecondary achievements and labor market might widen. First, the results present significant evidence that female students withdraw from the AMC exams faster than males and that the gap has continued to increase over the years, which may cause the program to become a male-dominated platform in the near future. Although the overall participation in the AMC has shrunk over the past two decades, still hundreds of thousands of students participate in one of the AMC programs every year. Moreover, rather than being a simple competition, the AMC program has played a pivotal role in motivating many American high school students to reach high levels of mathematics competence (Campbell & Walberg, 2011) and served as a talent development path for many who are mathematically gifted (Andreescu et al., 2008; Wu, 1996). Second, given that high performance in the AMC competitions (particularly top 5 to 6 percentiles) might help applicants gain admission to top universities’ STEM programs (Andreescu et al., 2008; Ellison & Swanson, 2010), an upward trend in gender disparity in participation, which favors males, may serve to increase women’s underrepresentation in STEM-related college programs. However, this finding should be interpreted with caution, because as suggested earlier, the females who decline to enter the AMC contests may be choosing to participate in other talent development options, such as advanced courses (AP, IB, or dual enrollment), university-based programs (Duke TIP, CTY, or CTD), or many other similar opportunities. Future research should examine the trend in gender disparities in competitive programs as well as those in noncompetitive programs including AP programs so that we can have a better understanding of the status quo for females in STEM pipelines.

Trend in Gender Disparity in the American Mathematics Competition Performance

One major goal of this study was to investigate the trend in gender disparities at the top mathematics achievement. The analysis of the second research question suggested four important findings: (1) an established disparity that favored males was found for all competitions in both the top 1% and 5% levels for each year; (2) the trend in the MFR over a decade was stable, except for the top 1% of the population in the AMC 8, in which there was a significant increasing trend that favored males; (3) the disparities increased toward the upper end of the right tail; and (4) the disparities increased with the participants’ ages.

The findings of this study, in particular Items (1), (3), and (4), were consistent with most prior studies that have documented that the ratios of males to females in the highest score ranges favored males across grades and such ratios increased through the upper right tail of the distribution and higher ages (Andreescu et al., 2008; Benbow & Stanley, 1980, 1983; Desjarlais, 2009; Ellison & Swanson, 2010; Hedges & Nowell, 1995; Hyde et al., 1990; Linn, 2010; Makel et al., 2016; Niederle & Vesterlund, 2010; Olszewski-Kubilius & Lee, 2011; Reis & Park, 2001; Wai, Lubinski, et al., 2010; Wai et al., 2018; Xie & Shauman, 2003).

With regard to Finding 2 regarding the stability in the trend in the MFR, the finding was not consistent with the findings of prior studies. Studies that have examined the trend in the gender gaps in the extreme right tail of mathematics achievement among seventh-grade talent search students who were assessed with SAT and ACT tests, found that the MFR has declined sharply over the past four decades. For example, in one of the first studies, Benbow and Stanley (1980) reported a 13.50 to 1.00 MFR in the highest tail in mathematics (score range 700-800). In later years, Olszewski-Kubilius and Lee (2011) found a MFR of 3.7 to 1 in 2000 and 3.20 to 1.00 in 2008. Finally, Makel et al. (2016) found that there were approximately 2.50 males for every female in the score range 700 to 800 (which was identified as top 0.01% by the authors). However, the mean MFR values for the similar age group (AMC 8 participants) were found to be 2.76 to 1.00 even for the top 5% and 3.70 for the top 1% levels in this study. Furthermore, different from the prior studies that reported a MFR decline in the right tail of the mathematics ability, the trend found in this study was stable at the top 5% and even upward at the top 1% between 2009 and 2019.

I offer two possible scenarios for why these findings were different from that of prior studies. The first scenario suggests that the inconsistencies between this study and others might be due to the differences in the nature (items, testing procedures, etc.) of the SAT/ACT and AMC contests. If this is the case, then we will be left with various exam-specific trends in the right tail of mathematics ability. Although this option might sound reasonable, it requires us to underestimate the differences in knowledge and ability, which is not realistic as most talented students show similar performances across different type of examinations in the same domain.

In the second scenario, referring back to the results of the first research question, a high and significantly increasing MFR found in participation in the AMC can be thought to account for why the MFR in top percentiles did not drop while many other findings found significant declines over years. Noting that the MFRs reported in general participation in prior studies (Benbow & Stanley, 1983; Hedges & Nowell, 1995; Makel et al., 2016; Olszewski-Kubilius & Lee, 2011; Wai, Cacchio, et al., 2010) were stable and in parity across the years, the second scenario seems to hold true, and ultimately, we can conclude that when females are less likely to participate in mathematical tasks, it is more likely that higher MFR values will appear in the upper right end of the distribution, which adequately explains why the trend in the MFR among high achievers in the AMC was stable or partially increasing while it was found to be declining in many other studies.

Regardless of the directions of the trends, the findings still present very high MFR values among high-achieving students in mathematics. In fact, prior studies have highlighted that the gender disparity in the general mathematics achievement diminished completely due to various sociocultural factors including but not limited to the increased number of female role models, particularly in STEM fields (OECD, 2011), availability of advanced courses for girls (Ceci et al., 2014; Stanley, 1994; Wai, Lubinski, et al., 2010), and increased emphasis on equity and access to teacher preparation programs that provide teachers with more equitable instructional strategies (Hyde et al., 2008). At this point an important question may arise: Why have these factors helped close the gender gap in school mathematics achievement in the general population but not among top-achieving students? Some researchers have attributed this disparity to gender differences in cognitive abilities (Benbow, 1988; Gallagher et al., 2000; Wai et al., 2009; Webb et al., 2007), such as mathematical reasoning (Benbow, 1988) or spatial ability (Wai et al., 2009). Although this might sound like reasonable evidence to explain the gender disparities among top-performing students, historical declines found in the MFR among high achievers over the past four decades would call for further explanations. In addition, if the disparities among high achievers were only attributable to the differences in cognitive abilities, it would be expected to be constant over different cultures and ethnicities, too. However, Makel et al. (2016) found that the magnitude of MFR in the extreme right tail is much lower among Indian students compared with a U.S. sample.

Extending the efforts to answer this question: “Why have these factors helped close the gender gap in school mathematics achievement in the general population but not among top-achieving students?” I present evidence from large-scale studies (Else-Quest et al., 2010; Hyde et al. 1990; Lindberg et al., 2010; McGraw et al., 2006) that indicated the factors that contributed to decrease the gender disparity in the general population have affected all students regardless of their position in the normal distribution. However, the disparities between females and males have been much wider in the upper end of the distribution than of the general population because being in the extreme right tail requires possession of further psychosocial and personal attributes as well as cognitive factors. For example, differences in individuals’ preferences and willingness to develop in a particular task/domain can play a pivotal role to be in the right tail of the distribution. However, these preferences do not only stem from cognitive abilities but also from social context that is highly influenced by someone’s self-confidence, self-perception, and many other psychosocial factors. Furthermore, considering mathematics has long been identified as a masculine discipline (Fennema & Sherman 1977; Sherman 1980), females may still hold more negative attitudes toward mathematics and have lower confidence in their mathematical ability than do males (Andreescu et al., 2008). Particularly given that it is highly competitive to move upward in the extreme right tail of the curve in any domain, females may have less interest in competing to advance to higher performance levels in mathematics due to lower parental and societal expectations (Mayr et al., 2012; Niederle & Vesterlund, 2010). In conclusion with this and other related work, we can claim that psychosocial factors and personal attitudes, including but not limited to social expectations, gender biases, differences in competitive preferences, self-confidence, and self-perception, might have decisive influences on determining who places in the upper tail of the normal curve in mathematics as well as cognitive abilities.

Analyses of the influences of the psychosocial and cognitive factors on the gender disparity in the right tail of performance in mathematics is never an easy task because the results should be interpreted considering the juxtaposition of psychosocial, personal attitudes, and cognitive abilities together. Although earlier research has sought associations between gender disparities and each of these phenomena, little is known thus far about how psychosocial factors and personal attitudes, including self-confidence, motivation, competitive preferences, and self-perception affect the gender differences among the high-achieving students. In a report about the gender differences in mathematics and science, a group of leading scholars asserted that:

We conclude that early experience, biological factors, educational policy, and cultural context affect the number of women and men who pursue advanced study in science and math, and these effects add and interact in complex ways. (Halpern, 2007, para. 1)

Future multivariate studies that explores the disparity qualitatively and longitudinally are necessary to explore these relations and to make more accurate conclusions. Such a research endeavor is crucial because differences in gender disparities in certain tasks not only predict educational choices (Buser et al. 2014) and other educational achievements (Dreber et al., 2014) but also access to economic gains, such as occupational income (Favara, 2012; Niederle & Vesterlund, 2007) and resources in society (Mayr et al., 2012).

Limitations

Although a large number of students from over hundreds of schools across the nation participate in the AMC contests every year, these students tend to be above average, and most of them are self-selected because of their interest in participation (Desjarlais, 2009). As Ellison and Swanson (2010) suggested, these participants slightly overrepresent high-performing schools in relatively affluent areas. Therefore, it is highly possible that participants in the AMC contests do not represent the entire student population in the United States well. Thus, gender disparities in the AMC participants’ performances may not be able to be generalized to the general population. However, readers should consider these as a contribution of new information to the literature rather than a mere limitation because this study investigated gender disparities in the AMC’s top performers purposefully.

Conclusion

The persistence of the gender disparities over decades indicates that efforts and policies to promote parity have not been successful to diminish gender disparities in the right tail of the distribution. Unfortunately, the findings of this study are also not encouraging. The trend in the gender disparity in participation in the AMC competitions increased significantly from 2009 to 2019 and favored males. In addition, the trend in gender disparities among top performers is clearly very large, and in contrast to that in the general population, it is very stable rather than declining. Although the juxtaposition of these findings with the results of previous studies might allow us to infer that the gender disparities in top-level mathematics performance might account in part for the underrepresentation of women in STEM fields, the crux of the matter remains vague and with all of these dilemmas we face, we still need to understand why more males than females appear in the upper end of the distribution in mathematical tasks. Moreover, given that earlier differences may lead to later disparities in STEM outcomes (Makel et al., 2016), they should be monitored through robust and scientifically sound analysis tools.

Typically, the decision whether students can continue along a trajectory of talent development in a STEM field is made before college (Bahar & Maker, 2011; Bahar & Adiguzel, 2016). Although, altering the disparity issues is not an easy task and might take generations to reverse, we should continue to encourage girls to develop their talents in mathematics and science. Increasing females’ participation in these programs will not only bring parity in exam rooms but also will increase the number of females among top achievers and, furthermore, may help them reach parity in occupational outcomes.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

Open Science Disclosure Statement

The data in this study were obtained from Mathematical Association of America’s (MAA) online public database, which is available at . The code used to generate the findings reported in the article are not available for purposes of reproducing the results or replicating the study. There are no newly created, unique materials that were used to conduct the research.

ORCID iD

A. Kadir Bahar

Author Biography

A. Kadir Bahar is an assistant professor in the Department of Educational Psychology at the University of Georgia. His research interests include mathematical creativity, problem solving, mathematical ability, and equity/access. Before his position at University of Georgia, he was a professor at the University of Wisconsin–Stevens Point, served as the coordinator of graduate programs in Gifted Education and directed youth programs including Youth in College and STEM for Young Scholars. He is the recipient of numerous awards including, Math Hero of the Year Award and Edith May Sliffe—Distinguished Teaching Award.

References

Andreescu

Gallian

Kane

J. M.

Mertz

J. E.

(2008). Cross-cultural analysis of students with exceptional talent in mathematical problem solving. Notices of the American Mathematical Society, 55(10), 1248-1260. http://www.ams.org/notices/200810/fea-gallian.pdf

Bahar

Adiguzel

(2016). Analysis of factors influencing interest in stem career: Comparison between high ability and motivated American and Turkish high school students. Journal of STEM Education, 17(3), 64-69.

Bahar

Maker

C. J.

(2011). Exploring the relationship between mathematical creativity and mathematical achievement. Asia-Pacific Journal of Gifted and Talented Education, 3(1), 33-48. https://www.researchgate.net/publication/271699531_Exploring_the_Relationship_between_Mathematical_Creativity_and_Mathematical_Achievement

Bahar

Maker

C. J.

(2015). Cognitive backgrounds of problem solving: A comparison of open-ended vs. closed mathematics problems. Eurasia Journal of Mathematics, Science & Technology Education, 11(6), 1531-1546. https://doi.org/10.12973/eurasia.2015.1410a

Bahar

A. K.

Maker

C. J.

(2020). Culturally responsive assessments of mathematical skills and abilities: Development, field testing, and implementation. Journal of Advanced Academics, 31(3), 211-233. https://doi.org/10.1177/1932202X20906130

Bandura

(1994). Self-efficacy. In Ramachaudran

V. S.

(Ed.), Encyclopedia of human behavior (Vol. 4, pp. 71-81). Academic Press. (Reprinted in H. Friedman [Ed.], Encyclopedia of mental health. Academic Press, 1998).

Benbow

C. P.

(1988). Sex differences in mathematical reasoning ability in intellectually talented preadolescents: Their nature, effects, and possible causes. Behavioral and Brain Sciences, 11(2), 169-232. https://doi.org/10.1017/S0140525X00049244

Benbow

C. P.

Stanley

J. C.

(1980). Sex differences in mathematical ability: Facts or Artifact? Science, 210(12), 1262-1264. http://doi.org/10.1126/science.7434028

Benbow

C. P.

Stanley

J. C.

(1983). Sex differences in mathematical reasoning ability: More facts. Science, 222(4627), 1029-1031. https://doi.org/10.1126/science.6648516

10.

Buser

Niederle

Oosterbeek

(2014). Gender, competitiveness and career choices. Quarterly Journal of Economics, 129(3), 1409-1447. https://doi.org/10.1093/qje/qju009

11.

Campbell

J. R.

(1996). Early identification of mathematics talent has long-term positive consequences for career contributions. International Journal of Educational Research, 25(6), 495-534. https://doi.org/10.1016/S0883-0355(97)86728-6

12.

Campbell

J. R.

(2002, August). Academic competitions: One of the secrets of America’s success at developing exceptional talent [Paper presentation]. International Conference on Education for the Gifted in Science, Busan, Korea.

13.

Campbell

J. R.

Walberg

H. J.

(2011). Olympiad studies: Competitions provide alternatives to developing talents that serve national interests. Roeper Review, 33(1), 8-17. https://doi.org/10.1080/02783193.2011.530202

14.

Ceci

S. J.

Donna

K. G.

Shulamit

Wendy

M. W.

(2014). Women in academic science: A changing landscape. Psychological Science in the Public Interest, 15(3), 75-141. https://doi.org/10.1177/1529100614541236

15.

Ceci

S. J.

Williams

W. M.

(2007). Are we moving closer and closer apart? Shared evidence leads to conflicting views. In Ceci

S. J.

Williams

W. M.

(Eds.), Why aren’t more women in science: Top researchers debate the evidence. American Psychological Association. https://doi.org/10.1037/11546-004

16.

Ceci

S. J.

Williams

W. M.

(2010). The mathematics of sex: How biology and society conspire to limit talented women and girls. Oxford University Press.

17.

College Board. (2009). AP Data: AP Report to the Nation 2009. https://research.collegeboard.org/programs/ap/data/nation/2009

18.

College Board. (2019a). AP Program Participation and Performance Data 2019. https://research.collegeboard.org/programs/ap/data/participation/ap-2019

19.

College Board. (2019b). SAT Suite of Assessments Annual Report. https://reports.collegeboard.org/pdf/2019-total-group-sat-suite-assessments-annual-report.pdf

20.

Comeig

Grau-Grau

Jaramillo-Gutiérrez

Ramírez

(2016). Gender, self-confidence, sports, and preferences for competition. Journal of Business Research, 69(4), 1418-1422. https://doi.org/10.1016/j.jbusres.2015.10.118

21.

Datta Gupta

Poulsen

Villeval

M. C.

(2013). Gender matching and competitiveness: Experimental evidence. Economic Inquiry, 51(1), 816-835.

22.

Desjarlais

M. A.

(2009). Gender differences on the American mathematics competition AMC 8 contest [Doctoral dissertation]. University of Nebraska–Lincoln. http://digitalcommons.unl.edu/cehsdiss/39

23.

Dreber

von Essen

Ranehill

(2014). Gender and competition in adolescence: Task matters. Experimental Economics, 17(1), 154-172. https://doi.org/10.1007/s10683-013-9361-0

24.

Dweck

C. S.

(1986). Motivational processes affecting learning. American Psychologist, 41(10), 1040-1048. https://doi.org/10.1037/0003-066X.41.10.

25.

Dweck

C. S.

(2007). Is math a gift? Beliefs that put females at risk. In Ceci

S. J.

Williams

W. M.

(Eds.), Why aren’t more women in science: Top researchers debate the evidence (pp. 47-55). American Psychological Association. https://doi.org/10.1037/11546-004

26.

Eccles

J. S.

Roeser

Vida

Fredricks

Wigfield

(2006). Motivational and achievement pathways through middle childhood. In Balter

Tamis-LeMonda

C. S.

(Eds.), Child psychology: A handbook of contemporary issues (pp. 325-355). Psychology Press.

27.

Ellison

Swanson

(2010). The gender gap in secondary school mathematics at high achievement levels: Evidence from the American mathematics competitions. Journal of Economic Perspectives, 24(2), 109-128. https://doi.org/10.1257/jep.24.2.109

28.

Else-Quest

N. M.

Hyde

J. S.

Linn

M. C.

(2010). Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 136(1), 103-127. https://doi.org/10.1037/a0018053

29.

Environmental Protection Agency. (2009). Statistical analysis of groundwater monitoring data at RCRA facilities: Unified guidance. Environmental Protection Agency, Office of Resource Conservation and Recovery. https://www.itrcweb.org/gsmc-1/Content/Resources/Unified_Guidance_2009.pdf

30.

Favara

(2012). The cost of acting “girly”: Gender stereotypes and educational choices (IZA Discussion Paper No. 7037). http://ftp.iza.org/dp7037.pdf

31.

Feingold

(1988). Cognitive gender differences are disappearing. American Psychologist, 43(2), 95-103. https://doi.org/10.1037/0003-066X.43.2.95

32.

Fennema

(1990). Teachers’ beliefs and gender differences in mathematics. In Fennema

Leder

(Eds.), Mathematics and gender: Teacher and student influences. Teachers College Press.

33.

Fennema

Carpenter

T. P.

(1981). Sex-related differences in mathematics: Results from national assessment. The Mathematics Teacher, 74(7), 554-559. https://doi.org/10.2307/27962588

34.

Fennema

Peterson

P. L.

Carpenter

T. P.

(1990). Teachers’ attributions and beliefs about girls, boys, and mathematics. Educational Studies in Mathematics, 21(1), 55-69. https://doi.org/10.1007/BF00311015

35.

Fennema

Sherman

(1977). Sex-related differences in mathematics achievement, spatial visualization, and affective factors. American Educational Research Journal, 14(1), 51-71. https://doi.org/10.3102/00028312014001051

36.

Flory

Leibbrandt

List

(2015). Do competitive workplaces deter female workers? A large-scale natural field experiment on job entry decisions. Review of Economic Studies, 82(1), 122-155. https://doi.org/10.1093/restud/rdu030

37.

Gallagher

A. M.

De Lisi

(1994). Gender differences in Scholastic Aptitude Test: Mathematics problem solving among high-ability students. Journal of Educational Psychology, 86(2), 204-211. https://doi.org/10.1037/0022-0663.86.2.204

38.

Gallagher

A. M.

De Lisi

Holst

P. C.

Mcgillicuddy-De Lisi

A. V.

Morely

Cahalan

(2000). Gender diﬀerences in advanced mathematical problem solving. Journal of Experimental Child Psychology, 75(3), 165-190. https://doi.org/10.1006/jecp.1999.2532

39.

Gavin

M. K.

(1996). The development of math talent: Influences on students at a women’s college. Journal of Secondary Gifted Education, 7(4), 476-485. https://doi.org/10.1177/1932202X9600700406

40.

Gneezy

Niederle

Rustichini

(2003). Performance in competitive environments: Gender differences. Quarterly Journal of Economics, 118(3), 1049-1074. https://doi.org/10.1162/00335530360698496

41.

Halpern

D. F.

(2007). Science, sex, and good sense: Why women are underrepresented in some areas of science and math. In Ceci

S. J.

Williams

W. M.

(Eds.), Why aren’t more women in science: Top researchers debate the evidence (pp. 121-130). American Psychological Association. https://doi.org/10.1037/11546-010

42.

Halpern

D. F.

(2012). Sex differences in cognitive abilities (4th ed.). Psychology Press.

43.

Hedges

L. V.

Nowell

(1995). Sex differences in mental test scores, variability, and numbers of high-scoring individuals. Science, 269(5220), 41-45. https://doi.org/10.1126/science.7604277

44.

Hirsch

R. M.

Slack

J. R.

Smith

R. A.

(1982). Techniques of trend analysis for monthly water quality data. Water Resources Research, 18(1), 107-121. https://doi.org/10.1029/WR018i001p00107

45.

Hyde

J. S.

(2005). The gender similarities hypothesis. American Psychologist, 60(6), 581-592. https://doi.org/10.1037/0003-066X.60.6.581

46.

Hyde

J. S.

(2007). Women in Science: Gender similarities in abilities and sociocultural forces. In Ceci

S. J.

Williams

W. M.

(Eds.), Why aren’t more women in science? Top researchers debate the evidence (pp. 131-145). American Psychological Association. https://doi.org/10.1037/11546-011

47.

Hyde

J. S.

Fennema

Lamon

S. J.

(1990). Gender difference in mathematical performance: A meta-analysis. Psychological Bulletin, 107(2), 139-155. https://doi.org/10.1037/0033-2909.107.2.139

48.

Hyde

J. S.

Lindberg

S. M.

Linn

M. C.

Ellis

A. B.

Williams

C. C.

(2008). Gender similarities characterize math performance. Science, 321(5888), 494-495. https://doi.org/10.1126/science.1160364

49.

Hyde

J. S.

Linn

M. C.

(2006). Gender similarities in mathematics and science. Science, 314(5799), 599-600. https://doi.org/10.1126/science.1132154

50.

Iriberri

Rey-Biel

(2020). Competitive pressure widens the gender gap in performance: Evidence from a two-stage competition in mathematics. Economics Journal, 129(620), 1863-1893. https://doi.org/10.1111/ecoj.12617

51.

Kendall

M. G.

(1975). Rank correlation methods (4th ed.). Charles Griffin.

52.

Lazear

E. P.

Rosen

(1990). Male-female wage differentials in job ladders. Journal of Labor Economics, 8(1), 106-123. https://doi.org/10.1086/298246

53.

Lindberg

S. M.

Hyde

J. S.

Petersen

J. L.

Linn

M. C.

(2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136(6), 1123-1135. https://doi.org/10.1037/a0021276

54.

Linn

M. C.

(2010). Designing standards for lifelong science learning. Journal of Engineering Education, 99(2), 103-105. https://doi.org/10.1002/j.2168-9830.2010.tb01047.x

55.

Lubinski

D. S.

Benbow

C. P.

(2007). Sex differences in personal attributes for the development of scientific expertise. In Ceci

S. J.

Williams

W. M.

(Eds.), Why aren’t more women in science? Top researchers debate the evidence (pp. 79-100). American Psychological Association. https://doi.org/10.1037/11546-007

56.

Lubinski

D. S.

Benbow

C. P.

(2021). Intellectual precocity: What have we learned since Terman? Gifted Child Quarterly, 65(1), 3-28. https://doi.org/10.1177/0016986220925447

57.

Maccoby

(1966). The development of sex differences. Stanford University Press.

58.

Maccoby

Jacklin

C. N.

(1974). The psychology of sex differences. Stanford University Press.

59.

Makel

M. C.

Wai

Peairs

Putallaz

(2016). Sex differences in the right tail of cognitive abilities: An update and cross cultural extension. Intelligence, 59(1), 8-15. https://dx-doi-org.web.bisu.edu.cn/10.1016/j.intell.2016.09.003

60.

Mann

H. B.

(1945). Non-parametric tests against trend. Econometrica, 13(3), 163-171. https://doi.org/10.2307/1907187

61.

Mathematical Association of America. (2020). About AMC. https://www.maa.org/math-competitions/about-amc

62.

Mayr

Wozniak

Davidson

Kuhns

Harbaugh

(2012). Competitiveness across the life span: The Feisty Fifties. Psychology and Aging, 27(2), 278-285. https://doi.org/10.1037/a0025655

63.

McGraw

Lubienski

S. T.

Strutchens

M. E.

(2006). A closer look at gender in NAEP mathematics achievement and affect data: Intersections with achievement, race/ethnicity, and socioeconomic status. Journal of Research in Mathematics Education, 37(2), 129-150. https://doi.org/10.2307/30034845

64.

National Science Board. (2018). Science and Engineering Indicators 2018 (NSB-2018-1). https://www.nsf.gov/statistics/2018/nsb20181/assets/nsb20181.pdf

65.

Niederle

Vesterlund

(2007). Do women shy away from competition? Do men compete too much? Quarterly Journal of Economics, 122(3), 1067-1101, https://doi.org/10.1162/qjec.122.3.1067

66.

Niederle

Vesterlund

(2008). Gender differences in competition. Negotiation Journal, 24(4), 447-463. https://doi.org/10.1111/j.1571-9979.2008.00197.x

67.

Niederle

Vesterlund

(2010). Explaining the gender gap in math test scores: The role of competition. Journal of Economic Perspectives, 24(2), 129-144. https://doi.org/10.1257/jep.24.2.129

68.

OECD. (2011). Education at a glance 2011: OECD Indicators. http://www.oecd-ilibrary.org/education/education-at-a-glance-2011_eag-2011-en

69.

Olszewski-Kubilius

Lee

S. Y.

(2011). Gender and other group differences in performance on off-level tests: Changes in the 21st century. Gifted Child Quarterly, 55(1), 54-73. https://doi.org/10.1177/0016986210382574

70.

Reis

S. M.

Callahan

C. M.

(1989). Gifted females: They’ve come a long way—or have they? Journal for the Education of the Gifted, 12(2), 99-117. https://doi.org/10.1177/016235328901200203

71.

Reis

S. M.

Park

(2001). Gender differences in High-Achieving students in math and science. Journal for the Education of the Gifted, 25(1), 52-73. https://doi.org/10.1177/016235320102500104

72.

Roberts

B. W.

Walton

K. E.

Viechtbauer

(2006). Patterns of mean-level change in personality traits across the life course: A meta- analysis of longitudinal studies. Psychological Bulletin, 132(2), 3-27. https://doi.org/10.1037/0033-2909.132.1.1

73.

Robinson

J. P.

Lubienski

S. T.

(2011). The development of gender achievement gaps in mathematics and reading during elementary and middle school: Examining direct cognitive assessments and teacher ratings. American Educational Research Journal, 48(2), 268-302. https://doi.org/10.3102/0002831210372249

74.

Sen

P. K.

(1968). Estimates of the regression coefficient based on Kendall’s tau. Journal of the American Statistical Association, 63(324), 1379-1389. https://doi.org/10.2307/2285891

75.

Shaw

E. J.

Marini

J. P.

Mattern

K. D.

(2013). Exploring the utility of Advanced Placement participation and performance in college admission decisions. Educational and Psychological Measurement, 73(2), 229-253. https://doi.org/10.1177/0013164412454291

76.

Sherman

(1980). Mathematics, spatial visualization, and related factors: Changes in girls and boys, Grades 8–11. Journal of Educational Psychology, 72(4), 476-482. https://doi.org/10.1037/0022-0663.72.4.476

77.

Sidanius

Pratto

(1999). Social dominance: An intergroup theory of social hierarchy and oppression. Cambridge University Press. https://doi.org/10.1017/CBO9781139175043

78.

Stanley

J. C.

(1994). Gender differences for able elementary school students on above-grade-level achievement tests. In Colangelo

Assouline

S. G.

Ambroson

D. L.

(Eds.), Talent development (Vol. 2, pp. 141-148). Ohio Psychology Press.

79.

Stumpf

Stanley

J. C.

(1996). Gender-related differences on the College Board’s Advanced Placement and Achievement tests, 1982–1992. Journal of Educational Psychology, 88(2), 353-364. https://doi.org/10.1037/0022-0663.88.2.353

80.

Swiatek

M. A.

Lupkowski-Shoplik

(2000). Gender differences in academic attitudes among gifted elementary school students. Journal for the Education of the Gifted, 23(4), 360-377. https://doi.org/10.1177/016235320002300403

81.

U.S. Department of Education, National Center for Education Statistics. (2018). Table 203.50: Enrollment and percentage distribution of enrollment in public elementary and secondary schools, by race/ethnicity and region: Selected years, fall 1995 through fall 2027. https://nces.ed.gov/programs/digest/d17/tables/dt17_203.50.asp?referer=raceindicators

82.

Wai

Cacchio

Putallaz

Makel

M. C.

(2010). Sex differences in the right tail of cognitive abilities: A 30-year examination. Intelligence, 38(4), 412-423. https://doi.org/10.1016/j.intell.2010.04.006

83.

Wai

Hodges

Makel

M. C.

(2018). Sex differences in ability tilt in the right tail of cognitive abilities: A 35-year examination. Intelligence, 67(March-April), 76-83. https://doi.org/10.1016/j.intell.2018.02.003

84.

Wai

Lubinski

Benbow

C. P.

(2009). Spatial ability for STEM domains: Aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817-835. https://doi.org/10.1037/a0016127

85.

Wai

Lubinski

Benbow

C. P.

Steiger

J. H.

(2010). Accomplishment in science, technology, engineering, and mathematics (STEM) and its relation to STEM educational dose: A 25-year longitudinal study. Journal of Educational Psychology, 102(4), 860-871. https://doi.org/10.1037/a0019454

86.

Wai

Putallaz

Makel

M. C.

(2012). Studying intellectual outliers: Are there sex differences, and are the smart getting smarter? Current Directions in Psychological Science, 21(6), 382-390. https://doi.org/10.1177/0963721412455052

87.

Webb

R. M.

Lubinski

Benbow

C. P.

(2007). Spatial ability: A neglected dimension in talent searches for intellectually precocious youth. Journal of Educational Psychology, 99(2), 397-420. https://doi.org/10.1037/0022-0663.99.2.397

88.

Wise

L. L.

McLaughlin

D. H.

Steel

(1979). The Project TALENT data bank. American Institutes for Research.

89.

Wozniak

Harbaugh

Mayr

(2010). Choices about competition: Differences by gender and hormonal fluctuations, and the role of relative performance feedback (MPRA Paper No. 31374). https://mpra.ub.uni-muenchen.de/31374/2/MPRA_paper_31374.pdf

90.

W. T.

(1996). Growing up in Taiwan: The impact of environmental influences on the Math Olympians. International Journal of Educational Research, 25(6), 479-484. https://doi.org/10.1016/S0883-0355(97)86729-8

91.

Xie

Shauman

K. A.

(2003). Women in science: Career processes and outcomes. Harvard University Press.

92.

P. S.

Yang

T. C.

Chou

C. C.

(2002). Effects of climate change on evapotranspiration from paddy fields in southern Taiwan. Climate Change, 54(2), 165-179. https://doi.org/10.1023/A:1015764831165