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CHAPTER 1

Mathematics Gender Achievement Gap

Some things will drop out of the public eye and will go away, but there will always be science, engineering, and technology. And there will always, always be mathematics.

—Katherine Johnson, Mathematician and Recipient of the Presidential Medal of Freedom

What do educators know (or think they know) about girls learning mathematics? This chapter will address this question through the primary lens of the much-talked-about mathematics gender achievement gap. We will also begin discussion about the influence of teachers on girls’ learning mathematics and deepen our discussions on what we mean by perceptions, possibilities, and priorities.

First, however, start this journey by considering what some are saying about girls in mathematics. Perhaps you can recollect statements from conversations with friends and family, from the media, or unsolicited from strangers who learn that you are involved with the teaching and learning of mathematics. Complete the chart in figure 1.1 to record some of these recollections about girls in mathematics.

Figure 1.1: Educator recollections of what’s said about girls in mathematics.

Visit go.SolutionTree.com/mathematics for a free reproducible version of this figure.

Circle the statements in figure 1.1 that are positive. How many of the statements did you circle? We would like all the statements to be positive, but that is most likely not the case. Often this is due to the negative portrayal of girls in mathematics. Many times girls have seen the field of mathematics portrayed as a male-dominated field, thus they are typically excluded from the narrative. Nonetheless, what we strive for is an environment that supports girls studying mathematics and for girls to receive positive influences to continue their trajectory in mathematics. When what is said about girls in mathematics is positive, the actions taken to support girls are more likely to be positive. Furthermore, because what people say to and about children easily influences them, the more we can make sure girls hear positive statements about their learning of mathematics, the better chance we have of positively influencing girls in their study of mathematics. (Who else would you consider for what they have to say about girls in mathematics? Feel free to replicate figure 1.1, page 7, using other groups of people to further the discussion.)

Before we continue, we ask you to share your own feelings (figure 1.2). Reflect on your own thoughts about girls as learners of mathematics using the questions and prompts. Your responses will help you examine and frame your thinking and reflections as you continue to read this book and as you teach mathematics to girls. If you are engaged in a book study with Making Sense of Mathematics for Teaching Girls in Grades K–5, you can also use the items to promote helpful discussions about girls’ experiences with mathematics.

Figure 1.2: Educator reflection on the gender gap in mathematics learning.

Visit go.SolutionTree.com/mathematics for a free reproducible version of this figure.

Consider the voices of two elementary school girls as they reflect on their experiences with mathematics. Christina, a kindergarten student, says:

When I do math in school, I write numbers, and I can say them and count them and stomp them and clap them, and learning math is fun…. I think I will use math when I’m older to make money and be able to go places, and I will know how to do math to show other teachers all the math I know. (C. Latanza, personal communication, September 5, 2017)

Now, consider fifth grader Julia’s remarks:

At school when I learn math, I think that it’s fun, especially when I get to pick the strategy that works best for me to do the math…. I don’t really know all of the math that I would need yet (when I grow up), but I think I might want to be an engineer, and I know that I would have to use math every day for the planning and the building that I would be doing in that job. (J. Clements, personal communication, December 2, 2017)

Use figure 1.3 to detail what you would say to these students to maintain their interest.

Figure 1.3: Remarks to maintain girls’ interest in mathematics.

As you read the girls’ perspectives of learning mathematics, you heard ideas of positivity and promise that these girls will continue to pursue opportunities for mathematics in their schooling and beyond. However, whether or not these girls will continue to achieve and believe in themselves as mathematics learners in the pivotal years to come is unknown because it is a continuous process that will take time. The key is exposing girls to opportunities; however, ultimately it is their decision whether to pursue the opportunity. We have hope! Their early experiences are already impacting the likelihood that they will pursue coursework and careers in the field of mathematics, even in implicit ways that these girls may not yet realize. We want these girls and all other girls to realize their potential in mathematics.

Exploring the Mathematics Gender Achievement Gap

Gender differences in mathematics achievement in North America have been widely discussed and studied (Cheema & Galluzzo, 2013; Damarin & Erchick, 2010; Fryer & Levitt, 2010; Leyva, 2017; Lubienski, Robinson, Crane, & Ganley, 2013; Marks, 2008; Penner & Paret, 2008; Riegle-Crumb & Humphries, 2012; Robinson & Lubienski, 2011). However, differences in population, test formats, content assessed, and other variables yield results that are not necessarily generalizable and at times even offer mixed results, thus complicating the discussion and making implications fuzzy. In the sections that follow, we will explore both sides of the issue—data that say there is a mathematics gender achievement gap and data that contend there is not a mathematics gender achievement gap. While the primary focus of this book is on girls in grades K–5, it is important to understand the broader discussion on the mathematics gender achievement gap in the context of gender differences that appear in college and career settings.

Evidence Pointing to a Gender Gap in Mathematics

In this section, we’ll dive deeper into the research that shows there is a mathematics gender achievement gap. We’ll explore the representation of women in science, technology, engineering, and mathematics (STEM) fields; differences in mathematics achievement scores; differences in student responses regarding self-concept in mathematics; differences in problem-solving approaches among boys and girls; and differences in spatial skills among boys and girls.

Representation of Women in Science, Technology, Engineering, and Mathematics Fields

The representation of women in college programs and career pathways related to science, technology, engineering, and mathematics is societal evidence of a mathematics gender gap. Catherine Riegle-Crumb and Barbara King (2010) and many other researchers suggest that there is a disproportionally low number of women (compared to men) in both STEM programs in colleges and universities and in STEM careers (Lubienski et al., 2013; Mendick, 2005; Riegle-Crumb & Humphries, 2012; Snyder & Dillow, 2011).

In regard to STEM college programs, Ryan Noonan (2017) reports that “while nearly as many women hold undergraduate degrees as men overall, they [women] make up only about 30 percent of all STEM degree holders” (p. 1). In order for any student to pursue a STEM degree in college, he or she benefits from having a good school background in STEM subjects, mathematics being one such subject.

In this same report, “Women in STEM: 2017 Update,” Noonan (2017) also addresses the presence of women in STEM careers:

Women filled 47 percent of all US jobs in 2015 but held only 24 percent of STEM jobs. Likewise, women constitute slightly more than half of college educated workers but make up only 25 percent of college educated STEM workers. (p. 1)

Hence, the gender imbalance among STEM degrees is reflected in the gender imbalance in STEM careers. Every opportunity to encourage girls to have interest in and study fields in STEM, specifically mathematics, provides an opportunity to increase the representation of women in STEM. As it relates to representation, the quote by Marian Wright Edelman (2015), “It’s hard to be what you can’t see,” comes to mind. Therefore, it is important that girls have positive role models in their respective fields who they can look up to and follow.

You may ask why this is happening. Why are there more men than women studying in STEM programs, such as mathematics? Why are there more men than women employed in STEM fields? Economist and statistician David Beede and colleagues (2011) suggest that “there are many possible factors contributing to the discrepancy of women and men in STEM jobs, including: a lack of female role models, gender stereotyping, and less family-friendly flexibility in the STEM fields” (p. 1). While the key factor (or possible intersection of multiple factors) cannot be confirmed, we believe that continuing the dialogue and inquiry around the representation of women in STEM is warranted.

Use figure 1.4 to brainstorm other factors that influence the number of women in STEM fields.

Figure 1.4: Reflections on the factors that impact the number of women in STEM.

Differences in Mathematics Achievement Scores

The National Assessment of Educational Progress (NAEP), which assesses students in grades 4, 8, and 12, is the most commonly cited U.S. assessment in mathematics. NAEP has been administered approximately every four years since 1973; however, there have been changes in test administration since its inception that impact statistical comparisons. For example, since 1990, students have been assessed by grade rather than by age, and there was variation in the allowance of accommodations at some testing sites in 1996 and 2000.

From 2003 to 2017, there has been a slight gender difference based on the average fourth-grade mathematics assessment scores, with boys scoring significantly higher than girls during each assessment administration (National Center for Education Statistics [NCES], 2017). For example, in 2003, boys scored higher (with statistical significance) when scores were analyzed by average scale score, percentile, and proficiency level. There were significant differences that favored the performance of boys at the 25th, 50th, 75th, and 90th percentiles, and the gap between boys’ and girls’ scores increased as the scores increased (with a five-point difference at the 90th percentile). According to the NAEP proficiency data from 2003, boys also outperformed girls in the categories of advanced (5 percent compared to 3 percent), at or above proficient (35 percent compared to 30 percent), and at or above basic (78 percent compared to 76 percent; NCES, 2017). For example, the average scale score of fourth-grade boys was 236 compared to the average scale score of 233 for fourth-grade girls, a seemingly small but statistically significant difference. Additionally, according to the proficiency data from 2003, fourth-grade boys outperformed girls in four of the five content strands: number and operations, data analysis, algebra and functions, and measurement, with the discrepancy in measurement being the largest (NCES, 2017). This is consistent with gaps in the measurement strand from the 1996 administration of the NAEP, which Ellen Ansell and Helen M. Doerr (2000) analyze to reveal that fourth-grade boys were more accurately able to choose appropriate units or read and use a measuring instrument (such as a speedometer, thermometer, or ruler). When Ansell and Doerr (2000) further analyze the gender gaps within racial groups and across content strands, they find significant differences that still favored boys for white and Hispanic groups in number operations and measurement and Asian and Pacific islanders in measurement. This analysis also reveals, however, that African American girls outperformed African American boys in geometry and data analysis at the fourth-grade level.

While NCES (2017) documents that fourth-grade boys achieve higher scores in mathematics than girls, the achievement gap between boys and girls has not widened between 2003 and 2017, with the most recent 2017 data revealing an average scale score of 241 among boys and 239 among girls. This means that the mathematics achievement gap between grade 4 boys and grade 4 girls persists, but it has not grown in recent years.

There is more research that speaks to the matter of the mathematics gender achievement gap. For instance, Sean F. Reardon, Erin M. Fahle, Demetra Kalogrides, Anne Podolsky, and Rosalía C. Zárate (2018) report on a study (“Gender Achievement Gaps in U.S. School Districts”) of students in grades 3–8 across ten thousand U.S. school districts:

Both math and ELA gender achievement gaps vary among school districts and are positively correlated—some districts have more male-favoring gaps and some more female-favoring gaps. We find that math gaps tend to favor males more in socioeconomically advantaged school districts. (p. 2)

More specifically, among Reardon, Fahle, et al.’s (2018) findings, the distribution of mathematics gaps “implies that 95% of districts have math gaps that are between -0.07 and +0.13 standard deviations, favoring males in 72% of school districts and females in 28%” (p. 21). Additionally, this research finds that in wealthier districts and districts with more economic inequality among adult men and women, mathematics gaps favored boys on average. These analyses show that the mathematics gender achievement gap is not necessarily across the board or applicable for all students.

When considering the research presenting differences in mathematics achievement scores between boys and girls, we find that if there are differences, they are often small and are typically evident among higher-performing students (Lindberg, Hyde, Petersen, & Linn, 2010; Reardon, Fahle, et al., 2018).

Differences in Student Responses Regarding Self-Concept in Mathematics

In addition to achievement data, NAEP (NCES, 2017) reports data based on students’ questionnaire responses about their beliefs about mathematics and themselves as learners. For example, when asked to consider the statement “I am good at mathematics,” students could choose the answers “A lot like me,” “A little like me,” or “Not like me.” Among fourth-grade students, boys were significantly more likely than girls to identify the following statements as being a lot like themselves: “I like mathematics” (50 percent boy, 43 percent girl), “I am good at mathematics” (56 percent boy, 43 percent girl), and “I understand most of what goes on in mathematics class” (58 percent boy, 55 percent girl).

Additional data from the Education Quality and Accountability Office (Casey, 2017) support the idea that gaps in students’ self-concept may not be limited to the United States. For example, although girls and boys earned similar grades during the 2016 to 2017 academic year:

Only 49 percent of Grade 3 girls in Ontario agreed that they were good at math compared to 62 percent of boys. The difference widens in Grade 6, where 46 percent of girls said they were good at math compared to 61 percent of boys. (Casey, 2017)

Differences in Problem-Solving Approaches Among Boys and Girls

In 1980, Problem Solving in School Mathematics (Krulik & Reys, 1980) initiated a shift in mathematics education that proposed problem solving to be central to mathematics instruction and across mathematics curriculum. Along with this notion, the discussion of methods, strategies, and heuristics for problem solving abound in mathematics publications and conference presentations. In addition, starting from this point, research on problem solving became more visible in the discipline. For example, Elizabeth Fennema, Thomas P. Carpenter, Victoria R. Jacobs, Megan L. Franke, and Linda W. Levi (1998) find that boys were more likely than girls to use novel or invented problem-solving approaches when given mathematics tasks. Comparison observations find that girls were more inclined to use the specific procedures that the teacher taught in previous instruction for a given problem type. The researchers further explain that the use of invented algorithms appeared to be important for students to develop key concepts in mathematics, such as place value and number sense, and for students to be flexible in new situations, such as extensions of learned mathematics. Ana Villalobos (2009) offers additional research findings that explore “strategy socialization” with regard to risk-taking and rule-following, and suggests that girls are disproportionally represented in the development of “algorithmic strategies” and boys in “problem solving strategies” (p. 27). In this study, the author suggests that over-rewarding a single strategy, especially when the strategy yields accurate solutions, can lead to difficulties in switching strategies, which is necessary when “solving unfamiliar problems that require new approaches later in the curriculum” (Villalobos, 2009, p. 27).

Although this research took place prior to specific curriculum standards that advocate for multistrategy instruction and problem-solving experiences, it suggests that additional research is warranted to determine if girls are unintentionally limiting their own explorations in problem solving in the classroom with their inclination to follow taught procedures. The different ways that boys and girls engage in problem solving may affect how they use problem solving to learn mathematics.

It is also important to consider the role of the teacher in girls’ engagement with problem solving. Education Week reporter Sarah Schwartz (2018) challenges us to consider this:

Students in classes where teachers have a “multi-dimensional” approach to problem solving that allows for multiple strategies are more likely to have a growth mindset at the end of the course than students of teachers who value speed or memorization. This effect can be more pronounced for some students than others. For example, separate research found that when female teachers had more anxiety around doing math, the girls in their classes had lower achievement. The boys in their classes did not see these same negative effects.

Sian L. Beilock, Elizabeth A. Gunderson, Gerardo Ramirez, and Susan C. Levine (2010) also note this correlation between a woman teacher’s confidence with mathematics and her students’ confidence. Given that most elementary teachers in the United States and Canada are women (Organisation for Economic Co-operation and Development [OECD], 2016), we can say with certainty that women teachers have a great reach in their access and interactions with learners. Therefore, it is important to consider this research that suggests that how a teacher responds to mathematics is an issue that can impact how certain populations of students, such as girls, will respond to mathematics.

Differences in Spatial Skills Among Boys and Girls

Some research suggests that boys demonstrate more sophisticated spatial skills than girls (Klein, Adi-Japha, & Hakak-Benizri, 2010). The National Council of Teachers of Mathematics (NCTM, 2000) calls for instructional programs from prekindergarten through twelfth grade to enable each and every student to “use visualization, spatial reasoning, and geometric reasoning to solve problems.” A gender gap in this area is noteworthy because in addition to being a part of content standards at all grade levels, research shows that greater spatial skills are a predictor of higher mathematics performance in later years of schooling and that they also positively impact the selection of STEM-related careers (Tzuriel & Egozi, 2010). Despite this reported gender imbalance, much of this same research suggests targeted intervention can improve girls’ deficits in spatial skills, even to the extent that it eliminates gender discrepancy. There is an impact on girls’ exposure to the instructional experiences that have the potential to positively impact the development of students’ spatial skills. To foster these experiences, teachers can:

■ Explain to young people that spatial skills are not innate but developed.

■ Encourage children and students to play with construction toys, take things apart and put them back together again, play games that involve fitting objects into different places, draw, and work with their hands.

■ Use handheld models when possible (rather than computer models) to help students visualize what they see on paper in front of them. (Hill, Corbett, & St. Rose, 2010, p. 56)

Use figure 1.5 to reflect on why the gender achievement gap appears in some contexts but not others.

Figure 1.5: Reflection on disparities in gender achievement gap across contexts.

Evidence Challenging a Gender Gap in Mathematics

The following is evidence that challenges the notion of a gender gap in mathematics. Specifically, we highlight marginal differences between boys’ and girls’ mathematics achievement scores and student confidence levels impacting mathematics achievement.

Marginal Differences Between Boys’ and Girls’ Mathematics Achievement Scores

As previously indicated, some data challenge the presence of a mathematics gender achievement gap. For instance, Jennifer E. V. Lloyd, John Walsh, and Manizheh Shehni Yailagh (2005) conducted an analysis of grades, standardized test scores, and self-efficacy responses among sixty-two fourth graders and ninety-nine seventh graders and conclude that “girls’ mathematics achievement met or exceeded that of boys’” (p. 384).

The NCES (2017) report of NAEP data for 2003–2017 indicates that there is not a mathematics gender achievement gap except for grade 4, as we previously outlined. Although NCES (2017) reports the presence of the gap for just one grade, that is one grade too many! Why this phenomenon exists for grade 4 in particular is a point for further study. A variety of factors, such as grade 4 mathematics curriculum, assessment item structures, and much more, could influence this outcome, and researchers continue to explore it (Reardon, Kalogrides, Fahle, Podolsky, & Zarate, 2018). Nonetheless, it is clearly important for educators to take a closer look at the mathematics experiences of girls in elementary school, which is why we chose to focus this book on grades K–5.

Student Confidence Levels Impacting Mathematics Achievement

There are other variables that need examination. For instance, what we tell students about their mathematics performance or about anticipating their mathematics performance really matters. How can we encourage students? How can we empower students to be successful in mathematics, simply by what we say to them? How can we even the playing field for boys and girls in mathematics? Perhaps there are many answers to these questions and to the previous questions. Here is one simple answer: “When test administrators tell students that girls and boys are equally capable in math, … the difference in performance essentially disappears” (Hill et al., 2010, p. xv). So, what we say to students can have a great deal of influence on how they perform in mathematics. To send direct messages about the nature of intelligence as dynamic and to reduce stereotypes, teachers and administrators can:

■ Teach students that intellectual skills can be acquired—Explain that, like muscles, the more we use our brains, the stronger they become. Help students learn that their brains form new connections as they stretch themselves and work hard to learn something new.

■ Praise students for their effort (not their outcomes)—Give feedback about students’ processes and how they arrive at conclusions.

■ Highlight the role of struggle in education—Help convey to students that challenges, hard work, and mistakes are valuable and admirable. Explain to them that the process of struggling and overcoming challenges has been at the core of most scientific and mathematical contributions in our society.

Use figure 1.6 to rate your confidence teaching and learning mathematics.

Figure 1.6: Educator reflection on anxiety toward mathematics and its impact on students.

Considering the Impact of Teachers’ Mindsets

We briefly mentioned the teacher’s influence in the previous section. Here we deal with this topic in a bit more detail. Elementary mathematics teachers play an important role in the mathematics learning experiences of young girls. Interestingly, studies even suggest that teachers may impact girls’ perceptions of and achievements in mathematics beyond the mathematics lessons taught in the classroom, especially if that teacher is a woman (Beilock et al., 2010; Klass, 2017). Regardless of teacher effectiveness, girls’ mathematics achievement may actually be lower in classrooms where a woman teacher has mathematics anxiety, meaning that she is not confident in either her own mathematics abilities, her ability to teach mathematics, or both (Beilock et al., 2010). Young girls may implicitly be forming a gender stereotype since they assume the teacher’s knowledge and ability to learn applies to them.

Teachers’ perceptions of student achievement in mathematics also offer potential for gender gaps. Joseph P. Robinson-Cimpian of Economics and Education Policy at New York University Steinhardt and colleagues Sarah Theule Lubienski, Colleen M. Ganley, and Yasemin Coper-Gencturk (2014) explore how teachers engage in unintentional “differential ratings,” comparing teachers’ projections of their students’ mathematics achievement scores to their actual scores (p. 1264). In their findings (Robinson-Cimpian et al., 2014), teachers perceived boys’ mathematical performance to be higher than their girl counterparts, even when boys and girls perform the same. Gender stereotypes and bias that impact teachers’ perceptions of their students’ mathematics performance, achievement, and aptitude may drive the process of differential ratings.

In general, trends suggest that as early as second grade, girls are less confident in their ability to engage in mathematics tasks and are more anxious than boys about mathematics performance (Casey, 2017; Ganley & Lubienski, 2016a; Post, 2015). These gender differences in self-perceptions are larger than actual achievement gaps, however, as highlighted by the NAEP self-concept in mathematics achievement data and other examples shared earlier in this chapter. How are mathematics teachers and teams contributing to these young students’ individual beliefs? Ganley and Lubienski (2016c) suggest that girls’ attitudes toward mathematics should receive greater emphasis in day-to-day classroom experiences with teachers rather than in the short, out-of-classroom experiences and interventions such as camps and after-school programs that are often developed to increase the representation of girls and women in STEM. This position leads to placing great value on the teacher-student relationship and the way this relationship can influence students’ learning.

Conclusion

In our society, gender is a factor in many situations that dictates who can do what, who can learn what, who can have what, and so on. This perspective is also present in schools and classrooms. In the context of this book, it is present in the form of the mathematics gender achievement gap. When there is one instance in which girls do not receive support to achieve in mathematics in the same ways as boys do, this is one instance too many. Whether the achievement gap is real or perceived is not the issue. The fact of the matter is there are girls in our schools who are not engaging, excelling, or both to their potential in mathematics. We have an opportunity and responsibility to improve on this issue. That is the singular aim of this book.

Use figure 1.7 to determine what actions you can take to help parents and guardians do their part to close the gap.

Figure 1.7: Actions to improve parents’ and guardians’ perspectives about girls learning mathematics.

Reflections

Answer the following five questions independently or in your book study to further your understanding and goals related to teaching girls mathematics.