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.
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.”
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.”
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.
Switching from high school science to middle and high school gifted students has reawakened that sometimes uncomfortable sense of discovery of new teaching, where so much seems imperfect … I’m working with the mantra of imperfection.
That’s a good mantra for my students as well. Some students have never swung a hammer, threaded a needle, or made a model that was not outlined on card stock. Common day experiences have been digitized in our world, and access to extra materials is extremely limited for others. My solution: create a makerspace in my classroom and offer design challenges students can do with little more than string, glue, and cardboard. Cardboard, my makerspace material of choice, is available in every home in America.
From mac and cheese boxes to a shoebox, cardboard is a material that puts students on a level playing field. It’s free. Students can cut thin stuff with scissors or score corrugated material with a pair of safety scissors, and tape is cheap enough that I can send a partial roll home with a student who needs it. Kids in families who cannot afford clay or craft kits or have little money for additional classroom supplies can still imagine something using materials that belong to them. That equals the playing field among students who ‘have not’ with students who ‘have’ adequate resources.
Sure, many educators say, but this is learning time. How can cardboard be transformed into learning strategies benefiting students across disciplines? Here are four sample cardboard projects to get started.
1. Three-dimensional thinking by building artifacts. While it may seem unusual to us as educators, take the time to ask students how many have been in a barn, gone to a zoo, camped in a tent, or taken care of an animal. So many readings describe experiences for which students have no background knowledge. For example, Finding Winnie, the winner of the 2015 Caldecott Medal, is filled with unfamiliar venues. It took the illustrator, Sophie Blackall, over a year of research to visit all the places referenced in the book. My youngest middle school students are trying to build a single item model for just one scene in the book, ranging from an ocean liner to a tree to an antique car.
2. Imagining a Character. Middle school students love the idea of cosplay. Designing cardboard armor to imagine a warrior or superhero in a story is a simple way to use materials to portray their vision. The prompt can be as simple as, “Design a character to defend the castle.” It’s powerful to have the ability to create even an imperfect vision, instead of a project executed primarily by an overly helpful parent. Student processes are best remembered when the mistake or chance for failure becomes the driver for the learning.
3. Design thinking prototypes. The goal of design thinking is to solve a problem using a process of listening and developing empathy. Students struggle with this because they often design for themselves, rather than for a specific audience. After reading spooky stories that tie into both the Halloween season and the idea of justice, my students still struggled with the idea of putting themselves in another person’s shoes. How America is dealing with the idea of ‘liberty and justice for all’ is an example of a difficult idea. We used design thinking as the introduction to a conversation on empathy. Before the extended conversations at the end of the unit, I wanted to know if students could listen carefully. For one assignment, I asked them to set up a display prototype that combined scary elements from the stories and a building to contain a prisoner. While the artist of the classroom created a skeleton playing a trumpet by using scissors, this student didn’t follow directions, and his client (the teacher) was unsatisfied with the result. In contrast, the winner of the challenge created two ghosts out of cardboard shoulder pads and a turret out of thin cardboard, creating a powerful classroom lesson about utility versus perfection as well as listening.
4. Modeling. How does osmosis take place? What caused the creation of the universe? These are powerful questions, deep questions, and ones for which a teacher might not have the answer; however, they are just the type of questions my gifted students might ask. I pair students with an outside mentor via Skype or Google Hangouts by using the power of social media to find willing experts. To help students process difficult ideas, the Next Generation Science Standards recommend models as tools. Students often don’t think about making their own models unless teachers expose them to the idea as a strategy. Cardboard models are one way to go deeper in visible thinking and to augment visual notetaking. As described in Harvard’s Project Zero, initiatives like Agency by Design requires students to look closely at what they are doing to help discover complex ideas. When the students push back, I remind them of James Watson and Francis Crick, and how the cardboard models they created led to an understanding of DNA.
Tips on Creating a Cardboard Makerspace
Collect one or two plastic tubs of materials for your classroom.
In the first tub, start saving oddly-formed shapes of cardboard packaging from the IT department, or even toilet paper rolls. Corrugated cardboard is especially hard for younger students to cut. Resist the temptation to put full boxes in the box, or students will simply use them without modification (something I learned in this challenge).
In the second tub, place tape, string, and remnants of duct tape. I simply placed a box at my local church and asked for donations of half-used tape, white glue, and crochet thread.
Find donated materials. Reach out to close friends on Facebook, or check with a hardware store or custodian for unwanted materials.
Get a grant or donation from a big box store, or organize a campaign onDonorsChoose.
Build rubrics so students have a framework of expectations, but be willing to revise them as needed. The first creations may not be as rich as you expect, but this provides opportunities for further learning.
Building creations and making cardboard artists will also build memories in the journey of learning. Along the way, new skills and collaboration will help us become better learners.
Corvallis seventh grade students Madelyn Shepherd and Amanda Boelman carry their balloon to the launch site at the CHS football field with the help from their teacher Jennifer Powell (center).
MICHELLE MCCONNAHA – Ravalli Republic
Corvallis Middle School seventh grade students spent three days of designing, cutting and gluing to create a hot-air balloon from tissue paper.
On Thursday morning, they tested the air-worthiness of their creations with a launch at the school’s football field and track.
Educator Stacy Jessop said the annual event is a 20-year tradition.
“We used to do an entire unit on aviation,” Jessop said. “Now there are so many other things to teach we just have a few days for this. We talk about structure, panels, design and the history of flight. We view the hot-air balloon show that happens each year in Albuquerque, New Mexico.”
Each balloon has a sign that says “If found return to Corvallis Middle School.”
“We have had a few fly away and we want to track how high and how far they go,” Jessop said. “We have had them go as far as Woodside, a mile or two.”
The 137 students were launching, chasing and repairing their balloons in groups of two and three. With the heat at 65 degrees and no breeze, most of the balloons did not fly farther than the field. The few that went further stuck in trees of homes in East Corvallis.
Teacher Dave Bradshaw said students were creative.
“Students make their own design,” Bradshaw said. “They glue the panels together and use a template to cut it out then they glue the pieces together. The balloons are very delicate. If there is any little hole the kids will find out when they put the hot air in there.”
Corvallis Middle School science teacher Chris Maul-Smith said he looks forward to the balloon project.
“It is a great way to celebrate the end of the year for students and for the teachers as well,” he said. “It is a way to bring everyone together and have fun constructing a balloon.”
Maul-Smith said the balloons rise up to 200 feet and travel usually 200 to 300 yards, depending on the weather. The colder the day the higher the balloons fly.
“We fill each balloon with hot air from a stove pipe that is attached to a heater donated from Mom’s Rentals in Hamilton,” he said. “They do this every year and make this possible. We hold the opening of each balloon over the stovepipe until it is super-filled and super-warm and then let it go. If there is enough temperature difference, they fly really well. Today is a much better temperature than yesterday.”
Maul-Smith and Dave Chimo filled the balloons and released them into the air.
The balloon team of Amanda Boelman and Madelyn Shepherd said it was a fun project.
“We learned about hot-air balloons and it was great,” Boelman said.
Stephanie Weber and Alexa Sunderland said creating and launching their balloon was cool.
“I was hoping it would go higher,” Weber said. “We’ve got the streamers on ours to make it extra fancy.”
Sunderland said, “It went farther than I thought but it would have been cool to go further and out of the field.” Ramsey Snider and Carter Humphrey repaired their balloon’s several holes after their first launch. This is Jennifer Powell’s first year to teach seventh grade. She was delighted to be included in this project that she has heard about for years.
“Both my own children participated in this fun science project,” she said. “It is just the perfect day and the perfect ending to a great year of school.”
Mountain View, Calif. — THE humanities are kaput. Sorry, liberal arts cap-and-gowners. You blew it. In a software-run world, what’s wanted are more engineers.
At least, so goes the argument in a rising number of states, which have embraced a funding model for higher education that uses tuition “bonuses” to favor hard-skilled degrees like computer science over the humanities. The trend is backed by countless think pieces. “Macbeth does not make my priority list,” wrote Vinod Khosla, a co-founder of Sun Microsystems and the author of a widely shared blog post titled “Is Majoring in Liberal Arts a Mistake for Students?” (Subtitle: “Critical Thinking and the Scientific Process First — Humanities Later”).
The technologist’s argument begins with a suspicion that the liberal arts are of dubious academic rigor, suited mostly to dreamers. From there it proceeds to a reminder: Software powers the world, ergo, the only rational education is one built on STEM. Finally, lest he be accused of making a pyre of the canon, the technologist grants that yes, after students have finished their engineering degrees and found jobs, they should pick up a book — history, poetry, whatever.
As a liberal-arts major who went on to a career in software, I can only scratch my head.
Fresh out of college in 1993, I signed on with a large technology consultancy. The firm’s idea was that by hiring a certain lunatic fringe of humanities majors, it might cut down on engineering groupthink. After a six-week programming boot camp, we were pitched headfirst into the deep end of software development.
My first project could hardly have been worse. We (mostly engineers, with a spritzing of humanities majors) were attached to an enormous cellular carrier. Our assignment was to rewrite its rating and billing system — a thing that rivaled maritime law in its complexity.
I was assigned to a team charged with one of the hairier programs in the system, which concerned the movement of individual mobile subscribers from one “parent” account plan to another. Each one of these moves caused an avalanche of plan activations and terminations, carry-overs or forfeitures of accumulated talk minutes, and umpteen other causal conditionals that would affect the subscriber’s bill.
This program, thousands of lines of code long and growing by the hour, was passed around our team like an exquisite corpse. The subscribers and their parent accounts were rendered on our screens as a series of S’s and A’s. After we stared at these figures for weeks, they began to infect our dreams. (One I still remember. I was a baby in a vast crib. Just overhead, turning slowly and radiating malice, was an enormous iron mobile whose arms strained under the weight of certain capital letters.)
Our first big break came from a music major. A pianist, I think, who joined our team several months into the project. Within a matter of weeks, she had hit upon a method to make the S’s hold on to the correct attributes even when their parent A was changed.
We had been paralyzed. The minute we tweaked one bit of logic, we realized we’d fouled up another. But our music major moved freely. Instead of freezing up over the logical permutations behind each A and S, she found that these symbols put her in the mind of musical notes. As notes, they could be made to work in concert. They could be orchestrated.
On a subsequent project, our problem was pointers. In programming language, a pointer is an object that refers to some master value stored elsewhere. This might sound straightforward, but pointers are like ghosts in the system. A single misdirected one can crash a program. Our pointer wizard was a philosophy major who had no trouble at all with the idea of a named “thing” being a transient stand-in for some other unseen Thing. For a Plato man, this was mother’s milk.
I’ve worked in software for years and, time and again, I’ve seen someone apply the arts to solve a problem of systems. The reason for this is simple. As a practice, software development is far more creative than algorithmic.
The developer stands before her source code editor in the same way the author confronts the blank page. There’s an idea for what is to be created, and the (daunting) knowledge that there are a billion possible ways to go about it. To proceed, each relies on one part training to three parts creative intuition. They may also share a healthy impatience for the ways things “have always been done” and a generative desire to break conventions. When the module is finished or the pages complete, their quality is judged against many of the same standards: elegance, concision, cohesion; the discovery of symmetries where none were seen to exist. Yes, even beauty.
To be sure, each craft also requires a command of the language and its rules of syntax. But these are only starting points. To say that more good developers will be produced by swapping the arts for engineering is like saying that to produce great writers, we should double down on sentence diagraming.
Here the technologists may cry foul, say I’m misrepresenting the argument, that they’re not calling to avoid the humanities altogether, but only to replace them in undergraduate study. “Let college be for science and engineering, with the humanities later.” In tech speak, this is an argument for the humanities as plug-in.
But if anything can be treated as a plug-in, it’s learning how to code. It took me 18 months to become proficient as a developer. This isn’t to pretend software development is easy — those were long months, and I never touched the heights of my truly gifted peers. But in my experience, programming lends itself to concentrated self-study in a way that, say, “To the Lighthouse” or “Notes Toward a Supreme Fiction” do not. To learn how to write code, you need a few good books. To enter the mind of an artist, you need a human guide.
For folks like Mr. Khosla, such an approach is dangerous: “If subjects like history and literature are focused on too early, it is easy for someone not to learn to think for themselves and not to question assumptions, conclusions, and expert philosophies.” (Where some of these kill-the-humanities pieces are concerned, the strongest case for the liberal arts is made just in trying to read them.)
How much better is the view of another Silicon Valley figure, who argued that “technology alone is not enough — it’s technology married with liberal arts, married with the humanities, that yields us the result that makes our heart sing.”
WHEN STUDENTS (ESPECIALLY non-science majors) take required science classes, there is a reason. It’s not so that they can learn about the names of the planets or which plants you can eat (but that is useful to know). The primary reason that students are required to take a science class is to help them understand the nature of science.
Let’s focus on just one aspect of the nature of science that often gives students (and all sorts of people) problems.
Science Is a Creative Process
Here are some examples from the history of science.
Einstein used curved space-time to explain gravity (and other things).
Euler and Lagrange created the calculus of variations in order to solve the brachistochrone problem (path between two points with the shortest time). Oh, and calculus of variations is used in Lagrangian Mechanics—so it’s sort of a big deal.
This is my quick summary of science: Science is all about making models. These can be physical models, or a mathematical model or even a conceptual model. If the model agrees with real life, then that’s great. If there is an experiment that disagrees with a model, then we have to change that model. That’s it.
If you want to explore the unknown, you first have to follow a trail to get to the uncharted regions.
The creative part of science comes into play in the creation of models. In order to have a model to test, you need to build a model. You can’t just stop by the model shop and pick up a model—no, in real science you have to make these models yourself. You might start off with a terrible model, but you need to start somewhere. Once you have a model, you need an experiment. Sometimes these experiments are simple to see—but other times you need to think of a creative way to collect data. Just look at the LIGO experiment and the detection of gravitational waves as an example. Scientists have to be creative.
Unfortunately, a common idea about the nature of science is that scientists have to follow procedures without using any creativity. In fact, have you ever heard anyone say “I wouldn’t be a good scientist because I’m not creative”? No, instead people say “I’m not any good at math” or “I don’t like following boring procedures.” Yes, there are procedures in science—but that’s not the main objective. Scientists follow procedures so they can reproduce a result that someone else obtained. Procedures are sort of like a map into the wilderness. If you want to explore the unknown, you first have to follow a trail to get to the uncharted regions.
Science Is Creative, Science Classes Are Not
Perhaps the problem with creativity and science is our science classes. What do students do in a chemistry lab? Welcome to lab. Make sure you have your safety goggles and closed-toe shoes. Now carefully measure 2.3 mL of water and add it into the mixture. It goes on and on. Instructions. No wonder students don’t think science is creative.
But wait! If you don’t give students detailed instructions in lab, they are going to mess stuff up—or worse, get hurt—or even worse, fail the lab. It’s not just in chemistry lab that we (instructors) overuse instructions; it happens in physics and biology as well. The problem is that we wish to take our students to the wilderness—but it is an especially long journey. Even with a map, it can take 4 years of classes to get to the cool stuff.
Creativity Is Difficult to Grade
It’s not just that chemistry and physics are complicated. It’s also that creativity in science is difficult to grade, whereas following instructions is easy to grade. In this regard, science should be considered to be similar to art. In both cases, the student really needs to use some form of creativity—but it’s easier to just have them copy some work of art and see how close they can get to the original.
But there are plenty of opportunities for real creativity in science classes. One of my favorite classes is a physics class for elementary education majors. We use the textbook (really, it’s more like a workbook) Physics and Everyday Thinking. The primary goal of this course is to help students understand the nature of science (since they will be teaching science to kids). In one chapter, students try to create a model to explain what happens when you rub a nail with a magnet (it makes the nail act like a magnet). They then look at new experiments to refine their model.
Students often hate this chapter. They hate that there are no clear answers or a rigid set of procedures (there are procedures, just not for making the initial model). Although the students might not be happy, this is what happens in science—you have to create stuff.
You can also introduce creativity into the physics lab (at all levels) by giving fewer instructions. Yes, it can be scary at first—but I find that it works out quite well. One of my favorite labs is conservation of momentum in collisions. I used to give very detailed guidelines on how to collide two carts and show that momentum is conserved. Now, I just show them the carts and let them play for a bit. Students can find all sorts of cool collisions to explore. They can even be creative in their methods for measuring the initial and final velocities (I still give guidance, but they have more freedom).
Finally, there is another simple way to introduce creativity in the introductory physics courses—have the students create something. Yes, in this case I am talking about students creating a numerical model with code. Really, you should try this with your class. Students might be a little cautious at first but once they start making stuff, it’s going to be awesome. It’s even easy to grade. I have the students create a numerical calculation and create a short 5 minute screencast that shows how their program runs and what it does. Not only is it creative, using numerical calculations is just part of the way we do science now. You should be using coding in your physics class (there are no more excuses).
Students at Cheney Middle School in West Fargo had a tall task when they were given a week-and-a-half to research, design and test a new innovation to help Iditarod dog mushers during a fictitious race across North Dakota.
In the “I Will Survive!” project, 96 seventh-grade students in groups of two or three created a tangible invention to help the dogs or mushers complete and survive the long race across North Dakota. They presented their projects Friday in the school’s lunch commons.
Before students started their projects, they heard a presentation from a local veterinarian who discussed the problems and obstacles dogs and mushers face during an Iditarod race. The real Iditarod race began in Alaska in 1973, with a route from Anchorage to Nome. Mushers and dogs can face whiteout conditions and extremely cold temperatures.
Grace Planteen and Victoria Smith created a “doggy care kit” that includes a blanket with a heating system, a dog booty for paws and organic dog treats.
“We spent like a whole day thinking of many different designs and it just came to us,” Smith said.
“There was so much stuff that the mushers need that they can’t always fit all of their stuff they need for the dogs and so we thought, ‘Why can’t the dogs carry their own,’” Planteen added.
Items in the doggy care kit fit into a lightweight pack the girls designed to fit on the dogs. They even tested the packs on their own dogs.
Smith and Planteen said they both enjoyed working on the project. “I really liked creating the prototype,” Smith said. “I thought it was really fun to interact with it and just working with another person on making this happen.”
Two other students, Abigail Carlson and Elizabeth Lokosang, created a better braking system for sleds used in the Iditarod race that would make it safer for the mushers to slow down.
“We had a lot of ideas, but this is the one we really wanted to do because the mushers were falling off their sleds and getting hurt,” Lokosang said.
Carlson said she enjoyed the hands-on design part of the project and not the research, but said the project required her to become a better researcher.
Abigail Carlson and Elizabeth Lokosang talk about their Total Terrain project for the STEM survival, Iditarod unit. David Samson
The new braking system uses a hand brake to slow or stop the sled instead of the musher stepping on two brakes on the rear of the sled. Carlson said the current braking system leads to mushers falling off the sleds more easily.
Another pair of students created “Iditabars,” an energy bar snack for dogs to help them get the nutrients and energy they need to complete the race. Madison Huber and Jonny Schatz developed the recipe after extensive research. They also had to develop a way to keep the bars together after baking them proved impossible.
“Instead of baking them we froze them, so they’re like frozen dog treats,” Huber said.
Huber tested the treats on her own dog.
“He loved it,” she said. “He was just wagging his tail and he was running all night.”
Cheney Middle School seventh-grade teacher Karen Lietz said the project helps students prepare for future solution-based career fields.
“These kids when they graduate, they will have all of those 21st-century skills, with collaboration, creativity,” Lietz said. “They’ll be able to communicate effectively with others. They’ll have developed those soft skills as well as the problem-solving skills that are real-world.”