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Math Problematic for U.S. Teens

More girls than boys find math, science toughest classes

It’s no myth that American students trail students from Asian countries in mathematics. Although U.S. eighth-graders scored above the international average in the 2003 Trends in International Mathematics and Science Study (TIMSS), students in Singapore, Hong Kong, Chinese Taipei, Korea, and Japan outperformed their American peers, just as they did in previous surveys. Students in four European countries — Belgium, Estonia, Hungary, and the Netherlands — also outpaced U.S. students.

According to the study, only 23% of U.S. eighth-graders reach the high international benchmark, meaning they can «solve multistep word problems involving addition, multiplication, and division» and «use their understanding of place value and simple fractions to solve problems.»

Given that more than three-quarters of U.S. students could not meet this threshold, it’s not surprising that, according to the latest Gallup Youth Survey*, more teenagers name math than any other subject as the course they find most difficult in school. Twenty-nine percent name math generally, 6% specifically mention algebra, and 2% name geometry.

About equal numbers of teens mention the sciences and English as the most difficult subject: 20% and 18%, respectively. Foreign languages, history, and social studies are each mentioned by less than 10% of the sample.

In 2004, Gallup asked teens to name their favorite subject, and math ranked at the top — although by a much smaller margin (23%) than the percentage of teens who say math is their most difficult subject (37%)**. More students also identify English as an area they lag in rather than an area they enjoy (18% vs. 13%), and there is gap for science (20% say it is the most difficult subject, while 12% say it is their favorite).

Gender Patterns in Academic Achievement

American students’ math results on the 2003 TIMSS showed significant differences in boys’ and girls’ performance, with boys somewhat outperforming girls. Gallup data show a large gap in the percentage of male teens and female teens saying math is their most difficult subject: 44% of girls vs. 31% of boys. Boys also appear to be more comfortable with science: only 15% of boys vs. 23% of girls name one of the sciences as their toughest subject. The reverse is true when it comes to English: 25% of boys vs. 10% of girls say English is their worst subject.

However, when boys and girls were asked in 2004 to name their favorite subjects, similar percentages of girls and boys named math as their favorite subject, and similar percentages said science was their favorite. More girls than boys named English/literature as their favorite subject.

A Different Perspective

While American students may lag behind students in Asia and elsewhere in high mathematical achievement, a majority, 64% met the standards for intermediate mathematical understanding:

Students can apply basic mathematical knowledge in straightforward situations. They can read, interpret, and use different representations of numbers. They can perform operations with three and four-digit numbers and decimals. They can extend simple patterns. They are familiar with a range of two-dimensional shapes and read and interpret different representations of the same data.

And although the 64% significantly trails the percentage proficient in basic math in Asia and parts of Europe, it may be sufficient for the American workforce. When Gallup asked U.S. adult workers in 2003 to rate the relevance of various subject areas to their work, 56% said basic math was critical or very important to the work they do***. Only 23% said the same of advanced mathematics.

Bottom Line

There is no question American students could and should be doing better than they are in math. In what New York Times columnist Thomas Friedman describes as a «flat world,» American students are going to find themselves competing in a global workforce, where the outsourcing of formerly U.S.-based technical jobs will be seamless because of the Internet and other computer technologies. According to Friedman, this exportation already is seamless.

What should not get lost in the scramble to improve U.S. mathematical competency is that «right brain» skills — creative thinking and problem solving — as well as interpersonal skills, are rated most important to job success by American workers. More than four in five workers told Gallup in 2003 that these are highly important factors in doing their jobs well. Is it possible that in the new «flat» economy, Americans will have just enough mathematical competency to get by, but will continue to thrive based on a superior ability to invent, synthesize, organize, get along with people, and manage others?

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*These results are based on telephone interviews with a randomly selected national sample of 1,028 teenagers in the Gallup Poll Panel of households, aged 13 to 17, conducted Jan. 17 to Feb. 6, 2005. For results based on this sample, one can say with 95% confidence that the maximum error attributable to sampling and other random effects is ±3 percentage points. In addition to sampling error, question wording and practical difficulties in conducting surveys can introduce error or bias into the findings of public opinion polls.

**The Gallup Youth Survey is conducted via an Internet methodology provided by Knowledge Networks, using an online research panel that is designed to be representative of the entire U.S. population. The current questionnaire was completed by 785 respondents, aged 13 to 17, between Jan. 22 and March 9, 2004. For results based on the total sample, one can say with 95% confidence that the maximum margin of sampling error is ±4 percentage points.

***Results are based on telephone interviews with 588 adults employed full or part time, aged 18 and older, conducted Aug. 4-6, 2003. For results based on the total sample of national adults, one can say with 95% confidence that the margin of sampling error is ±4 percentage points.

Brain study reveals how much of math ability is genetic

A bad relationship with math can start early, and anxiety or a lack of confidence around numbers can compound over time — transforming from a grade school phobia to a career hurdle.

But some math ability may not be shaped in the classroom. According to new research, some percentage of math ability might have deeper, biological roots.

Scientists in Germany argue that about one-fifth of math ability can be traced back to grey matter volume in the brain, influence by a gene, called ROBO1.

This gene is linked to the development of grey matter volume in the right parietal cortex, a region of the brain that’s involved in number representation. Patterns in grey matter volume were, in turn, positively associated with math test scores when children involved in the study reached second grade, their ages ranged from 7 to 9-years-old.

When the scientists initially measured the grey matter in the children’s brains they were between the ages of 3 and 6-years-old and had not been formally trained in math. Because different variants of the ROBO1 gene influence grey matter volume, the authors propose that may have laid the groundwork for their math performance. They reasoned it was genetic variability’s effect on grey matter that influenced whether or not a child was more skilled.

The paper was published Thursday in PLOS Biology.

Melissa Libertus is an associate professor at the University of Pittsburgh who studies learning and development. She says that the study is “compelling” and does appear to prove that there’s a chain of influence stretching from ROBO1 to math ability.

However, it’s not undeniable proof that one-fifth of differences in math abilities are definitely genetic.

“It is possible that we only see the associations between genes, brain volume, and math ability in the present study because the children tested here grew up in an environment that exposed them to mathematical concepts from a very young age,” she says.

The authors argue that a gene involved with grey matter volume may explain about 20 percent of differences in math ability.

Hill Street Studios/ Getty Images

Are math skills genetic?

The study authors suggest that genetic influences, like ROBO1, actually “sculpt” the way the brain perceives numbers. Still, Libertus cautions it’s not just genes doing the sculpting.

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Math instruction, even informally during early childhood, may prove to be the more important launching pad into a better understanding of math concepts.

Libertus adds that variations in pre-school children’s math abilities are influenced by how often parents or teachers talk about numbers or how often they engage in math-based activities like “playing board games that require counting, talking about money while shopping, or measuring and counting while cooking.»

Those informal conversations about math could be at play in this study too.

This study was conducted in two samples of children: a 77-person “exploration sample” and a 101-person replication study. In both samples, the scientists collected grey matter measurements between 3 and 6-years-old (before math instruction) and then examined math test results when the children reached second grade.

Those two data collection periods are two snapshots in time. We don’t know what happened in the crucial period of early childhood between those two snapshots. Even if it’s not traditional math instruction, early childhood exposure to math concepts plays a big role in math performance later on.

Quantifying what happened between these two snapshots is outside the scope of this paper. But Libertus says it is “highly likely” that exposure to math at home and in other out of school settings may have been a factor, suggesting that genetics are part of a bigger puzzle.

Inheriting math ability – Scientists have long tried to tease apart how much of math ability is nature and how much is nurture.

On the genetic side, Libertus says that there is evidence that genetics may influence math ability. Genetic conditions like Williams syndrome, Fragile X syndrome, or Turner syndrome “are associated with poor math abilities,” she says.

«This leaves more than 80% of the variance in children’s math abilities unexplained

She also points to dyscalculia, a math learning disability where children struggle to develop a basic sense of numbers. A 2001 study on 39 children with dyscalculia found that 66 percent of mothers, 40 percent of fathers, 53 percent of siblings, and 44 percent of second-degree relatives also had the condition.

There’s also evidence that intuitive “number sense” runs in families. In a 2017 study, Libertus found that parent’s scores on math tests could predict how well their children did on math exams in early childhood. But again, families also tend to share environments, so it’s not slam-dunk proof of the mathematical ability genetics.

As compelling as these studies are, the big picture is still unchanged. Math ability may have some genetic ties, it probably only explains a small fraction of that ability. Even in the current study, genes only explained 20 percent of math ability on its own.

“This leaves more than 80% of the variance in children’s math abilities unexplained,” Libertus says.

Abstract: Mathematical ability is heritable and related to several genes expressing proteins in the brain. It is unknown, however, which intermediate neural phenotypes could explain how these genes relate to mathematical ability. Here, we examined genetic effects on cerebral cortical volume of 3–6-year-old children without mathematical training to predict mathematical ability in school at 7–9 years of age. To this end, we followed an exploration sample (n = 101) and an independent replication sample (n = 77). We found that ROBO1, a gene known to regulate prenatal growth of cerebral cortical layers, is associated with the volume of the right parietal cortex, a key region for quantity representation. Individual volume differences in this region predicted up to a fifth of the behavioral variance in mathematical ability. Our findings indicate that a fundamental genetic component of the quantity processing system is rooted in the early development of the parietal cortex.

Demystifying Math 55

Illustration of a boy leaning against a blackboard and a girl writing Math 55 on it with chalk.

Few undergraduate level classes have the distinction of nation-wide recognition that Harvard University’s Math 55 has. Officially comprised of Mathematics 55A “Studies in Algebra and Group Theory” and Mathematics 55B “Studies in Real and Complex Analysis,” it is technically an introductory level course. It is also a veritable legend among high schoolers and college students alike, renowned as — allegedly — the hardest undergraduate math class in the country. It has been mentioned in books and articles, has its own Wikipedia page, and has been the subject of countless social media posts and videos.

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Most recently, Harvard junior Mahad Khan created a TikTok video dedicated to Math 55 that has received over 360,000 views to date. His is only one of many — his older brother created one, too — but it has the distinction of an insider’s perspective. “I thought it would be interesting if I cleared up the misconceptions about Math 55,” Khan said. While he hadn’t taken the course himself, he wanted to go beyond its reputation. “I wanted to get a real perspective by interviewing a former student and current course assistant.”

Over the years, perception of Math 55 has become based less on the reality of the course itself and more on a cumulative collection of lore and somewhat sensationalist rumors. It’s tempting to get swept up in the thrill of hearsay but while there might be kernels of truth to some of the stories, many of them are outdated and taken out of context. At the end of the day, however, Math 55 is a class like any other. Below, we take a stab at busting some of the more well known and persistent myths about the class. Or, at the very least, offering an extra layer of clarity.

Myth #1: Math 55 is only for high school math geniuses

Most articles or mentions of Math 55 refer to it as filled with math competition champions and genius-level wunderkinds. The class is supposedly legendary among high school math prodigies, who hear terrifying stories about it in their computer camps and at the International Math Olympiad. There are even rumors of a special test students have to take before they are even allowed into Math 55. But while familiarity with proof-based mathematics is considered a plus for those interested in the course, there is no prerequisite for competition or research experience.

In fact students whose only exposure to advanced math has been through olympiads and summer research programs can have a harder time adjusting. Their approach to the material tends to be understandably more solitary and that can be a disadvantage for the level of collaboration higher level mathematics require. “It has become a lot more open to people with different backgrounds,” said Professor Denis Auroux, who teaches Math 55,. “Our slogan is, if you’re reasonably good at math, you love it, and you have lots of time to devote to it, then Math 55 is completely fine for you.”

Also, there is no extra test to get into the class.

Myth #2: Just take a graduate class, instead

Math 55 is hard. Whether you’re just 55-curious, or a past or present student in the class, this is something everyone agrees on. The course condenses four years of math into two semesters, after all. “For the first semester, you work on linear and abstract algebra with a bit of representation theory,” said sophomore math concentrator Dora Woodruff. “The second semester is real and complex analysis, and a little bit of algebraic topology. That’s almost the whole undergraduate curriculum.” Woodruff — incidentally, the student Khan interviewed — took Math 55 as a freshman and returned her second year as a course assistant. She is intimately familiar with the course’s difficulty level.

So why not just take an upper level undergraduate course to begin with or even one at a graduate level, if you’re really looking for a challenge? What justifies the existence of a class with the difficulty level of Math 55? One argument is that the course helps structure and systemize the knowledge with which many students come to Harvard. It gives them a firm background in preparation for the rest of their math education. Math 55 is difficult and it is purposefully structured that way as it’s meant to help students mature as mathematicians rather than as simple course takers.

But more importantly, “it’s just not true that Math 55 is at the level of a graduate class,” Auroux said. “It goes through several upper division undergraduate math classes with maybe a bit more advanced digressions into material here and there, but it sticks very close to what is taught in 100-level classes. The difference is we go through it at a faster pace, maybe with more challenging homework, and ideally as a community of people bringing our heads together.”

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A core goal of Math 55, according to Auroux, is to build a sense of community. Other schools might encourage advanced first-year students to take upper level undergraduate or even graduate classes, but Math 55 helps build a cohort of like-minded people who really like math, are good at it, and want to do a lot of it during their time at Harvard. That’s the experience Woodruff had, as well. “The community can be very strong,” she said. “You meet a lot of other people very interested in math and stay friends with them for the rest of college.”

Myth #3: Homework takes between 24 and 60 hours

Horror stories of endless homework are synonymous with the class. You’ll read or hear about “24 to 60 hours per week on homework” in almost every reference to Math 55. But one, there is a world of difference between 24 and 60 hours that is never explained, and two, this timeframe is quite misaligned with reality.

Auroux frequently sends out surveys to his students asking how long homework takes them and the average for most is closer to 15 hours a week. Those with more extensive prior math backgrounds can take as little as five to ten hours. The key factor is collaboration. “This class doesn’t lend itself to self-study,” Auroux stressed. Once they have thought about each problem set on their own, students are welcome and encouraged to talk to their friends and collaborate. “As soon as I see that something took over 30 hours I ask the student, do you know you’re supposed to be working with people and come ask me questions when you’re stuck?”

It is true that between reviewing lectures, digesting the material, and solving the problem sets, students usually end up devoting between 20 and 30 hours a week to the class. However, that includes the time dedicated to homework. So while students are discouraged from taking too many difficult classes and extracurriculars in the same semester as Math 55, they are also not expected to spend the time equivalent to a full-time job on their problem sets every week.

Myth #4: less than half of the class makes it to the second semester

Math 55 is just as infamous for its attrition rate as it is for its difficulty. Most sources like to cite the 1970 class, which began with 75 students and — between the advanced nature of the material and the time-constraints under which students had to work — ended with barely 20. Since then, the rumor has been that the Math 55 class shrinks by half its original size or more before the first semester is over. The reality is much less shocking and a bit more complicated.

Enrollment in this past fall semester’s Math 55A peaked at (ironically) 55 students. Well into the spring semester’s Math 55B, 47 students were still enrolled in the course. “On average, a drop of about 10-15 percent is much closer to what I would expect,” Auroux said. And those numbers become even more flexible if one takes into consideration the weeks math students have at the beginning of each semester to try out different classes and “shop” around before they have to commit to anything. This means students find their way in and out of Math 55 in a variety of ways over the course of the academic year.

According to Auroux, some students shop Math 55 in the fall and switch to the less intense Math 25 for the remainder of the semester. Others start out in Math 25 and, if not sufficiently challenged, switch to Math 55. Even people who end up in academia are not exempt from this. During his time as a student, our own Department of Mathematics’ Professor Emeritus Benedict Gross switched to the lower level Math 21 after two weeks in Math 55. In fact, those two weeks almost made him reconsider his desire to pursue mathematics. “By the beginning of sophomore year, I had decided to major in physics,” he recalled. “But during shopping period that fall, I walked past a math class taught by Andrew Gleason and stopped in to listen. It turned out to be Math 55.” He enrolled and by the end of the semester had found his vocation in mathematics.

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All this means that Auroux sees student numbers vacillate up and down throughout the academic year. “There are about four or five students in this spring semester’s Math 55 that took Math 25 or even Math 22 in the fall, and they’re doing mostly fine,” he said. “It’s a lot of work, but I think they’re having a great time.”

Myth #5: 55-er culture is cult-y and exclusionary

Even though her experience with Math 55 was a positive one, Woodruff is very aware of the unhealthy culture the class has been rumored to cultivate. It’s easy for students to form exclusionary cliques that consist only of other Math 55 students, and some look down on anyone taking lower level math classes. But Woodruff also stressed that the instructors are very aware of this and actively take steps to curb that kind of toxic behavior. She said Auroux frequently brings up the importance of keeping the Math 55 community inclusive through Slack messages and lecture references.

Some students come to Harvard just for the opportunity to take Math 55. Some view enrolling in the class as proof of their mathematical gumption and competence. A Harvard Independent article called Math 55 the “premiere mathematical challenge for overachieving and…ridiculously mathy freshmen” and a piece in The Harvard Crimson referred to it as “a bit of a status thing as far as math majors here are concerned.” Over the years, the Harvard Department of Mathematics has taken steps to correct these assumptions.

For one thing, neither the Math 55A nor the Math 55B official course descriptions boast the dubious honor of referring to it as “probably the most difficult undergraduate math class in the country” (don’t trust everything you read on Wikipedia). For another, “we’re trying to emphasize that there’s no magic to Math 55,” Auroux said. “It contains the same material as some of the other classes we have. People who take it are not intrinsically better or smarter than the ones who don’t.”

Myth #6: You have to take Math 55 if you’re serious about going into academia

One reason math concentrators could feel pressured to enroll in Math 55 is because they view it as a prerequisite for a career in academia. It’s a sort of badge of honor and proof of their commitment to the field of mathematics. It is true that quite a few graduates of the course have gone on to pursue a career in mathematics. Woodruff herself believes that will be the most likely path for her, and several faculty members in our own Department of Mathematics took Math 55 during their days as Harvard freshmen.

“Several times in my research career when I understood something fundamental, I would realize that this was what Math 55 was trying to teach us,” Gross said. “It was an amazing introduction to the whole of mathematics and it was transformative for me.” In fact, Gross met Higgins Professor of Mathematics Joe Harris when they took the class together, forging a lifelong friendship. When they returned to Harvard as faculty, they took turns teaching Math 25 and Math 55.

However, Auroux is quick to point out that while many graduates of the course do end up in academia, most professional mathematicians have likely never even heard of Math 55. “I would like to think that it’s a success story if people end up doing math, because the goal of Math 55 is to show students how beautiful math can be,” he said. “If they love it enough to go to grad school and become mathematicians, that’s wonderful. And if they want to take that math knowledge and do something else with their life, that’s just as wonderful.”

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