Show me the data: Boys, girls, and skills
Differences in constrained skills are temporary. Longer-lived differences lie with unconstrained skills.
Note: Unconstrained Kids unpacks, translates, and integrates academic research and data about constrained and unconstrained skills for people that run, fund, and assist organizations that teach and serve kids. This post presents a series of charts I created from among four nationally representative datasets to illustrate proficiency patterns in representative groups of constrained and unconstrained reading and math skills, unconstrained nonacademic skills, and unconstrained general knowledge. For reference, see this working list of constrained and unconstrained skills. Like everything on this Substack, this post is a work-in-progress. I will make updates as needed. A list of the skills included in these charts is included at the end. Questions, comments, and suggestions are welcome.
Last updated: March 15, 2025
Three big ideas
There are small early gaps in constrained reading and math skills between boys and girls. Girls have slightly higher proficiency in reading. Boys have slightly higher proficiency in math. These gaps close by the end of middle school if not sooner.
Girls have a small advantage over boys in unconstrained reading skills through middle school. Boys have a small(er) advantage over girls in unconstrained math skills, though it’s possible this may have narrowed in recent years.
This does not apply to all unconstrained skills. Girls appear to start school with higher levels of working memory and cognitive flexibility. But these differences in nonacademic (executive) skills appear to close in elementary school. And there are no significant differences between boys and girls in general knowledge at least in early elementary school.
About these data
The data in these charts come from three sources: the Early Childhood Longitudinal Study, Kindergarten Class of 1998-99 (ECLS-K), Early Childhood Longitudinal Study, Kindergarten Class of 2010-11 (ECLS-K:2011), and the National Assessment of Educational Progress Long-Term Trend Assessment (NAEP LTT). I've provided an overview of these and other datasets I used to analyze constrained and unconstrained skills. The ECLS-K data were collected between Fall 1998 and Spring 2007. It’s the best dataset I’ve found to dig deep into discrete K-8 reading and math skills. It’s also unique in its inclusion of data about general knowledge. The ECLS-K:2011 data were collected between Fall 2010 and Spring 2016. It’s the best dataset I’ve found to dig deep into executive function skills. I used the EdSurvey R package to analyze the ECLS-K and ECLS-K:2011 data. The NAEP LTT data were collected in 2020 prior to school closures due to the pandemic. I used the NAEP Data Explorer to analyze the NAEP LTT data.
Boys, girls, and skills
In recent years, some have raised concerns about the academic progress of boys relative to girls. Girls appear to be thriving. Boys on multiple measures—school readiness, GPA, advanced placement classes in high school—are reported to be behind girls. In this post, I examine constrained and unconstrained skills for boys and girls across four sets of skills: reading skills, math skills, nonacademic skills, and general knowledge. An important caveat is that my best information for skill proficiency of boys and girls is limited to elementary school and middle school. I’ve not yet found a source of differentiable data for both math and reading skills to provide a good picture for high school.
Skill is the capacity to act in an organized way in a specific context (Fischer & Bidell, 2006). Knowledge is the ability to use facts, principles, and ideas to decide and do complex tasks (Cantor et al., 2021). Knowledge is an essential part of skill building. The core difference between constrained and unconstrained skills is opportunity. Most kids appear to reach high levels of proficiency in constrained skills by the end of middle school (if not sooner). There are greater differences in mastery of unconstrained skills. Constrained skills involve limited amounts of information. Everyone has relatively equal access to this information. Constrained skills are relatively straightforward to teach and assess in classroom settings. Of course this requires explicit and systematic instruction and extra supports for kids with learning differences.
By contrast, unconstrained skills involve acquisition and mastery of broader amounts of information. Not everyone has equal access to the same information. Unconstrained skills are not as easily taught and assessed. But they can be taught. (And anything can be measured.) Unconstrained skills benefit from instruction, experiences, and practice inside and outside of the classroom. There are greater gaps between kids in unconstrained skills than constrained skills.
Let’s see what we find for boys and girls.
Boys, girls, and reading
Observers for years have noted that girls outperform boys on assessments of reading achievement. Some have noted that this gap also extends to writing. This concern is not limited to the United States. We first begin with constrained reading skills and then turn to unconstrained reading skills.
Constrained reading skill
The first chart shows the growth pattern for sight words. This is the highest level of constrained reading skill included in the ECLS-K study. Kids need to be able to automatically recognize in the neighborhood of 200 common words to be proficient readers (Snow & Matthews, 2016).1 In spring of kindergarten, girls have a slight 3 point advantage (17% vs 14%) over boys in sight word proficiency. By the end of third grade this gap had narrows to a single point (98% vs 99%) and completely closes by the end of elementary school.
Figure 1. Ability to recognize common words by sight.
Astute observers will note recognition of common sight words is not equivalent to decoding or reading fluency. The ECLS-K did not include a direct measure of these (constrained) reading skills. It did include, however, a measure of kids’ ability to complete the missing word in simple sentences (a cloze test). While word comprehension is an unconstrained skill, proficiency on this task provides some indication of word reading ability. Girls had a six point advantage (50% vs 44%) on reading words in context by end of first grade. However, by fifth grade this gap closed to a single percentage point (96% for boys and 97% for girls). It appears that boys and girls were on equal footing for constrained reading skills by the end of elementary school.
Unconstrained reading skill
We next shift to an unconstrained reading skill: interpreting narrative text. (Skill definition is at the end of this post.) Besides requiring proficiency in (constrained) word reading skills, a child who is proficient in interpreting narrative text engages multiple unconstrained skills at once: vocabulary, grammar, perspective taking, inference, reasoning, text structure knowledge, comprehension monitoring, and background knowledge. At the end of first grade only 3% of boys and girls are proficient in this unconstrained reading skill. But over the next 7 years, a five point advantage gradually develops for girls by the end of middle school. Girls appear to go into high school with a small advantage in unconstrained reading skills.2
Figure 2. Ability to interpret narrative text using implicit cues and making connections with problems in the text.
These data from the ECLS-K study are over 15 years old. A great deal has occurred in education and society since 2007. Do we continue to see similar patterns today? To answer this question, we turn to data from collected in 2020 just before school closures caused by the pandemic.
The NAEP Long-Term Trend Assessment assessed a nationally representative sample of about 8,700 13-year-olds in reading and math. This next chart shows proficiency for boys and girls on a set of unconstrained reading skills. The reading skills are ordered from top to bottom from most to least constrained. (Definitions for these skills are included at the end of the post.) Girls appear to have a 4 to 9 point advantage over boys for every level of unconstrained reading skill.
Figure 3. Ability to read and comprehend written text (different levels of complexity).
2020 was not an outlier. I compared average reading scale scores on the NAEP LTT for 13-year-old boys and girls over a fifteen year period: 2008, 2012, 2020, and 2023. Girls had a statistically significant advantage over boys in reading achievement at each period ranging between 8 to 10 points. A more nuanced picture suggests that boys and girls reach eventual parity in constrained skills, with the overall advantaged in reading enjoyed girls due to higher performance in less constrained reading skills.
Boys, girls, and math
Observers for years have observed that boys outperform girls on assessments of math achievement. Some have noted this outperformance is in specific areas of math. Researchers at Stanford University found outperformance in the U.S. is concentrated in specific geographies. This issue is not limited to the United States. Once again, we start with constrained skills and then move to unconstrained skills.3
Constrained math skill
This first chart compares proficiency in multiplication and division between boys and girls. Multiplication and division is the highest level constrained math skill in the ECLS-K dataset. The data cover the period from spring of kindergarten through eighth grade. As we’d expect, this skill is virtually non-existent at the end of kindergarten. The small disparity between boys and girls (2% vs 1%) while statistically significant, certainly is not substantive. From this point, proficiency grows in tandem for boys and girls through late elementary school. Boys enjoy a 1 to 3 point advantage through elementary school. By the end of middle school this small gap is erased as girls fully catch up.
Figure 4. Ability to solve simple multiplication and division problems.
Unconstrained math skill
Next, we have a prototypical unconstrained math skill: problem solving. Math problem solving involves engaging and applying math facts and procedures (constrained) as well as math concepts (unconstrained). This entails mathematical thinking: understanding a problem, developing a plan to solve the problem, executing the plan, and checking your work to ensure you got the correct answer. This is an iterative process that engages both procedural and conceptual math knowledge (Rittle-Johnson et al., 2001; Rittle-Johnson et al., 2015).
This next chart includes data from the ECLS-K, starting in spring of first grade through eighth grade. Children are asked to use their knowledge of rate and measurement to solve word problems. At the end of first grade, boys and girls are on a level playing field: neither has any proficiency in this unconstrained math skill. A year later, however, boys have a five point advantage over girls (16% vs 11%). This small advantage persists through the end of eighth grade. Skill is context specific (Fischer & Biddell, 2006). The advantage girls have in unconstrained reading skills and constrained math skills does not add up enough to close the gap in math word problem solving.
Figure 5. Ability to solve math word problems involving rate and measurement.
These data are from 15-25 years in the past. Much has occurred in American education, including efforts to support girls in STEM fields. For a more recent perspective, we turn again to the NAEP Long-Term Trend Assessment. The data in this next chart are for 13-year-olds in 2020 just before the pandemic closed schools across the country. The chart shows proficiency for boys and girls on a set of unconstrained math skills. The skills are ordered top to bottom from most to least constrained.
Although we can’t directly compare these data to the ECLS-K assessment, girls in 2020 appear to have caught up to some degree in math skills. There is parity between boys and girls for the first two levels of math skills. Boys have a five point advantage for the least constrained math skill — moderately complex math procedures and reasoning. (Skill definitions are included at the end of this post.)
Figure 6. Understanding of numerical operations and solve math problems (different levels of complexity).
I compared average math scale scores on the NAEP LTT for 13-year-old boys and girls over a fifteen year period: 2008, 2012, 2020, and 2023. Boys had a statistically significant advantage over girls in math achievement at each period except for 2012 in which they were statistically tied. Statistically significant differences in scale scores for the three other periods ranged from 3 to 7 points. (This is smaller than the 8 to 10 point difference for girls in reading.) A more nuanced picture suggests that boys and girls reach eventual parity in constrained math skills, with the overall advantage in math enjoyed by boys due to higher performance in less constrained math skills.
Boys, girls, and nonacademic skills
So far, we’ve seen parity between boys and girls on constrained reading and math skills by late elementary and/or middle school. Girls have a small advantage in unconstrained reading skills. Boys have a smaller advantage in unconstrained math skills. However, unconstrained skills are not limited to reading and math. Nonacademic skills — also known as executive skills — play an important role in supporting goal-oriented behavior (Stafford-Brizard, 2016).
Executive skills — working memory, attention control, attention shifting, and inhibition control — support all goal-oriented human activity. Research studies demonstrate these skills also directly and indirectly support reading and math achievement (Cragg et al., 2017; Cartwright, 2023). To compare boys and girls on nonacademic skills, we turn to a third dataset: the Early Childhood Longitudinal Study, Kindergarten Class of 2011. The ECLS-K:2011 followed a nationally representative sample of roughly 18,000 kids from kindergarten through fifth grade (Fall 2010 through Spring 2016). In this post, we examine two nonacademic skills — working memory and cognitive flexibility (attention shifting).
Working memory
Working memory is the ability to hold and process information in our minds while performing complex tasks (Dawson and Guare, 2018). There are two types of working memory – visual and verbal. Working memory helps us to do a wide range of daily tasks. The environments in which children grow up – positive and negative – can significantly shape the development of their working memory. Working memory has been shown to have an indirect effect on reading and math achievement (Cragg et al., 2017; Kim, 2020).
This next chart shows the percentage of boys and girls with average or higher scores for working memory from kindergarten through fifth grade.4 There is a four point gap (54% to 58%) in working memory between boys and girls at the start of elementary school. By second grade this small gap is erased. Apparent differences at second and fifth grade are not statistically significant (they fall within the margin of error.)5
Figure 7. Verbal working memory capacity.
Cognitive flexibility (Attention shifting )
Cognitive flexibility is the ability to consider multiple pieces of information or ideas at one time and switch between them while engaging in a task (Cartwright, 2023). This ability helps us to adjust our plans or actions in the face of obstacles or changing conditions (Dawson and Guare, 2018). Cognitive flexibility is developed through consistent practice in everyday routines and experiences. Differences in children’s environments and experiences affect their ability to adjust their thought patterns, look at issues from alternative perspectives, and learn to adapt to change. In reading, cognitive flexibility is thought to help, for example, in actively shifting our attention back and forth between sounds and meanings of printed words (Duke and Cartwright, 2021; Cartwright, 2023). Cognitive flexibility can also help students evaluate different strategies and approaches for solving math problems.
This next chart shows the percentage of boys and girls with passing scores for cognitive flexibility from kindergarten through fifth grade.6 Similar to working memory, there is a small 3 point gap in the fall of kindergarten between boys and girls. This gap widens to six points in favor of the girls by second grade. However, this gap closes by the end of elementary school. The one point difference in fifth grade is not statistically significant (it falls within the margin of error.)7
Figure 8. Capacity to shift attention (cognitive flexibility).
Boys, girls, and general knowledge
Knowledge is the ability to use facts, principles, and ideas to decide and do complex tasks (Cantor et al., 2021). Sometimes knowledge itself is referred to as a skill in the context of reading or mathematics (e.g. background or content knowledge). Indeed, the ability to access and use facts, principles, and ideas to engage in goal-oriented behavior is an important part of skill development. Children’s knowledge about the world around them is an essential part of skill building.
The ECLS-K study included an assessment of K-1 children’s general knowledge of basic natural science and social studies concepts. These are topics that were not formally included in typical kindergarten and first grade curricula in the late 1990s. In fact, researchers expected children’s knowledge in these areas to stem from “his or her family background, home educational environment, and preschool experiences” (Rock & Pollack, 2002).8
Unlike reading and math skills, it isn’t possible to assign proficiency levels to children’s general knowledge (Rock & Pollack, 2002). ECLS-K researchers instead constructed a scale score based upon a two-stage assessment process. Children received a first-stage assessment that consisted of 12 questions. If they got 7 or more questions correct, they were routed to the higher-level assessment at the second stage. Otherwise, they received the lower-level form.
To make it easier to interpret the results, in this next chart I show the average number of questions answered correctly by boys and girls on the first-stage assessment. The chart shows results at three points in time: fall kindergarten, spring kindergarten, and spring first grade. There is rough parity between boys and girls in fall of kindergarten (4.9 for boys and 4.7 for girls). The general knowledge of boys and girls and boys grow in tandem through the end of first grade. Although the minute one-tenth difference in favor of boys is statistically significant, substantively boys and girls are equivalent.9
Figure 9. General knowledge about natural science and social studies concepts.
Summing up
We reviewed data for boys and girls across four sets of skills. “Gaps” and “advantages” should be understood to refer to average group differences in proficiency or ability. These terms do not refer to individual children:
Reading skills. Despite early gaps in constrained reading skills in favor of girls, there is parity between boys and girls by middle school (if not sooner). For unconstrained skills, however, girls appear to hold a consistent small advantage. Depending upon the specific reading skill, this appears to be a 5 to 9 point advantage at least through middle school.
Math skills. Despite early gaps in constrained math skills favor of boys, there is parity between boys and girls by middle school (if not sooner). For unconstrained math skills, data from roughly 15 years ago suggest boys have a small advantage. But more recent data suggests this gap might have narrowed.
Nonacademic skills. Girls appear to start school with a small advantage in working memory at the start of school. But this gap between boys and girls appears to close quickly in early elementary school. (This is a distinctly different pattern than what we see for kids from different socioeconomic groups.) For cognitive flexibility (attention shifting), girls seem to have a small advantage at the start of school that widens temporarily. But by the end of elementary school this gap is completely closed as well. (Again, this is a different pattern than what we see across socioeconomic groups.)
General knowledge. Substantively, there is no major difference between girls and boys in general knowledge across the first two years of school. This is important to know as general knowledge is moderately correlated with K-1 reading and math achievement. Unfortunately, the ECLS-K dataset did not continue to assess general knowledge after first grade.
Constrained and unconstrained skills are constantly interacting with each other as children develop reading and math skills. Nonacademic skills and general knowledge support the development of these skills — as well as other higher order and more abstract skills. There appear to be temporary differences between boys and girls in constrained skills and unconstrained nonacademic skills. It appears that longer-lived differences between boys and girls in unconstrained reading and math skills drive overall differences in reading and math achievement.
But wait, there’s more
If you’d like to see more data about constrained and unconstrained skills, check out these other posts on Unconstrained Kids:
Skill definitions
ECLS-K Reading and Math Skills
The ECLS-K assessed elementary and middle school students on a range of constrained and unconstrained reading and math skills. The skills were considered hierarchical, i.e. one has to master the lower levels in the sequence before one could learn the material at the next higher level. The skills included in the charts in this post:
Sight words. Recognizing common words by sight. This is a constrained reading skill.
Interpreting beyond text. Evaluation – demonstrating understanding of author’s craft (how does the author let you know...), and making connections between a problem in the narrative and similar life problems. This is an unconstrained reading skill.
Multiplication and division. Solving simple multiplication and division problems and recognizing more complex number patterns. This is a constrained math skill.
Rate and measurement. Using knowledge of measurement and rate to solve word problems. This is an unconstrained math skill.
NAEP Long-Term Assessment Reading and Math Skills
The NAEP LTT has five performance levels each for reading and math that involve a mix of constrained and unconstrained skills. Each skill level involves successively greater degrees of unconstrained skills. The skill included in the charts in this post:
Partially developed skills and understanding. Readers at this level can locate and identify facts from simple informational paragraphs, stories, and news articles. In addition, they can combine ideas and make inferences based on short, uncomplicated passages. Performance at this level suggests the ability to understand specific or sequentially related information. This is a set of unconstrained reading skills.
Interrelate ideas and make generalizations. Readers at this level use intermediate skills and strategies to search for, locate, and organize the information they find in relatively lengthy passages and can recognize paraphrases of what they have read. They can also make inferences and reach generalizations about main ideas and the author's purpose from passages dealing with literature, science, and social studies. Performance at this level suggests the ability to search for specific information, interrelate ideas, and make generalizations. This is a set of unconstrained reading skills.
Understand complicated information. Readers at this level can understand complicated literary and informational passages, including material about topics they study at school. They can also analyze and integrate less familiar material about topics they study at school as well as provide reactions to and explanations of the text as a whole. Performance at this level suggests the ability to find, understand, summarize, and explain relatively complicated information. This is a set of unconstrained reading skills.
Beginning skills and understandings. Students at this level have considerable understanding of two-digit numbers. They can add two-digit numbers but are still developing an ability to regroup in subtraction. They know some basic multiplication and division facts, recognize relations among coins, can read information from charts and graphs, and use simple measurement instruments. They are developing some reasoning skills. This is a mix of constrained and unconstrained math skills.
Numerical operations and beginning problem solving. Students at this level have an initial understanding of the four basic operations. They are able to apply whole number addition and subtraction skills to one-step word problems and money situations. In multiplication, they can find the product of a two-digit and a one-digit number. They can also compare information from graphs and charts, and are developing an ability to analyze simple logical relations. This is a mix of constrained and constrained math skills.
Moderately complex procedures and reasoning. Students at this level are developing an understanding of number systems. They can compute with decimals, simple fractions, and commonly encountered percents. They can identify geometric figures, measure lengths and angles, and calculate areas of rectangles. These students are also able to interpret simple inequalities, evaluate formulas, and solve simple linear equations. They can find averages, make decisions based on information drawn from graphs, and use logical reasoning to solve problems. They are developing the skills to operate with signed numbers, exponents, and square roots. This is a set of unconstrained math skills.
Works Cited
Cantor, P., Osher, D., Berg, J., Steyer, L., & Rose, T. (2021). Malleability, plasticity, and individuality: How children learn and develop in context. In P. Cantor & D. Osher (Eds.), The science of learning and development: Enhancing the lives of all young people (pp. 3-54). New York: Routledge.
Cartwright, K. B. (2023). Executive skills and reading comprehension: A guide for educators. New York: The Guilford Press.
Cragg, L., Keeble, S., Richardson, S., Roome, H. E., & Gilmore, C. (2017). Direct and indirect influences of executive functions on mathematics achievement. Cognition, 162, 12-26.
Dawson, P., & Guare, R. (2018). Executive skills in children and adolescents: A practical guide to assessment and intervention. New York: The Guilford Press.
Duke, N. K., & Cartwright, K. B. (2021). The science of reading progresses: Communicating advances beyond the simple view of reading. Reading Research Quarterly, 56, S25-S44.
Fischer, K. W., & Bidell, T. R. (2006). Dynamic development of action and thought. In R. M. Lerner & W. Damon (Eds.), Handbook of child psychology: Theoretical models of human development (6th ed., pp. 313–399). New York: John Wiley & Sons, Inc.
Kim, Y. S. G. (2020). Hierarchical and dynamic relations of language and cognitive skills to reading comprehension: Testing the direct and indirect effects model of reading (DIER). Journal of Educational Psychology, 112(4), 667.
Najarian, M., Tourangeau, K., Nord, C., & Wallner-Allen, K. (2018). Early Childhood Longitudinal Study, Kindergarten Class of 2010–11 (ECLS-K: 2011), first-and second-grade psychometric report (NCES 2018-183). National Center for Education Statistics, Institute of Education Sciences, US Department of Education.
Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27, 587-597.
Rittle-Johnson, B., Siegler, R. S., & Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology, 93(2), 346-362.
Slotkin, J., Kallen, M., Griffith, J., Magasi, S., Salsman, J., & Nowinski, C. (2012). NIH toolbox. Technical Manual.
Snow, C. E., & Matthews, T. J. (2016). Reading and language in the early grades. The Future of Children, 57-74.
Stafford-Brizard, K. B. (2016). Nonacademic skills are the necessary foundation for learning. Education Week. Retrieved from http://www.edweek.org/ew/articles/2016/07/21/nonacademic- skills-are-the-necessary-foundation-for.html.
I’m generally in the Linnea Ehri camp on sight words: any word that a child can decode or recognize automatically is a “sight word.” In this case, however, the ECLS-K explicitly assessed kids’ ability to recognize common sight words — not their decoding skills.
ECLS-K researchers used a statistical method called “differential item functioning” to determine there was no bias in the K-8 reading assessments by gender.
The ECLS-K researchers also did not find gender bias for the K-8 math assessments.
Working Memory was assessed using the Numbers Reversed task from the Woodcock-Johnson III Tests of Cognitive Abilities. I followed guidance to compute the percentage of kids who received average or higher scores (25th percentile and higher) in kindergarten, second grade, and fifth grade (Najarian, et al., 2018).
Technically, it’s “confidence intervals” for estimates of the percentages of girls and boys with average or higher working memory scores. A confidence interval is a range of values on either side of this estimate that is likely to include the true population parameter. The margin of error represents just half of that range, essentially the "plus or minus" value around a point estimate within a confidence interval. We say there is no statistically significant difference if the confidence intervals overlap. If this footnote reads like ancient Greek, then stick with “they fall within the margin of error.” It’s close enough.
Cognitive flexibility was assessed using the Dimensional Change Card Sort Test (DCCS) task. The paper-based version was used in Grades K-1 and the computer-based version in Grades 2-5. I followed guidance on both versions of the DCCS to compute minimum passing scores across K-5 (Slotkin et al., 2012; Najarian, et al. 2018).
See footnote #2.
The K-1 general knowledge test was evaluated and found to be free from bias by gender (Rock & Pollack, 2002). In third, fifth, and eighth grades, a science assessment replaced the general knowledge assessment.
I found similar results when comparing boys and girls using the general knowledge scale score (range: 0-51). Boys have statistically significant higher scores at fall kindergarten (22.5 vs 22.1), spring kindergarten (27.4 vs 26.8), and spring first grade (34.5 vs 33.9).