Calculus Is the Peak of High School Math. Maybe It’s Time to Change That

EdWeek

May 22, 2018
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For more than 30 years, calculus has been seen as the pinnacle of high school math—essential for careers in the hard sciences, and an explicit or unspoken prerequisite for top-tier colleges.

But now, math and science professionals are beginning to question how helpful current high school calculus courses really are for advanced science fields. The ubiquitous use of data in everything from physics and finance to politics and education is helping to build momentum for a new path in high school math—one emphasizing statistics and data literacy over calculus.

“We increasingly understand the world around us through data: gene expression, identifying new planets in distant solar systems, and everything in between,” said Randy Kochevar, a senior research scientist at the Education Development Center, an international nonprofit that works with education officials. Statistics and data analysis, he said, “is fundamental to many of the things we do routinely, not just as scientists but as professionals.”

He and other experts are still debating the best way to integrate a new approach in an already crowded high school curriculum. One of the most difficult philosophical challenges: how to prevent a statistics path from replicating the severe tracking and equity problems that have long existed in classical mathematics.

“There’s a sense that calculus is up here and statistics is a step below,” said Dan Chase, a secondary mathematics teacher at Carolina Day School in North Carolina, adding that he often struggles to suggest to students that, “if you are interested in engineering, that might be a good reason to go to calculus, but if you are interested in business or the humanities or social sciences, there are different paths you might go, even if you are a top-achieving math student.”

On face value, new expectations for students already seem to be moving toward statistics. Both the Common Core State Standards, on which many states’ math requirements are based, and the Next Generation Science Standards call for teaching data analysis and statistics, both on their own and in the process of learning other concepts.

But Kochevar warned: “There’s a huge disconnect; if you look closely at the science standards, they are expecting students to have tremendous faculty with using data by middle school, but if you look at the courses, it’s really not clear where those skills are supposed to be filled.”

Both sets of standards need more integration of data and statistics, he and others argue, because they were developed in the early years of the big data boom. Studies tracking data worldwide through the years have found people produced 1.5 exabytes of new data in 1999—or roughly 250 megabytes of data for every person alive—but by 2011, when states were adopting and implementing the math standards, people produced more than 14 exabytes a year. Today, people worldwide produce 2.5 exabytes of data every day, and the total data have doubled every two years.

Ironically, the rapid expansion of big data and statistics use in the broader society and economy comes at the same time American students seem to be struggling with those concepts. From 2007 to 2017, 4th and 8th students’ scores on the National Assessment of Educational Progress in mathematics fell significantly on problems related to data analysis, statistics, and probability—a decline that helped drive overall dips on the math test in 2017.

In part, experts say, that’s because statistics and data analysis have traditionally taken a back seat to calculus in high school math, and most students already have difficulty completing the classical path.

“The idea that statistics is hard is grounded in that fact that if you took statistics 10 years ago, you had to take calculus first, and the statistics used formal probability … with theorems that built on calculus,” said Uri Treisman, a mathematics professor and the executive director of the Charles A. Dana Center at the University of Texas at Austin. He’s been working with K-12 and university systems to develop a statistics pathway as an alternative to classical calculus.

It’s an idea that others have pushed back on, by situating a high school statistics pathway as either advanced material only suitable for students who have already passed calculus—or a less-rigorous path for students who can’t hack it in classical math.

“Any time you have multiple pathways, the advantaged will capitalize on one and that will become the ‘real’ one,” Treisman said. “If we are going to create data science pathways, they had better be anchored in things that lead to upward social mobility and have a rigor to them. We have to make sure new pathways have at least equal status as the traditional one—and ensure everyone has access to them. If we allow [statistics and data] to be the easy or weaker path, we relinquish the commitment to equity we started with.”

Mixed Signals in Calculus

For a picture of how severe that inequity can get, one only has to look at calculus.

Until about 1980, calculus was seen as a higher education course, primarily for those interested in mathematics, physics, or other hard sciences, and only about 30,000 high school students took the course. That began to change when school reformers glommed onto calculus as an early example of a rigorous, college-preparatory course, said David Bressoud, a mathematics professor at Macalester College and a former president of the Mathematical Association of America, who has examined the evolution of calculus studies.

“The more schools did this, the greater the expectation that they would do it” from parents, and district leaders—and in particular from colleges and universities, Bressoud said. “It’s not just math majors or engineering majors; this has become an accepted requirement for admission to top universities. You are not going to get into Duke if you haven’t taken calculus, even if you plan to major in French literature.”

Today, some 800,000 students nationwide take calculus in high school, about 15 percent of all high schoolers, and nearly 150,000 take the course before 11th grade. Calculus classes have been and remain disproportionately white and Asian, with other student groups less likely to attend schools that offer calculus or the early prerequisites (like middle school algebra) needed to gain access to the course.

For example, in 2015-16, black students were 9 percentage points less likely than their white peers to attend a high school that offered calculus and half as likely to take the class if they attended a school that offered it. And if black students did get into a class, their teachers were also less likely to be certified to teach calculus than those of white students, according to an Education Week Research Center analysis of federal civil rights data.

And despite the rapid growth of calculus as a gold standard, university calculus experts argue it is a much weaker sign that a student is actually prepared for postsecondary math in the science fields than it appears.

In fact, a new report by the Mathematics Association of America and the National Council of Teachers of Mathematics found many students who took Advanced Placement Calculus AB still ended up retaking calculus in college—and 250,000 students end up needing to take even lower-level courses, like precalculus or algebra.

In the end, the report found taking calculus in high school was associated with only a 5 percentage point increase on average in calculus scores in college—from 75 percent to 80 percent. Rather, the best predictor of earning a B or better in college calculus was a student earning no less than As in high school Algebra 1 and 2 and geometry.

So if high school calculus isn’t the best indicator of a student prepared for college-level math, what does it signify in college admissions? In a word: Money.

More than half of students who take calculus in high school come from families with a household income above $100,000 a year, according to a study this month in the Journal for Research in Mathematics Education. By contrast, only 15 percent of middle-income students and 7 percent of those in the poorest 25 percent of families take the course.

“Math is even more important to upward mobility now than it was 20 or 30 years ago, because … it’s seen as related to your general ability to solve problems quickly,” Treisman said, adding that as a result, “there’s general anxiety and panic about equity issues for anything new, even though the current [calculus] pathway is a burial ground for students of color.”

Forging a New Path

Statistics and data literacy advocates hope diversifying the field of interesting and rigorous math courses could broaden students’ path to STEM and other careers. As of 2017, the U.S. Bureau of Labor Statistics estimations showed that jobs that require data literacy and statistics are among the 10 fastest-growing occupations in the country.

“We have two paths forward,” said William Finzer, a senior scientist at the Concord Consortium, which works with school districts to improve their math curricula. “The easier one—like the path computer science took—is to develop a course or a subject area and get schools to give it time. … The problem of that is, it doesn’t spread the opportunity very widely. It becomes concentrated in the small group of kids who elect to take the course—and it’s just one more subject to take.”

Progression for Statistics and Data

EDC’s Oceans of Data Institute is building learning progressions for statistics and data literacy at different grades. Randy Kochevar, who directs the institute, said they are based on the acronym CLIP, meaning students learn how to use:

Complex, multi-variable data (“We’re not just looking at hours of sunlight and heights of bean plants,” he said);

Larger data sets than students need to answer any one question, so they are forced to sort and understand relevance;

Interactively accessed data, rather than sample graphs just written out on paper; and

Professionally collected data that forces students to think about how and why it was collected—and what biases may exist in the samples.

Finzer instead envisions a more holistic approach in which at least one class a year—be it math, biology, or even civics or history—asks students to grapple with making sense of large data sets. Such an approach, he said, “would make a huge difference, because it would mean when you came out of high school, data would not be foreign to you.”

EDC’s Oceans of Data Institute is building learning progressions for statistics and data literacy at different grades. The progression would include concepts in statistics and data literacy, but also computer science—to be able to use common programming and tools used by data professionals—and more philosophical concepts, such as the ethical use of statistics and privacy protections.

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10 Great Movies for the STEM Classroom

Common Sense Media

Use these powerful films to teach problem-solving and nurture students’ curiosity.

February 20, 2018
Danny WagnerSENIOR EDITOR, EDUCATION RATINGS & REVIEWS

Common Sense Education

If you’re looking to get kids excited about STEM (science, technology, engineering, and math), show them the ways that popular media uses — and misuses — the concepts you teach daily. Used as part of a lesson, clips from movies can reinforce topics, spark discussion, and promote new perspectives.

There’s still a great need to introduce kids, and especially girls, to STEM fields like neurobiology, nanotechnology, and civil engineering. Whether it’s a short clip from a Hollywood film to reinforce the concept of gravity or a feature-length documentary that highlights the work of engineers, incorporating movies into your lessons can help kids connect what they’re learning in the classroom to the world at large. And even after the credits roll, you can extend the learning: Create a model, start a debate, or begin a community project that the film — and your teaching — inspires.

Here are 10 film picks that showcase essential STEM skills for school, home, the workplace, and beyond.

 

The Lego Movie

Grades 1+

This hilarious save-the-world tale appeals to the builder in all of us; creative engineering solutions abound as the heroes embark on their block-building journey.

Teacher tips: Have students identify the engineering design process at work in the movie. Bring some Lego bricks into the classroom (or use Minecraft) and have students develop solutions to common problems, creating prototypes, testing designs, and iterating on their own designs. Students can document their findings and share the highs and lows of the creative process.

Discussion questions: Which of the movie’s creations was your favorite, and why? How might real-life engineers change the design process when they have to make quick decisions? How do the characters in the film demonstrate teamwork, and why is this important for engineers?

 

Big Hero 6

Grades 2+

In this Disney adaptation of a comic with the same name, a 14-year-old genius invents special microbots to join his brother’s university robotics program. After tragedy ensues, a group of heroes unites and uses their strengths in chemistry and engineering to overtake a crafty villain.

Teacher tips: Try some of the experiments provided by the film’s producers. From there, ask students to choose a problem in their school or community and work together in teams to brainstorm, design, and build solutions using their own unique talents.

Discussion questions: How can engineering solutions and inventions help — and sometimes hurt — humankind? What skills do you have that might help a team overcome an obstacle? Which events or traits fuel each character’s creativity in the movie? Is creativity always positive?

 

Dream Big: Engineering Our World

Grades 2+

This documentary highlights engineers from various backgrounds — many of whom are women — and the projects they’re designing, from earthquake-proof structures to footbridges in developing countries.

Teacher tips: Use the powerful stories about engineering and robotics clubs in schools to inspire your students to join (or create) their own. Have students research other engineering projects from around the world that are currently in the works, and discuss what kind of global impact they might have. Also be sure to check out the film’s education guide.

Discussion questions: How does engineering affect our everyday lives? How might engineers adapt as technology becomes more prevalent? Why do you think the movie highlights so many women engineers? Why is this type of diversity important?

 

Hidden Figures

Grades 4+

This inspiring true story of African American women at NASA in the 1950s and ’60s helps shine a light on the need for humans even as technology continues to automate.

Teacher tips: Build off the film’s education guide: Have students construct and solve their own mathematical equations to describe the orbits of planets, or use computer simulations to model Newton’s second law of motion. Talk about how technology makes these calculations easier.

Discussion questions: What are the positive and negative implications of technology taking over roles humans once held? What role did gender play in STEM fields in the 1950s and ’60s? How much have those roles changed today?

 

Underwater Dreams

Grades 4+

An underdog tale, this documentary tells the story of a robotics team from a lower-income high school that took on university teams — including MIT — in an underwater robotics competition.

Teacher tips: Introduce students to robots they can build and code like SpherolittleBits Invent, and Cue. Have students work in teams to focus on the design process and complete challenges. And while you’re at it, why not start or promote a robotics club at your school?

Discussion questions: What is it about the kids on this team that made them able to overcome such huge obstacles? What makes underwater robotics such a challenging problem to tackle? Besides through robotics clubs, what are some other ways to do STEM activities outside the classroom?

 

Apollo 13

Grades 6+

A classic and powerful take on the story of the doomed NASA spacecraft, this film highlights the technical issues astronauts faced (along with some of the do-it-yourself solutions they inspired) to land Apollo 13 on the moon.

Teacher tips: Use the rocket launch and reentry scenes to model physics concepts. Have students build or code their own rockets and create journals to document the kinds of small adjustments and iterations needed to create a successful launch. Tip: Pairs well with a game like Kerbal Space Program.

Discussion questions: How has technology changed since the 1960s? Where should NASA focus its efforts in space exploration today? What does the film say about the role of engineers and their ability to use common items to fix highly technical problems?

 

Interstellar

Grades 6+

While some of the film’s ideas veer into science fiction, there’s enough real science in this edge-of-your-seat thriller to make the heroes’ search for habitable planets worth your time.

Teacher tips: After taking a look at the educator’s guide and some TED-Ed lessons, have students talk about misconceptions and analyze the accuracy of some of the film’s scientific questions. Students can hold a debate around what’s a fact, what may be possible, and what’s simply unattainable.

Discussion questions: What technological issues are holding humans back from interstellar travel? If you were building your own robot companion for space travel, what qualities would you deem most important? What are some ways viewers can separate fact from fantasy in science fiction movies?

 

The Martian

Grades 6+

This sci-fi space thriller follows an astronaut who’s stuck on Mars and must problem-solve his way to safety using real scientific principles.

Teacher tips: Let students know it’s a movie about risk-taking and creativity and that, although the story is fictional, it’s rooted in scientific fact. Have students take a look at some of the main character’s creations in the movie: a sextant for navigation, his potato farm, or the water he makes from rocket fuel. Next, design a lesson where students are given a limited set of tools, a goal, and some constraints, then see what sort of innovative DIY projects they can launch.

Discussion questions: What is the hexadecimal system, and why is language so important in science and math? How important was it for the film’s main character to keep a log? Why do we not yet have the technology to go to Mars?

If You Build It

Grades 7+

Want to show students that they have the talent and ability to make a difference? Then check out this documentary that follows 10 high school students who design and build a new farmer’s market for their rural community.

Teacher tips: Kids will be inspired not only by the students’ abilities but by their actions. Harness that sentiment to get kids out into their own communities. Have your students interview neighbors, collect data, and embark on a cross-curricular project-based learning assignment to solve an issue. Teach your students the necessary skills to build something, and then set them free to create.

Discussion questions: Which engineering processes did you notice throughout the movie? Were some more successful than others? What obstacles might you face if you were to promote a change at your school?

 

The Imitation Game

Grades 7+

Cryptologists and mathematicians are front and center in this historical drama about the British government’s attempt to crack the German Enigma code during WWII.

Teacher tips: There’s a lack of Hollywood movies that incorporate math in meaningful ways. Take advantage of kids’ interest in this movie to host a code-breaking challenge event. Or, use cryptograms as an introduction to a matrix unit. If you provide Genius Hour time, let students dig in and explore a topic of their interest. You could also have kids research other examples where STEM skills have helped shape significant historical events.

Discussion questions: Would computers today be able to pass Turing’s test to determine intelligence? Why do we typically see more movies and stories about biologists or engineers instead of mathematicians?

The surprising thing Google learned about its employees — and what it means for today’s students

 December 20, 2017

(Marcio Jose Sanchez/AP)

The conventional wisdom about 21st century skills holds that students need to master the STEM subjects — science, technology, engineering and math — and learn to code as well because that’s where the jobs are. It turns out that is a gross simplification of what students need to know and be able to do, and some proof for that comes from a surprising source: Google.

This post explains what Google learned about its employees, and what that means for students across the country.  It was written by Cathy N. Davidson, founding director of the Futures Initiative and a professor in the doctoral program in English at the Graduate Center, CUNY, and author of the new book, “The New Education: How to Revolutionize the University to Prepare Students for a World in Flux.” She also serves on the Mozilla Foundation board of directors,  and was appointed by President Barack Obama to the National Council on the Humanities.

By Cathy N. Davidson

All across America, students are anxiously finishing their “What I Want To Be …” college application essays, advised to focus on STEM (Science, Technology, Engineering, and Mathematics) by pundits and parents who insist that’s the only way to become workforce ready.  But two recent studies of workplace success contradict the conventional wisdom about “hard skills.” Surprisingly, this research comes from the company most identified with the STEM-only approach: Google.

Sergey Brin and Larry Page, both brilliant computer scientists, founded their company on the conviction that only technologists can understand technology. Google originally set its hiring algorithms to sort for computer science students with top grades from elite science universities.

In 2013, Google decided to test its hiring hypothesis by crunching every bit and byte of hiring, firing, and promotion data accumulated since the company’s incorporation in 1998. Project Oxygen shocked everyone by concluding that, among the eight most important qualities of Google’s top employees, STEM expertise comes in dead last. The seven top characteristics of success at Google are all soft skills: being a good coach; communicating and listening well; possessing insights into others (including others different values and points of view); having empathy toward and being supportive of one’s colleagues; being a good critical thinker and problem solver; and being able to make connections across complex ideas.

Those traits sound more like what one gains as an English or theater major than as a programmer. Could it be that top Google employees were succeeding despite their technical training, not because of it?  After bringing in anthropologists and ethnographers to dive even deeper into the data, the company enlarged its previous hiring practices to include humanities majors, artists, and even the MBAs that, initially, Brin and Page viewed with disdain.

Project Aristotle, a study released by Google this past spring, further supports the importance of soft skills even in high-tech environments. Project Aristotle analyzes data on inventive and productive teams. Google takes pride in its A-teams, assembled with top scientists, each with the most specialized knowledge and able to throw down one cutting-edge idea after another. Its data analysis revealed, however, that the company’s most important and productive new ideas come from B-teams comprised of employees who don’t always have to be the smartest people in the room.

Project Aristotle shows that the best teams at Google exhibit a range of soft skills: equality, generosity, curiosity toward the ideas of your teammates, empathy, and emotional intelligence. And topping the list: emotional safety. No bullying. To succeed, each and every team member must feel confident speaking up and making mistakes. They must know they are being heard.

Google’s studies concur with others trying to understand the secret of a great future employee. A recent survey of 260 employers by the nonprofit National Association of Colleges and Employers, which includes both small firms and behemoths like Chevron and IBM, also ranks communication skills in the top three most-sought after qualities by job recruiters. They prize both an ability to communicate with one’s workers and an aptitude for conveying the company’s product and mission outside the organization. Or take billionaire venture capitalist and “Shark Tank” TV personality Mark Cuban: He looks for philosophy majors when he’s investing in sharks most likely to succeed.

STEM skills are vital to the world we live in today, but technology alone, as Steve Jobs famously insisted, is not enough. We desperately need the expertise of those who are educated to the human, cultural, and social as well as the computational.

No student should be prevented from majoring in an area they love based on a false idea of what they need to succeed. Broad learning skills are the key to long-term, satisfying, productive careers. What helps you thrive in a changing world isn’t rocket science. It may just well be social science, and, yes, even the humanities and the arts that contribute to making you not just workforce ready but world ready.

CAN ROBOTS HELP GET MORE GIRLS INTO SCIENCE AND TECH?

Wired

WONDER WORKSHOP
By Matt Simon

HERE’S A DEPRESSING number for you: 12. Just 12 percent of engineers in the United States are women. In computing it’s a bit better, where women make up 26 percent of the workforce—but that number has actually fallen from 35 percent in 1990.

The United States has a serious problem with getting women into STEM jobs and keeping them there. Silicon Valley and other employers bear the most responsibility for that: Discrimination, both overt and subtle, works to keep women out of the workforce. But this society of ours also perpetuates gender stereotypes, which parents pass on to their kids. Like the one that says boys enjoy building things more than girls.

There’s no single solution to such a daunting problem, but here’s an unlikely one: robots. Not robots enforcing diversity in the workplace, not robots doing all the work and obviating the concept of gender entirely, but robots getting more girls interested in STEM. Specifically, robot kits for kids—simple yet powerful toys for teaching youngsters how to engineer and code.

VAIDAS SIRTAUTUS

Plenty of toys are targeted at getting kids interested in science and engineering, and many these days are gender specific. Roominate, for instance, is a building kit tailored for girls, while the Boolean Box teaches girls to code. “Sometimes there’s this idea that girls need special Legos, or it needs to be pink and purple for girls to get into it, and sometimes that rubs me the wrong way,” says Amanda Sullivan, who works in human development at Tufts University. “If the pink and purple colored tools is what’s going to engage that girl, then that’s great. But I think in general it would be great if there were more tools and books and things that were out there for all children.”

So Sullivan decided to test the effects of a specifically non-gendered robotics kit called Kibo. Kids program the rolling robot by stringing together blocks that denote specific commands. It isn’t marketed specifically to boys or girls using stereotypical markings of maleness or femaleness. It’s a blank slate.

Before playing with Kibo, boys were significantly more likelyto say they’d enjoy being an engineer than the girls did. But after, boys had about the same opinion, while girls were now equally as likely to express an engineering interest as the boys. (In a control group that did not play with Kibo, girls’ opinions did not significantly change.) “I think that robots in general are novel to young children, both boys and girls,” Sullivan says. “So aside from engaging girls specifically, I think robotics kits like Kibo bring an air of excitement and something new to the classroom that gets kids psyched and excited about learning.”

There’s a problem, though. While Sullivan’s research shows that a gender-neutral robotics kit can get girls interested in engineering, that doesn’t mean it will sell. “If you look at sales data, it clearly shows that they’re not being used by girls,” says Sharmi Albrechtsen, CEO and co-founder of SmartGurlz, which makes a programmable doll on a self-balancing scooter. “Even the ones that are considered gender-neutral, if you look at the sales data it clearly shows a bias, and it’s towards boys. That’s the reality of the situation.” Gender sells—at least when it’s the parents doing the buying.

Regardless, companies are designing a new generation of toys in deliberate ways. Take Wonder Workshop and its non-gendered robots Dash and Cue. As they were prototyping, they’d test their designs with boys and girls. “One of the things we heard a lot from girls was this isn’t quite their toy,” says Vikas Gupta, co-founder and CEO of Wonder Workshop. “This is probably what their brother would play with.”

Why? Because they thought it looked like a car or truck. So the team covered up the wheels. “And all of a sudden girls wanted to play with it,” Gupta says. “Our takeaway from that in a big way was that every child brings their preconceived notions to play. So when they see something they map it back to something they’ve already seen.” Though not always. “What we do find actually, funnily enough,” says Albrechtsen of the SmartGurlz scooter doll, “is that a lot of boys actually end up edging in and wanting to play. So we have a lot of brothers who are also playing with the product.”

Whatever gets a child interested, it’s on parents and educators to make sure the spark stays alive. And maybe it’s the increasingly sophisticated, increasingly awesome, and increasingly inexpensive robots that can begin to transform the way America gets girls into science and tech. Short of becoming self aware and taking over the world, the machines certainly couldn’t hurt.

The Next Phase of the Maker Movement? Building Startups

Edsurge

The Next Phase of the Maker Movement? Building Startups
Zainab Oni, speaking at the Mouse 20th-anniversary event

“Everything that is old is new again!” Daniel Rabuzzi exclaims, his eyes light up with excitement that seems to match the glowing, handcrafted flower pinned on his vest. He’s talking about the next wave of the Maker Movement, big news buzzing amongst makers in the inner circle.

Rabuzzi is the executive director of Mouse, a national nonprofit that encourages students to create with technology. The organization, now celebrating 20 years in operation, is part of the worldwide Maker Movement, encouraging students to get creative (and messy) when using technology to build things. Rabuzzi calls his work at Mouse “shop and home economics for the 21st century,” and his students “digital blacksmiths.”

Mouse students showcasing green energy ideas

Rabuzzi, like many experts within the Maker Movement, believes the heavy emphasis on standardized testing in schools, which has pushed the arts, shop and home economics into the shadows, is what spurred outside groups like Mouse to begin hosting alternative makerspaces for students. Throughout the years, Rabuzzi has seen the movement evolve. Most recently, he’s seen technology become more directly integrated with making, along with an uptick of women in leadership.

“It can’t just be the boys tinkering in the basement anymore,” says Rabuzzi, pointing to women in maker leadership, like littleBits founder Ayah Bdeir, who encouraged more young girls to enter the space.

Now Rabuzzi, along with makers, investors, and journalists, are buzzing about what they describe as the next wave of making: the Maker economy, which many believe will transform manufacturing the United States by integrating with the Internet of Things (IOT), augmented reality (AR), virtual reality (VR) and artificial intelligence (AI).

“There is all this talk about bringing back manufacturing to America, and I feel like this is going to come back on a local level,” says Juan Garzon, former Mouse student, who started his hardware company. He believes that personalized goods designed and manufactured by Makers through mediums like 3D printing will drive the return of domestic manufacturing.

“The future of manufacturing is not a big plant, but someone designing what they want and developing custom made things. It sounds so sci-fi, but it is within my lifetime,” continues Garzon.

News reports from Chicago Inno show that custom manufacturing designed by makers might be an active part of the domestic economy sooner than Garzon realizes. Inno reports that several Maker-entrepreneur spaces are popping up in the city with hopes to develop places where creators can build scalable products to be manufactured, creating new businesses.

Audience members viewing Mouse student’s VR projects

For many, talk of 3D printing and merging Making with AI are bleeding edge topics, far away from today’s realities. But for technologists supporting Mouse, this the world they want to prepare students to be a part of.

Mouse students at the 20th-anniversary party are already getting started. At the event, some students proudly showed off projects they designed in 3D spaces that can be viewed and altered in virtual reality. Many of the projects students worked on required a mixture of creativity, technical skills and awareness of the societal needs. Displays showcasing green energy projects along with digitalized wearable technology for persons with disabilities were all throughout the room. Still, Rabuzzi imagines more.

He hopes that through making, students can test the limits of new technologies and do good for the society. “How do we use Alexa and Siri in the Maker Movement?” Rabuzzi wonders aloud. He describes his idea of using AI to support students in designing, prototyping and creating new learning pathways in future, but admits that he doesn’t have the funding or technology for such ambitious projects now. He hopes that some of Mouse’s corporate funding partners are interested in supporting the endeavors.

“We are preparing today’s young people for a cyber future,” he explains. “In the old days if you had a clever idea you had to go into a big company to get it done. Now you can make it yourself.”

The Way We Teach Math Is Holding Women Back

Time

March 29, 2017

A Stanford math professor encourages a different teaching approach

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.

Learning to Think Like a Computer

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A kindergartner organizes blocks into a sequence of commands at the Eliot-Pearson Children’s School at Tufts University. CreditCharlie Mahoney for The New York Times

In “The Beauty and Joy of Computing,” the course he helped conceive for nonmajors at the University of California, Berkeley, Daniel Garcia explains an all-important concept in computer science — abstraction — in terms of milkshakes.

“There is a reason when you go to the ‘Joy of Cooking’ and you want to make a strawberry milkshake, you don’t look under ‘strawberry milkshake,’ ” he said. Rather, there is a recipe for milkshakes that instructs you to add ice cream, milk and fruit of your choice. While earlier cookbooks may have had separate recipes for strawberry milkshakes, raspberry milkshakes and boysenberry milkshakes, eventually, he imagines, someone said, “Why don’t we collapse that into one milkshake recipe?”

“The idea of abstraction,” he said, “is to hide the details.” It requires recognizing patterns and distilling complexity into a precise, clear summary. It’s like the countdown to a space launch that runs through a checklist — life support, fuel, payload — in which each check represents perhaps 100 checks that have been performed.

Concealing layers of information makes it possible to get at the intersections of things, improving aspects of a complicated system without understanding and grappling with each part. Abstraction allows advances without redesigning from scratch.

It is a cool and useful idea that, along with other cool and useful computer science ideas, has people itching to know more. It’s obvious that computers have become indispensable problem-solving partners, not to mention personal companions. But it’s suddenly not enough to be a fluent user of software interfaces. Understanding what lies behind the computer’s seeming magic now seems crucial. In particular, “computational thinking” is captivating educators, from kindergarten teachers to college professors, offering a new language and orientation to tackle problems in other areas of life.

This promise — as well as a job market hungry for coding — has fed enrollments in classes like the one at Berkeley, taken by 500 students a year. Since 2011, the number of computer science majors has more than doubled, according to the Computing Research Association. At Stanford, Princeton and Tufts, computer science is now the most popular major. More striking, though, is the appeal among nonmajors. Between 2005 and 2015, enrollment of nonmajors in introductory, mid- and upper-level computer science courses grew by 177 percent, 251 percent and 143 percent, respectively.

In the fall, the College Board introduced a new Advanced Placement course, Computer Science Principles, focused not on learning to code but on using code to solve problems. And WGBH, the PBS station in Boston, is using National Science Foundation money to help develop a program for 3- to 5-year-olds in which four cartoon monkeys get into scrapes and then “get out of the messes by applying computational thinking,” said Marisa Wolsky, executive producer of children’s media. “We see it as a groundbreaking curriculum that is not being done yet.”

Computational thinking is not new. Seymour Papert, a pioneer in artificial intelligence and an M.I.T. professor, used the term in 1980 to envision how children could use computers to learn. But Jeannette M. Wing, in charge of basic research at Microsoft and former professor at Carnegie Mellon, gets credit for making it fashionable. In 2006, on the heels of the dot-com bust and plunging computer science enrollments, Dr. Wing wrote a trade journal piece, “Computational Thinking.” It was intended as a salve for a struggling field.

“Things were so bad that some universities were thinking of closing down computer science departments,” she recalled. Some now consider her article a manifesto for embracing a computing mind-set.

Like any big idea, there is disagreement about computational thinking — its broad usefulness as well as what fits in the circle. Skills typically include recognizing patterns and sequences, creating algorithms, devising tests for finding and fixing errors, reducing the general to the precise and expanding the precise to the general.

It requires reframing research, said Shriram Krishnamurthi, a computer science professor at Brown, so that “instead of formulating a question to a human being, I formulate a question to a data set.” For example, instead of asking if the media is biased toward liberals, pose the question as: Are liberals identified as liberal in major newspapers more often or less often than conservatives are identified as conservative?

Dr. Krishnamurthi helped create “Introduction to Computation for the Humanities and Social Sciences” more than a decade ago because he wanted students “early in their undergrad careers to learn a new mode of thinking that they could take back to their discipline.” Capped at 20 students, the course now has a waitlist of more than 100.

Just as Charles Darwin’s theory of evolution is drafted to explain politics and business, Dr. Wing argued for broad use of computer ideas. And not just for work. Applying computational thinking, “we can improve the efficiencies of our daily lives,” she said in an interview, “and make ourselves a little less stressed out.”

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In his computer science course for nonmajors at the University of California, Berkeley, Dan Garcia wants students to understand why computers are “not magical.” In this exercise, students sort a deck of shuffled cards into ordered suits while being timed. They sort solo, then in pairs, then fours, then eights. But more people don’t always make it go faster. Amdahl’s law offers an equation to show that even with many computers tackling a problem, the time to complete the task does not decrease linearly. There are bottlenecks.CreditJim Wilson/The New York Times

Computing practices like reformulating tough problems into ones we know how to solve, seeing trade-offs between time and space, and pipelining (allowing the next action in line to begin before the first completes the sequence) have many applications, she said.

Consider the buffet line. “When you go to a lunch buffet, you see the forks and knives are the first station,” she said. “I find that very annoying. They should be last. You shouldn’t have to balance your plate while you have your fork and knife.” Dr. Wing, who equates a child filling her backpack to caching (how computers retrieve and store information needed later), sees the buffet’s inefficiency as a failure to apply logical thinking and sequencing.

Computational thinking, she said, can aid a basic task like planning a trip — breaking it into booking flights, hotels, car rental — or be used “for something as complicated as health care or policy decision-making.” Identifying subproblems and describing their relationship to the larger problem allows for targeted work. “Once you have well-defined interfaces,” she said, “you can ignore the complexity of the rest of the problem.”

Can computational thinking make us better at work and life? Dr. Krishnamurthi is sometimes seduced. “Before I go grocery shopping, I sort my list by aisles in the store,” he said. Sharing the list on the app Trello, his family can “bucket sort” items by aisle (pasta and oils, canned goods, then baking and spices), optimizing their path through Whole Foods. It limits backtracking and reduces spontaneous, “i.e., junk,” purchases, he said.

Despite his chosen field, Dr. Krishnamurthi worries about the current cultural tendency to view computer science knowledge as supreme, better than that gained in other fields. Right now, he said, “we are just overly intoxicated with computer science.”

It is certainly worth wondering if some applications of computational thinking are trivial, unnecessary or a Stepford Wife-like abdication of devilishly random judgment.

Alexander Torres, a senior majoring in English at Stanford, has noted how the campus’s proximity to Google has lured all but the rare student to computer science courses. He’s a holdout. But “I don’t see myself as having skills missing,” he said. In earning his degree he has practiced critical thinking, problem solving, analysis and making logical arguments. “When you are analyzing a Dickinson or Whitman or Melville, you have to unpack that language and synthesize it back.”

There is no reliable research showing that computing makes one more creative or more able to problem-solve. It won’t make you better at something unless that something is explicitly taught, said Mark Guzdial, a professor in the School of Interactive Computing at Georgia Tech who studies computing in education. “You can’t prove a negative,” he said, but in decades of research no one has found that skills automatically transfer.

Still, he added, for the same reasons people should understand biology, chemistry or physics, “it makes a lot of sense to understand computing in our lives.” Increasing numbers of people must program in their jobs, even if it’s just Microsoft Excel. “Solving problems with computers happens to all of us every day,” he said. How to make the skills available broadly is “an interesting challenge.”

“It’s like being a diplomat and learning Spanish; I feel like it’s essential,” said Greer Brigham, a Brown freshman who plans to major in political science. He’s taking the course designed by Dr. Krishnamurthi, which this term is being taught by a graduate student in robotics named Stephen Brawner.

On a March morning at the Brown computer science center, Mr. Brawner projected a student’s homework assignment on the screen. Did anyone notice a problem? Nary a humanities hand was raised. Finally, a young woman suggested “centimeters” and “kilograms” could be abbreviated. Fine, but not enough.

Mr. Brawner broke the silence and pointed out long lines of code reaching the far side of the screen. With a practiced flurry, he inserted backslashes and hit “return” repeatedly, which drew the symbols into a neat block. It may all be directions to a machine, but computer scientists care a great deal about visual elegance. As Mr. Brawner cut out repeated instructions, he shared that “whenever we define a constant, we want that at the top of our code.” He then explained the new assignment: write a program to play “rock, paper, scissors” against a computer.

Mili Mitra, a junior majoring in public policy and economics who sat with a MacBook on her lap, would not have considered this class a year ago. But seeing group research projects always being handed off to someone with computing knowledge, she decided that she “didn’t want to keep passing them along.” She has learned to write basic code and fetch data sets through the internet to analyze things she’s interested in, such as how geographic proximity shapes voting patterns in the United Nations General Assembly.

Despite finding interactions with a computer much like “explaining things to a toddler,” Ms. Mitra credits the class for instilling the habit of “going step by step and building a solution.” She admits to being an impatient learner: “I jump ahead. In C.S. you don’t have a choice. If you miss a step, you mess up everything.”

Just as children are drilled on the scientific method — turn observations into a hypothesis, design a control group, do an experiment to test your theory — the basics of working with computers is being cast as a teachable blueprint. One thing making this possible is that communicating with computers has become easier.

“Block” programming languages like Scratch, released by the M.I.T. Media Lab a decade ago, hide text strings that look like computer keys run amok. That makes coding look less scary. Instead of keyboard letters and symbols, you might select from a menu and drag a color-coded block that says “say ( ) for ( ) secs” or “play note ( ) for ( ) beats.” The colors and shapes correspond to categories like “sound” or “motion”; the blocks can be fit together like stacked puzzle pieces to order instructions. Students use this to, say, design a game.

One need not be a digital Dr. Doolittle, fluent in hard-core programming languages like Java or Python, to code. Block languages cut out the need to memorize commands, which vary depending on the computer language, because the block “is read just the way you think about it,” Dr. Garcia said. Students in his Berkeley course use the block language Snap! for assignments — he doesn’t teach Python until the last two weeks, and then just so they can take higher-level courses. “We tell them, ‘You already know how to program,’ ” he said, because the steps are the same.

Computer Science A, which teaches Java, is the fastest-growing Advanced Placement course. (The number of students taking the exam in 2016 rose 18 percent over 2015 and nearly tripled in a decade.) But professors complained that “Java was not the right way” to attract a diverse group of students, said Trevor Packer, head of the A.P. program, so a new course was developed.

The course, Computer Science Principles, is modeled on college versions for nonmajors. It lets teachers pick any coding language and has a gentler vibe. There is an exam, but students also submit projects “more similar to a studio art portfolio,” Mr. Packer said. The course covers working with data and understanding the internet and cyber security, and it teaches “transferable skills,” he said, like formulating precise questions. That’s a departure from what the College Board found in many high schools: “They were learning how to keyboard, how to use Microsoft applications.” The goal is that the new course will be offered in every high school in the country.

President Obama’s “Computer Science for All” initiative, officially launched last year, resulted in educators, lawmakers and computer science advocates spreading the gospel of coding. It also nudged more states to count computer science toward high school graduation requirements. Thirty-two states and the District of Columbia now do, up from 12 in 2013, according to Code.org. It’s what Dr. Wing had hoped for when she advocated in her 2006 article that, along with reading, writing and arithmetic “we should add computational thinking to every child’s analytical ability.”

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After arranging blocks into a sequence of commands, kindergartners at the Eliot-Pearson Children’s School scanned the bar codes on the blocks into their yellow robot. It obeyed their commands.CreditCharlie Mahoney for The New York Times

In an airy kindergarten classroom at Eliot-Pearson Children’s School, in the Tufts University Department of Child Study and Human Development, children program with actual blocks. Marina Umaschi Bers, a child development and computer science professor, created wooden blocks that bear bar codes with instructions such as “forward,” “spin” and “shake” that are used to program robots — small, wheeled carts with built-in scanners — by sequencing the blocks, then scanning them. Each “program” starts with a green “begin” block and finishes with a red “end.”

Coding for the youngest students has become the trendy pedagogy, with plentiful toys and apps like Dr. Bers’s blocks. Dr. Bers, who with M.I.T. collaborators developed the block language ScratchJr, is evangelical about coding. Learning the language of machines, she said, is as basic as writing is to being proficient in a foreign language. “You are able to write a love poem, you are able to write a birthday card, you are able to use language in many expressive ways,” she said. “You are not just reading; you are producing.”

Peer-reviewed studies by Dr. Bers show that after programming the robots, youngsters are better at sequencing picture stories. Anecdotally, she said, when they ask children to list steps for brushing teeth, they get just a few, “but after being exposed to this work, they’ll have 15 or 20 steps.”

Dr. Bers embeds computing in activities familiar to young children like inventing stories, doing dances and making art. At the Tufts school on a recent morning, children puzzled over a question: How does a robot celebrate spring?

“He’s going to dance, and then he will pretend that he is wet,” offered Hallel Cohen-Goldberg, a kindergartner with a mane of curls.

Solina Gonzalez, coloring a brown, blue and red circle with markers, peered soberly through pink-framed glasses: “He just does a lollipop dance.” Solina’s partner, Oisin Stephens, fretted about the root beer lollipop drawing she had taped to a block. “The robot won’t be able to read this,” he said. (It’s an invalid input.)

As they lurched around the carpet on their knees, the children executed computer science concepts like breaking instructions into sequenced commands, testing and debugging. One team used “repeat” and “stop repeat” blocks, forming a programming “loop,” a sequence of instructions that is continually repeated until a certain condition is reached.