First Daughter Ivanka Trump and Education Secretary Betsy DeVos toured the National Air and Space Museum with a group of middle school students Tuesday, encouraging girls to pursue careers in science, technology, engineering and mathematics — even while President Donald Trump’s administration put forth a budget proposal that suggests cutting funding for education and research. There is nothing more important than advancing the STEM fields — and those groups who are underrepresented within them.
One area in desperate need of examination is the way we teach mathematics. Many Americans suffer from misconceptions about math. They think people are either born with a “math brain” or not — an idea that has been disproven — and that mathematics is all numbers, procedures and speedy thinking. In reality, mathematicians spend most of their working lives thinking slowly and deeply, investigating complex patterns in multiple dimensions. We sacrifice many people — women and students of color, in particular — at the altar of these myths about math.
Math is a prerequisite for most STEM fields, and the reason many students abandon STEM careers. In higher levels of mathematics, gender imbalances persist: In 2015, about 76% of math doctorates were awarded to men. This figure should prompt alarm in mathematics departments across the country — and encourage focus on an area that is shockingly neglected in discussions of equity: teaching methods in classrooms.
At Stanford University, I teach some of the country’s highest achievers. But when they enter fast-paced lecture halls, even those who were successful in high school mathematics start to think they’re not good enough. One of my undergraduates described the panic she felt when trying to keep pace with a professor: “The material felt like it was flying over my head,” she wrote. “It was like I was watching a lecture at 2x or 3x speed and there was no way to pause or replay it.” She described her fear of failure as “crippling.” This student questioned her intelligence and started to rethink whether she belonged in the field of math at all.
Research tells us that lecturers typically speak at between 100 and 125 words a minute, but students can take note of only about 20 words a minute, often leaving them feeling frustrated and defeated. “I’ve essentially given up in my math class right now,” another student of mine wrote. “In such a fast-paced environment where information is constantly coming at you, there just isn’t time to think deeply about what you are learning.”
The irony of the widespread emphasis on speed in math classrooms, with damaging timed tests given to students from an early age, is that some of the world’s most successful mathematicians describe themselves as slow thinkers. In his autobiography, Laurent Schwartz, winner of the world’s highest award in mathematics, described feeling “stupid” in school because he was a slow thinker. “I was always deeply uncertain about my own intellectual capacity; I thought I was unintelligent,” he wrote. “And it is true that I was, and still am, rather slow. I need time to seize things because I always need to understand them fully.”
When students struggle in speed-driven math classes, they often believe the problem lies within themselves, not realizing that fast-paced lecturing is a faulty teaching method. The students most likely to internalize the problem are women and students of color. This is one of the main reasons that these students choose not to go forward in mathematics and other STEM subjects, and likely why a study found that in 2011, 74% of the STEM workforce was male and 71% was white.
Women are just as capable as men of working at high speed, of course, but I’ve found in my own research that they are more likely to reject subjects that do not give access to deep understanding. The deep understanding that women seek, and are often denied, is exactly what we need to encourage in students of mathematics. I have taught many deep, slow thinkers in mathematics classes over the years. Often, but not always, they are women, and many decide they cannot succeed in mathematics. But when the message about mathematics has changed to emphasize slower, deeper processing, I’ve seen many of these women go on to excel in STEM careers.
When mathematics classes become places where students explore ideas, more often than they watch procedures being rapidly demonstrated by a teacher or professor, we will start to liberate students from feelings of inadequacy. In a recent summer camp with 81 middle school students, we taught mathematics through open, creative lessons to demonstrate how mathematics is about thinking deeply, rather than calculating quickly. After 18 lessons, the students improved their mathematics achievement on standardized tests by an average of 50%, the equivalent of 1.6 years of school. If classrooms across the country would dispel the myths about math and teach differently, we would improve the lives of many students and enable the creation of a more diverse STEM workforce. It will take a generation of young, creative, adaptable and quantitative thinkers to tackle our society’s problems — thinkers that we are currently turning away from mathematics classrooms and lecture halls in droves.
Jo Boaler is a Stanford professor, co-founder of youcubed.org and author of best-selling book, Mathematical Mindsets: Unleashing Students’ Potential through Creative Math, Inspiring Messages and Innovative Teaching.
Thirteen-year-old JoJo Siwa rolled up to school in a souped-up vintage car with a giant pink bow plastered on the grill. Inside the car, with her blond hair tightly pulled into a side ponytail and wrapped in a pastel yellow bow, she sang to her mother, “I don’t really care about what they say,” while a group of mean girls wearing not-so-pastel clothes snickered from a bench. (We know they’re mean girls because the words “mean girls” are displayed on the screen next to them.)
“Don’t let the haters get their way,” JoJo’s mother, also clad in yellow pastel, told her.
No worries. The new young teenage heroine of suburban America showed no fear. After winning a rowdy dance battle in her video “Boomerang,” which has gotten over 200 million views on YouTube, JoJo places a purple bow on the lead mean girl. Everyone becomes best friends.
Unlike the red, oversize scrunchie Heather Chandler wore in “Heathers,” which was a symbol of power and authoritarianism, the bow worn by JoJo is a symbol of confidence: believing in yourself and, more important, being nice to others.
Thirteen-year-old girls aren’t generally known for their oversize bows these days, but JoJo isn’t your typical teenager. She just signed a multiplatform deal with Nickelodeon, which includes consumer products, original programming, social media, live events and music.
Since June, JoJo’s Bows — made by H.E.R. Accessories, a licensee of JoJo’s — have been among the top sellers at Claire’s, the store popular among the middle-school set, according to Hind Palmer, Claire’s global brand marketing and public relations director.
“I can’t believe it’s a hair bow that’s doing this,” said Jennifer Roth Saad, the creative director of H.E.R. “I’ve never seen something like this.”
JoJo said in a phone interview that she had worn a side ponytail with a bow since she was 4, and she has worn it through most of her career, which includes stints on “Abby’s Ultimate Dance Competition” and “Dance Moms.” But recently, she has become well known to her 2.7 million YouTube subscribers for wearing a bow and being goofy by showing videos of her sick in bed, getting ready in the morning and playing pranks on another YouTube star.
“I’m 13, and I like being 13,” said JoJo, who divides her time between Omaha and Los Angeles. “A lot of people my age try to act 16. But just be your age. There’s always time to grow older. You can never grow younger.”
In Britain, where JoJo’s bows are even more successful than they are in the United States, the head teacher of a school in Bury banned the bows because they were distracting, while another school, in Long Eaton, permitted the bows so long as they conformed to dress code colors.
Shauna Pomerantz, a sociology professor at Brock University in Ontario and an author of “Smart Girls: Success, School and the Myth of Post-Feminism,” said school administrators had historically policed girls for wearing skirts that were too short or having exposed bra straps, not for an accessory reminiscent of the 1950s. “JoJo stands for being nice,” she said. “And the bow is a representation of JoJo. Ultimately the goal of that video is to suggest that meanness isn’t cool, and niceness is cool.”
In a world where parents of children ages 8 to 14 have long been concerned about hypersexualized clothing, early puberty and overly sophisticated media messages, JoJo is part of a growing group of girls documenting routine, age-appropriate behaviors and activities such as being nice, doing their chores, divulging what’s in their backpacks, making dresses out of garbage bags and working to pay for their own clothes.
The 12-year-old competitive gymnast Annie LeBlanc, a.k.a. Acroanna, has had a YouTube channel since she was 3. On her channel, which as been viewed a combined 174 million times, Annie documents herself making slime blindfolded and investigates what’s in her purse. But mostly she appears on her family’s channel, Bratayley, where 3.9 million subscribers follow her, her parents, her 8-year-old sister, Hayley (who also has her own channel), as well as archival footage of her brother Caleb, who died two years ago at age 13 of a heart condition. There are Bratayley sponsorship deals, Bratayley merchandise and a more recent invitation for Annie to participate in Nike’s Young Athletes program, which, naturally, was documented on Bratayley.
Many popular videos made by girls in the pre- and early teenage years live on nine connected YouTube channels. Seven Super Girls, the most successful of these channels, has over six million subscribers and its videos have been viewed a combined 6.9 billion times. Each channel — others are called Seven Cool Tweens, Seven Awesome Kids and Seven Twinkling Tweens — is run with more efficiency than some professional media sites: Each girl is responsible for making a video on a specific day of the week. (Annie was on Seven Awesome Kids from 2010 to 2011.) They follow a set of guidelines that include weekly themes, and precludes them from giving their surnames and location.
The SAKs channels, as they are known, were started in 2008 by seven families in Britain who, in the early days of YouTube, wanted to make sure their children were making family-appropriate content. The only remaining parent of that original partnership is Ian Rylett, who is currently in charge of the SAKs operation.
Mr. Rylett, who lives in Leeds, said producing the channels was essentially his full-time job. He and a team of six others take care of copyright issues, create sponsorship deals, come up with weekly themes, monitor the channels and arrange meet and greets. The tickets for a 1,000-seat event that is coming up in Orlando, Fla., are selling for $30 each.
Mr. Rylett receives an income from the channels, as do some of the girls. The girls own their own content, he said, but they have not signed contracts.
Alexis, a 12-year-old from Southern California whose parents wanted her surname withheld for privacy reasons, has made close to 200 videos for Seven Cool Tweens and Seven Awesome Kids over the past three years. Alexis wears her reddish-brown hair in a braid, no makeup and braces. Her bedroom isn’t catalog perfect. Her most popular videos revolve around silly antics like pranking family members (which received 23.2 million views), making a mess of herself and her outfit before the school dance and getting grounded for life. The appeal? “Kids want to watch kids,” Alexis said in a phone interview.
Emily (a screen name), 12, of Seven Awesome Kids is home-schooled in Southern California. Some of her most popular videos — she writes and edits them herself over two days — include walking through a mysterious forest and finding an angel potion. “She’s a little Stanley Kubrick, controlling everything,” said her father, Tim Gould.
While Alexis has received money from the SAKs channel (though she has not been involved in sponsorship deals), Emily has not received money, their parents said.
“They’re free to leave whenever they want,” Mr. Rylett said. “They can take their content with them. When they do get older, it is quite common for them to look back and say, ‘Eww.’”
The parents seemed ambivalent about the arrangement — knowing that allowing their children to have an online identity comes with risks of harassment or worse — but they don’t want to stop their daughters from dreaming of becoming a director or an editor or a writer. Or a television star.
Yet this YouTube activity, even depicting wholesome activities, is disconcerting for Emily Long, the director of communications and development at the Lamp, a media-based literary group. “It’s troublesome to me when I see this being celebrated as the herald of what our young girls should aspire to,” Ms. Long said. “That you, too, can go from being a YouTube star to having your own deal on Nickelodeon.”
She would like to see girls being recognized for more thoughtful content, she said, such as that of Marley Dias, 12, who started the #1000BlackGirlBooks campaign last year after recognizing a scarcity of black-girl protagonists.
“If I had a 13-year-old,” Ms. Long said, “I would push her toward someone like Marley Dias instead of JoJo. But Marley Dias doesn’t sell giant hair bows. Marley Dias sells social justice and social causes and writing and nerd culture. And there’s plenty to market there.”
My daughter started taking martial arts when she was five years old. I think it’s helped teach her confidence, self-discipline, and self-reliance. Life isn’t always cream puffs and unicorns. When dire circumstances warrant acute awareness, hyper-focus, and rapid response — kids trained in resilience are far more likely to endure hardship and advocate for peace with poise.
In my family, we ain’t raising no princess. We’re revolutionaries and unyielding warriors of justice. We do our research. We know where our food comes from. We’re intentional and informed with every purchase. We talk about environmental preservation, human rights and civil liberties. We look at labels and shop almost exclusively second-hand. We vehemently reject playground and corporate bullies seeking to profit on the backs of the little guy. In our house, we relentlessly root for the underdog and those doing the right thing. In our community, we show up with blood, sweat, tears, gluten-free chocolate chip banana bread, and baskets of homegrown organic veggies for those struggling to survive the day.
At our dinner table, no topic is taboo. We name the elephant in the room and promote discourse on all things controversial. We respectfully provide opportunity for everyone to express opinions, vet ideas, and workshop viable resolutions. When something makes the hair on the back of our necks stand up, we talk about it. We understand that safety is an illusion and control is a fairy tale; that on any given day, precious life is precarious, hanging in the balance like a feather on the wind. We reject hate-talk and dismiss fear-mongering. We embrace the practicality of living every moment — because life’s too short to pretend it’s not.
“Everybody dies” is a common mantra in our home. Not for fear of death, but as a compassionate reminder that in life there is no permanence. Our soulful six year old has given elaborate burials to expired honey bees found in our garden, respectfully thanking them for their invaluable contributions and wishing them safe passage to future endeavors. Living an active outdoor lifestyle in the heart of the Colorado Rockies, she’s become an avid student of wildlife biology, horticulture, and ethnobotany. True to her namesake, our astute Juniper is diligently learning the nuances of the food chain, life cycles, and the interconnectedness of all things.
We don’t have television. Juno’s exposure to cliché Disney princesses has largely been limited to the fiery, redheaded archer Merida from the movie “Brave.” Our favorite bedtime stories are about hardship, adversity and redemption, where the heroine needs no rescuing. Books like “The Paperbag Princess,” by Robert Munsch reveal protagonists’ inner strength and self-determination we want to nurture in our own daughter. Parents looking for inspiration can check this greatbook list (for older readers) with female characters who promote the kind of bravery and perseverance we should all seek to cultivate from an early age.
As a professional organizer and author, it’s my job to help people simplify, discover clarity, and become inspired by a rewarding life of purpose. You bet your ass my wife and I will be raising our daughter to be an independent thinker, a compassionate warrior, and a paragon of stewardship and integrity. Simon Sinek brilliantly reminds us, “Leadership is not about being in charge. Leadership is about taking care of those in your charge.” In my home, we’re far from perfect and that means approaching every heart-felt effort with humility and a commitment to personal growth. Will Durant’s famous interpretation of Aristotle states, “We are what we repeatedly do. Excellence, then, is not an act, but a habit.”
At six years old, Juno’s well on her way to understanding that intentional habits grounded in compassion, generosity, and getting after it like a warrior — will reliably deliver hard-won results now and for the rest of her life.
For all the emphasis placed on science, technology, engineering and math instruction, not much attention is given to a skill set that’s closely related with success in STEM: spatial skills.
The ability to mentally manipulate objects is key to success in many fields, including physics and engineering. Spatial skills are an early indicator of later achievement in mathematics, they “strongly predict” who will pursue STEM careers, and they are more predictive of future creativity and innovation than math scores. In fact, a review of 50 years of research shows that spatial skills have a “robust influence” on STEM domains.
However, women generally score lower than men on tests of spatial reasoning — particularly measures of spatial visualization and mental rotation. Some researchers point to evolution as the culprit, while others have tied the discrepancies to hormone levels or brain structure. As one researcher put it, “Sex differences in spatial ability are well documented, but poorly understood.”
Sheryl Sorby said she’s not interested in arguing about why the gap exists because training and practice can close it.
“A lot of people believe that spatial intelligence is a fixed quantity — that you either have good spatial skills or you don’t — but that’s simply not true,” said Sorby, an engineering professor. This misperception is particularly harmful to girls who may not be encouraged to engage in spatially rich activities that would set them up for later STEM success.
“We may start with this small biological difference, but it grows because of our environment,” said Sorby. For example, starting at an early age, boys are more likely to engage in activities that boost spatial reasoning. Research shows that boys play with spatial toys more than girls do — and spatial toys are often marketed explicitly to boys. In addition,studies find that parents are “less likely to restrain the exploratory behavior of boys,” such as allowing them to roam further from home than girls their same age.
The Ripple Effects of Spatial Reasoning
Boosting girls’ spatial skills can have a positive effect on other domains. Sorby believes that the small but persistent gender gap in standardized math scores can be largely explained by differences in spatial reasoning: Girls tend to do worse than boys on test items that have a spatial component.
A 2014 review of middle school physical science exam scores found that the gender difference boiled down to a few specific questions that required mental rotation. According to one report, “after students’ scores on the mental rotation assessment were taken into account, there was no longer a gender difference in physical science scores.”
Early in her career, Sorby wondered if spatial skills training could help colleges retain female students in engineering, a field with an acute gender disparity. As of 2011, 19 percent of all undergraduate degrees in engineering were awarded to women, and 3 percent were awarded to women of color. Sorby said that at many colleges, the first engineering courses for beginning students cover design graphics, which is highly spatial.
When Sorby taught at Michigan Technical University, she noticed that some female students — who otherwise excelled in math and science — would struggle with the class and choose to switch majors. “They assumed they didn’t have what it took to be an engineer,” said Sorby, “when the real issue was a weakness in spatial skills.”
From “Educational Research in Developing 3-D Spatial Skills for Engineering
Students” by Sheryl A. Sorby.
To help her incoming engineering students, Sorby developed a “short introduction to spatial visualization” class. The course is 15 hours of instructional time — “a miniscule amount of time” in the scheme of things — but the payoff has been worthwhile. Sorby taught students how to sketch figures from multiple perspectives, look at cross sections of objects and create 3-D objects through paper folding exercises. Students who took the class not only improved their spatial skills, but also their grades in all STEM classes improved, and they were more likely to graduate with an engineering degree.
In ninth grade at the Columbus School for Girls, students can take a version of Sorby’s spatial visualization course as a spring elective. The course is nine lessons and is taught by Linda Swarlis, director of information services. Swarlis says she often hears from graduates about how this course helped them in their college STEM classes. One young woman described how she found herself the only female enrolled in an inorganic chemistry class at a competitive college.
“The professor introduced the concept of chirality, and she recognized the concept as the right hand rule in engineering, something that she learned in her spatial visualization course,” said Swarlis.
Given that spatial skills can be learned, what can parents and teachers do? Sorby offers these suggestions:
Encourage Block Play: Playing with blocks and puzzles correlates with spatial development. Lego kits are particularly good for strengthening spatial visualization because kids have to examine a 2-D diagram and turn it into a 3-D model, said Sorby. She also recommends trying out some of the new engineering toys that have hit the market, such asGoldiblox.
Involve Girls in Practical Spatial Tasks: When planning a road trip, hand a map to your daughters and ask them to plan the route, said Sorby. When putting together a piece of IKEA furniture, involve girls in reading the instructions and screwing it together. These types of activities build skills and confidence.
Hold, Build and Sketch 3-D Objects: Sketching 3-D objects improves students’ mental visualization and rotation skills. Have children build an object out of blocks and then sketch it. Then have them rotate the object and sketch it again. Recent research also suggests that “holding an object in your hand seems to help you visualize it,” says Sorby. For example, showing students a 2-D model of a molecule does not help them nearly as much as handing them a model that they can hold, turn and examine from different angles.
Play 3-D Video Games: One study found that a mere 10 hours of “playing an action video game can virtually eliminate this gender difference in spatial attention and simultaneously decrease the gender disparity in mental rotation ability.” The authors speculate that more exposure to 3-D video games “could play a significant role as part of a larger strategy designed to interest women in science and engineering careers.”
Remember the power of expectation: “If we have a child with poor math skills, we don’t say, ‘That’s too bad — you’ll have poor math skills for the rest of your life.’ But with spatial skills we tend to do that,” said Sorby. “Instead we need to tell kids, ‘You can develop these skills just like you develop any skill.’ ”
By CAROLINE PAUL FEB. 20, 2016
Credit Lauren Tamaki
I WAS one of the first women in the San Francisco Fire Department. For more than a dozen years, I worked on a busy rig in a tough neighborhood where rundown houses caught fire easily and gangs fought with machetes and .22s. I’ve pulled a bloated body from the bay, performed CPR on a baby and crawled down countless smoky hallways.
I expected people to question whether I had the physical ability to do the job (even though I was a 5-foot-10, 150-pound ex-college athlete). What I didn’t expect was the question I heard more than any other: “Aren’t you scared?”
It was strange — and insulting — to have my courage doubted. I never heard my male colleagues asked this. Apparently, fear is expected of women.
This fear conditioning begins early. Many studies have shown that physical activity — sports, hiking, playing outdoors — is tied to girls’ self-esteem. And yet girls are often warned away from doing anything that involves a hint of risk.
One study focused on, coincidentally, a playground fire pole, is particularly revealing. It was published in The Journal of Applied Developmental Psychology and showed that parents cautioned their daughters about the dangers of the fire pole significantly more than they did their sons and were much more likely to assist them. But both moms and dads directed their sons to face their fears, with instruction on how to complete the task on their own.
I spoke recently to a friend who admitted that she cautioned her daughter much more than her son. “But she’s very klutzy,” the mom explained. I wondered, wasn’t there a way even a klutzy child could take risks? My friend agreed there might be, but only halfheartedly, and I could see on her face that maternal instinct was sparring with feminism, and feminism was losing.
I had been a klutzy child, too. I was also shy, and scared of many things: big kids, whatever might be under my bed at night, school. But I pored over National Geographic and “Harriet the Spy.” I knew all about Sir Lancelot and the Knights of the Round Table, who wandered the countryside swearing oaths of bravery and honor. None of these characters talked about fear. They talked about courage, exploration and exciting deeds.
So I biked down a steep country road (and hit a car). I sledded down an icy hill (and hit a tree). I don’t remember my parents freaking out; they seemed to understand that mishaps were part of childhood. I got a few stitches, and kept biking and sledding. Misadventures meant that I should try again. With each triumph over fear and physical adversity, I gained confidence.
I recently asked my mother why she never tried to stop me. She said that her own mother had been very fearful, gasping at anything remotely rough-and-tumble. “I had been so discouraged from having adventures, and I wanted you to have a more exciting childhood,” she told me.
My mom is an outlier. According to a study in The Journal of Pediatric Psychology last year, parents are “four times more likely to tell girls than boys to be more careful” after mishaps that are not life-threatening but do entail a trip to the emergency room. It seems like a reasonable warning. But there is a drawback, and the researchers remarked on it: “Girls may be less likely than boys to try challenging physical activities, which are important for developing new skills.” This study points to an uncomfortable truth: We think our daughters are more fragile, both physically and emotionally, than our sons.
Nobody is saying that injuries are good, or that girls should be reckless. But risk taking is important. Gever Tulley, the author of “50 Dangerous Things (You Should Let Your Children Do),” encourages girls and boys to own pocketknives, light fires and throw spears, arguing that dangerous activities under supervision can teach kids responsibility, problem-solving and confidence. It follows that by cautioning girls away from these experiences, we are not protecting them. We are failing to prepare them for life.
When a girl learns that the chance of skinning her knee is an acceptable reason not to attempt the fire pole, she learns to avoid activities outside her comfort zone. Soon many situations are considered too scary, when in fact they are simply exhilarating and unknown. Fear becomes a go-to feminine trait, something girls are expected to feel and express at will. By the time a girl reaches her tweens no one bats an eye when she screams at the sight of an insect.
When girls become women, this fear manifests as deference and timid decision making. We try to counter this conditioning by urging ourselves to “lean in.” Books on female empowerment proliferate on our shelves. I admire what these writers are trying to do — but they come far too late.
We must chuck the insidious language of fear (Be careful! That’s too scary!) and instead use the same terms we offer boys, of bravery and resilience. We need to embolden girls to master skills that at first appear difficult, even dangerous. And it’s not cute when a 10-year-old girl screeches, “I’m too scared.”
When I worked as a firefighter, I was often scared. Of course I was. So were the men. But fear wasn’t a reason to quit. I put my fear where it belonged, behind my feelings of focus, confidence and courage. Then I headed, with my crew, into the burning building.
Caroline Paul is the author of the forthcoming book “The Gutsy Girl: Escapades for Your Life of Epic Adventure.”