“It isn’t easy to be a citizen in 2018.” So begins Ted Underwood’s essay on machine learning. Underwood continues: “we are told to watch out for bots and biased search engines, but skepticism about new media can also make us easy prey for old-fashioned propaganda.”
For Underwood, a central aim for education needs to be preparing “students for a world where information is filtered by computers” and he argues that to do so, “we will need a stronger alliance between the humanities and math.” The rest of his essay explores how “this alliance has two reciprocal parts: cultural criticism of the mathematical models shaping our world, and mathematical inquiry about culture.”
Humanities and STEM?
The question of the relationship between the humanities and STEM is nothing new. Indeed, undergrads still regularly read texts like CP Snow’s classic 1959 essay “The Two Cultures,” which argued that the humanities and what we now call STEM are fundamentally divided and unable to speak to each other. Underwood subverts Snow’s thesis arguing that the only viable path forward for us is one that integrates the disciplines. We might intuit that humanities can help, well, humanize, STEM, but we might ask, “why does human culture need math? Underwood explains that “The challenges that confront 21st-century citizens are not always arguments that come one by one to be evaluated. Information is more likely to come in cascades, guided both by networks of friends and by statistical models that anticipate our preferences.” As a result of this cascade of information, Underwood argues that “Evaluating sources one by one won’t necessarily tell us whether these computational and social systems are giving us a biased picture. Instead, we need to think about samples and models—in other words, about math.”
The Connection Between Models
The connection between models in the humanities (i.e., a novel as a model of the human condition) and mathematical models is deeper than it may appear. Underwood illustrates this point with algorithms. He explains that in 21st century computing…
Instead of manually writing algorithms that directly govern a computer’s decisions, we often ask computers to write their own instructions by modeling the problem to be solved.
To illustrate this, he explains how email filters spam:
Undesirable email comes in many different shapes, and it would be hard to write an algorithm that could catch them all. A more flexible approach begins by collecting examples of messages that human readers have rejected, along with messages they approved. Then we ask the computer to write its own instructions, by observing differences between the two groups.
In other words, algorithms are models that continually update themselves to function better. This form of computing is known as machine learning, and as Underwood explains, “machine learning increasingly shapes human culture: the votes we cast, the shows we watch, the words we type on Facebook all become food for models of human behavior, which in turn shape what we see online.” He then notes that “since this cycle can amplify existing biases, any critique of contemporary culture needs to include a critique of machine learning.” That latter point means that just as we have a tradition of literary criticism that digs into the stories we tell in order to critique aspects that our problematic in service to helping us become better moral agents or citizens or lovers, so also we need to critique the algorithms that, for example, reinforce unhealthy and addictive behavior on social media. And since the English department has been a place where this criticism has flourished, programmers might learn a lot from taking some English classes, and on the other hand, English majors might benefit from taking a programming course and learning to think in code as another language.
Integrating Humanities and STEM
Integrating the humanities and STEM is not just helpful for ethics. The integration can also help us better understand and interpret the world: put differently, the integration can help us move closer to truth. Underwood writes that “to be appropriately wary, without succumbing to paranoia, students need to understand both the limits and the valid applications of technology.” And he suggests that “humanists can contribute to both halves of this educational project, because we’re already familiar with one central application of machine learning—the task of modeling fuzzy, changeable patterns implicit in human behavior.”
Now, the models of the world produced by the novelist may strike as “slippery and unscientific,” but Underwood asks us to recall that “machine learning can also be slippery and unscientific.” He writes: “Remember that we resorted to machine learning because we couldn’t invent a simple, universal definition of spam. Instead, we had to draw on the tacit knowledge of human readers who had rejected email for a range of reasons. A model based on this sort of evidence will never be stable. It will have to be updated every few years, as old scams die out and new ones emerge.” In other words, while total objectivity is impossible, some models are better than others at getting us closer to truth, and learning to discern between models is an essential part of a well-rounded education.
The integration that Underwood recommends is also essential for dealing with untrustworthy politicians and political pundits. Underwood explains that “tech leaders who argue that machine learning is more objective than other knowledge cannot be trusted. But we should just as fiercely distrust political leaders who use the perspectival complexity of the internet to imply that real knowledge is impossible, everything is fake, and we can only fall back on affinity and prejudice.” He stresses that “it is possible to build real knowledge by comparing perspectives from different social contexts. Historians have long known how.” The good historian sifts through all sorts of past culture – religious tomes and tax records, political treatises and recovered coinage – to figure out which accounts of history are most plausible. That skill-set parallels the work needed to sift through scientific studies, for example, to determine what is most plausible.
Underwood concludes his argument by reminding us that in order to understand ourselves and our world “we will need numbers as well as words.”
Underwood’s writing reminds me of two books that have shaped my thinking on this theme.
• Actual Minds, Possible Worlds explores the power of literature as a pathway to this important ability to imagine new possibilities.
• Robot-Proof: Higher Education in The Age of Intelligence blends theoretical and practical.
In a recent post on the Department of Education blog, the staff interviewed a military homeschool family. The writers introduce the interview by noting:
When asked to share their thoughts on the benefits of school choice and their homeschool experience, this military family did what they do every day: they turned the occasion into a learning opportunity. Dan, his wife Jenna, and their six kids gathered at the dinner table to shape a response – as individual, independent thinkers and as a family.
The family shared that what led them to homeschool was a mix of several factors:
• Their oldest child has Cystic Fibrosis and is especially susceptible to sickness in the classroom.
• Dan’s career as a Naval officer means the family moves a lot and homeschooling helps make the transitions easier.
• The customizability of homeschooling helps the children overcome learning challenges.
• The ability to choose curriculum allows the family to teach in keeping with their values.
When asked about what their homeschooling looks like in practice, the family responded:
We would describe our homeschool as academically rigorous, but eclectic and fun. We spend time researching and selecting curricula that best fit our family and our days together. Reading, writing, arithmetic, speaking, history, science, foreign language are all very important to us. Our ultimate goals, though, are that our kids would love (and know how) to learn, love to read, and love to see the beauty of the great things in life – God, nature, literature, art, music, recreation, travel, people, relationships.
Our kids are heavily involved in music and they enjoy athletic activities. We travel in the areas we are stationed, as well as when the Navy moves us to our next destination. We’ve had wonderful learning experiences in national parks and historical landmarks, as well as museums and nature.
Family read-aloud books are integral to our teaching and learning, even though our kids range in age from two to fourteen years. In fact, on Fridays, we parents read through Shakespeare with our three oldest kids. For us, the greatest part of exercising this school choice of homeschooling is getting to spend ample time as a family.
At the end of the interview, the family was asked about what school choice means to them. They responded: “School choice allows us the freedom to engage in the aforementioned activities and educational methods amidst health concerns, military moves, learning and behavioral challenges, and curriculum choices based on our worldview.”
At Demme Learning, we feel honored that quite a few service members use our Math-U-See and Spelling-You-See curricula. We are so thankful for their service, and offer them a 10% discount on all their orders. Contact us for more details.
Nathalie is mother to two intelligent, capable girls and doting wife to a handsome naval aviator. As with the family featured on the Ed.Gov blog, Nathalie and her family have found homeschooling to be a great fit. She wrote this in a recent blog post:
One might think it ambitious to consider homeschooling in an environment riddled with uncertainty and constant change. However, home education has proven to be a steady anchor for our family. (Forgive the pun. I couldn’t resist. Go Navy!) It is one element of our lives that we can truly say is consistent, no matter our destination. Even still, providing a stable home education for our children while navigating the tumultuous seas of military life requires a boatload of flexibility, creativity, and courage.
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In his TED Talk at the London Business School, speaker Alex Edmans considered the question of “…what to trust in a ‘post-truth’ world?” Edmans opened his talk with an exploration of confirmation bias: our propensity to accept a story (eg., a newspaper article) we like as being true, without being duly critical.
For example, if we read a story that interprets a data set in ways that support our preconceived beliefs, we rarely stop to ask, “Are there alternative explanations that can explain the data just as well if not better than my own explanation?” Edmans explains:
A story is not fact, because it may not be true. A fact is not data; it may not be representative if it’s only one data point. And data is not evidence — it may not be supportive if it’s consistent with rival theories.
How, then, can we know what is true? Edmans recognizes that this is a weighty question. He says, “When you’re at the inflection points of life, deciding on a strategy for your business, a parenting technique for your child or a regimen for your health, how do you ensure that you don’t have a story but you have evidence?”
Thankfully, Edmans has three tips which provide some guidance.
1) “Read and Listen to People You Flagrantly Disagree With”
Edmans points out that even if 90% of what they say seems wrong to you, there might still be 10% that you can learn from. Edmans recommends that you “surround yourself with people who challenge you, and create a culture that actively encourages dissent.”
2) “Listen to Experts”
Edmans recognizes that this is “perhaps the most unpopular advice that I could give you.” And of course the experts are often wrong, so how can we know who to trust? Edman suggests that “we should critically examine the credentials of the authors. Just like you’d critically examine the credentials of a potential surgeon. Are they truly experts in the matter, or do they have a vested interest?” And secondly, Edmans says, “We should pay particular attention to papers published in the top academic journals.” He notes that academics are often accused of being detached from the real world. But he explains that “this detachment gives you years to spend on a study. To really nail down a result, to rule out those rival theories, and to distinguish correlation from causation. And academic journals involve peer review, where a paper is rigorously scrutinized.”
3) “Pause Before Sharing Anything”
Edmans reminds us of the Hippocratic oath which states “First, do no harm.” Edmans warns that “what we share is potentially contagious, so be very careful about what we spread. Our goal should not be to get likes or retweets. Otherwise, we only share the consensus; we don’t challenge anyone’s thinking. Otherwise, we only share what sounds good, regardless of whether it’s evidence.”
• The way of thinking that Edmans’ talk is designed to foster is called Data Literacy. In his book Robot-Proof: Higher Education in The Age of Intelligence, Joseph E. Aoun, president of Northeastern University, highlights data literacy as a must needed emphasis for contemporary education. He argues that “there is little use in accumulating massive amounts of data unless we can arrange it into useful information and thence into understanding.” Data literacy allows us to benefit the data “by shifting through these giant sets of data to find the correlations in them that yield useful findings.”
• I’m never wrong, except when I’m disagreeing with my wife. Okay, fine, I admit that I’m often wrong and I’m not always the quickest to acknowledge when I’m wrong. Recently I watched Julia Galef’s TEDx talk on why we think we’re right — even when we’re wrong. Learn more about Galef’s insight on my website.
Fabiano Caruana is really good at chess. The 26 year old American is a grandmaster, and he is ranked second in the world after narrowly losing to reigning Norwegian Magnus Carlsen. According to his website, Caruana has been playing chess since he was five, but it was age 10 that he began to garner attention, after becoming the youngest American to defeat a Grandmaster in an official tournament. By age 12, he had earned the international title of FIDE Master. And then at age 14, he became the youngest grandmaster in US history, beating the record set by Bobby Fischer.
Caruana was homeschooled, and it was only because his parents believed in him that he was able to become the chess player he is today. CNBC reports:
As Caruana began getting more and more serious about the game, former world chess champion Garry Kasparov stepped in to warn his parents that a career in chess was “too risky” and that it would be difficult to make a living.
Thankfully his parents “disregarded the advice and let their son play chess while homeschooling him.” Lou Caruana explains that “we knew he was extremely intelligent, so we did have a degree of confidence that with or without formal education, he would be O.K.” Lou also explains that Fabiano “spent a tremendous amount of time reading, and so he is somewhat self-educated.” Commenting on Caruana’s education, journalist Daaim Shabazz writes:
His evolution makes a good case study for homeschooling and other ways of learning that enable young people to break free from the static environment of formal education in order to pursue their passions. It also makes for a good case study of what talent looks like in its earliest stages.
While Caruana likely had a lot of natural talent, his success as a chess player is tied to specific habits of mind that helped him develop that talent to become a champion. Shabazz notes that “one of the things I saw in Fabiano early on was not being afraid to play the strongest competition available. He didn’t fear losing. I once saw Caruana lose a game when he was around 9 or 10 and he didn’t seem to carry any of the usual childish pouting from a loss.” Shabazz speculates that “this self-control may have been developed because of his early diet of competitive open tournaments. In these competitions you must forget about a bad result quickly or risk distraction in the next game. In a recent interview, he mentioned his ability to come back from losses as one of his top strengths.”
The Power of Grit
Angela Duckworth – a psychology professor and 2013 MacArthur Fellow – has a word for the resiliency of mind that allows Caruana bounce back from losses: grit. In her book Grit: The Power of Passion and Perseverance she explains that the more she paid attention to both her teaching and the research she was conducting, the more she realized that innate talent isn’t a reliable indicator to future success and that instead it is an attitude of grit and a willingness to grow that best predicts student success. Duckworth introduces us to David, a freshman in a high school algebra course. David’s first math test came back with a D. In her interview with David, she asked him how he dealt with that disappointing result. He said: “I did feel bad – I did – but I didn’t dwell on it. I knew it was done. I knew I had to focus on what to do next. So I went to my teacher and asked for help. I basically tried to figure out, you know, what I did wrong. What I needed to do differently.” Duckworth reports that “by senior year, David was taking the harder of Lowell’s two honors calculus courses.”
The development of grit is aided by moving away from what Stanford University professor and researcher Carol Dweck calls a “fixed mindset” and instead embracing a “growth mindset.” In our blog post on growth mindset, we explain: “those with a fixed mindset believe that talent, intelligence, and ability are set and unchangeable—genetically determined or a gift that you either have or you don’t.” In contrast, “those with a growth mindset believe that through effort and perseverance we have the ability to improve and grow in any area to which we set our minds. Growth does not discount the existence of innate talent. Instead, it recognizes that natural talent undeveloped due to lack of effort will never reach its full potential.” We note that “in general, those with less “natural ability” that work diligently will ultimately achieve more than those “gifted” who do not cultivate their skills.” (Our Learning and Development Specialist Lisa Shumate has written this helpful post for tips on cultivating a growth mindset in our children and students.)
You Can Improve Yourself
While most of us will never be as good at chess as Fabiano Caruana, with the right kind of practice, we can all make meaningful improvements in chess or any other activity (yes, including math!). The book to read on good practice strategy is The Talent Code [my review] by Daniel Coyle. He opens his book by asking:
How does a penniless Russian tennis club with one indoor court create more top-twenty women players than the entire United States? How does a humble storefront music school in Dallas, Texas, produce Jessica Simpson, Demi Lovato, and a succession of pop music phenoms? How does a poor, scantily educated British family in a remote village turn out three world-class writers?
And he spends the rest of the book trying to answer those questions.
Coyle found that the world’s most accomplished athletes, musicians, chess players, etc., all sharpen their skill with a shared kind of practice, what he refers to as deep practice. Coyle explains that deep practice is characterized by “slow, fiftful struggle” where people purposely operate “at the edges of their ability” with full recognition that this means failing more often than succeeding. Coyle explains this paradox, noting that “experiences where you’re forced to slow down, make errors, and correct them – as you would if you were walking up an ice-covered hill, slipping and stumbling as you go – end up making you swift and graceful without your realizing it.” The key is to “choose a goal just beyond your present abilities” because “thrashing about blindly doesn’t help” but “reaching does.”
Coyle also writes about the coaching style he encountered most often. He notes that while our Hollywood stereotype of the successful coach emphasizes long, inspirational speeches and dramatic levels of energy and excitement, that isn’t what he found to be most successful. Instead he writes that the coaches were “quiet, even reserved” and that they “listened far more than they talked.” Rather than giving inspirational speeches, these coaches “spent most of their time offering small, targeted, highly specific adjustments.” These coaches had “an extraordinary sensitivity to the person they were teaching, customizing each message to each student’s personality.” Daniel Coyle calls these coaches “talent whispers.”
Now get out there and play some chess!
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The Global Family Research Project recently highlighted a new initiative in Michigan to get kids and parents learning math together by sending them materials in the mail. The Project reports:
Math in the Mail kits are designed to develop mathematical skills in three-year-olds by providing the tools that parents, guardians, and other caregivers need to build positive family relationships around math learning.
What’s Included in the Kits?
Each kit includes:
• Materials designed for hands-on play.
• Ideas for activities with the provided materials and extension activities using items found in any home, as well as a description of how these activities help children learn.
• A storybook that corresponds to the kit’s main topic that parents and children can enjoy together.
Inspired by Dolly Parton’s Imagination Library campaign which sends free books to low-income families, “the goal of Math in the Mail is to reach those families who will benefit from the materials most and have the least financial resources available.” Through this program, “children who meet economic eligibility requirements receive six kits in the mail over the course of a year.” The program is “currently serving Michigan children from Arenac, Bay, Clare, Gladwin, Gratiot, Isabella, Midland, and Saginaw counties” and these kits have reached more than “1,700 families from low-income homes to date.”
This initiative is a great example of how civil society can support family learning. The report explains that various organizations collaborated to make Math in The Mail possible. Specifically, “museums, libraries, and early childhood programs all help us get the word out about the work we do, and help us recruit families into the program by sharing our information with those who visit their spaces. Also, a variety of groups—like the Girl Scouts, parks and recreation departments, and local businesses—partner with us around our math kits, a win-win for everyone.”
Loris Malaguzzi was an Italian educator and the founder of the Reggio Emilia approach to education, which is similar to other models like Montessori and Waldorf. Like other theorists of the late 20th century, including Bruner, Piaget, and Vygotsky, Malaguzzi centers everything on the active child who, together with a nurturing and experienced guide, actively constructs her own learning. At the heart of the Reggio Emilia approach is an emphasis on personalized learning, an emphasis that is a cornerstone of our education philosophy at Demme Learning. In a seminar he gave in Italy in 1993, Malaguzzi provides wisdom for the importance of personalized learning in the context of meaningful relationships.
Malaguzzi says that we should never “think of the child in the abstract.” Instead, we need to give close attention to the particulars of the child right in front of us, recognizing that she is “already tightly connected and linked to a certain reality of the world — she has relationships and experiences.” Malaguzzi says that “we cannot separate this child from a particular reality” and so must recognize that she brings “these experiences, feelings, and relationships” into the classroom. This is also true of you, the parent and educator. He writes that “when you enter the school in the morning, you carry with you pieces of your life — your happiness, your sadness, your hopes, your pleasures, the stresses from your life. You never come in an isolated way; you always come with pieces of the world attached to you.”
This emphasis on relationship has significant implications for the structure of education, in form, content, pacing, etc. Malaguzzi points out that “the environment you construct around you and the children also reflects this image you have about the child. There’s a difference between the environment that you are able to build based on a preconceived image of the child and the environment that you can build that is based on the child you see in front of you— the relationship you build with the child, the games you play.” He observes that “an environment that grows out of your relationship with the child is unique and fluid.” Recognizing this unique fluidity should lead us as educators to strive for flexibility as much as we can. As Malaguzzi advises, “we need to be open to what takes place and able to change our plans and go with what might grow at that very moment both inside the child and inside ourselves.”
This approach to education also asks us to take seriously both our emotions and the emotions of our children and students. Malaguzzi writes: “Teachers need to learn to see the children, to listen to them, to know when they are feeling some distance from us as adults and from children, when they are distracted, when they are surrounded by a shadow of happiness and pleasure, and when they are surrounded by a shadow of sadness and suffering.”
Malaguzzi also has powerful insight especially relevant to families who have adopted children from troubled backgrounds. He says: “What we have to do now is draw out the image of the child, draw the child out of the desperate situations that many children find themselves in. If we redeem the child from these difficult situations, we redeem ourselves.” This reminds me of the book The Connected Child by Drs. Karyn Purvis and David Cross which my wife Anna and I read as part of our training to be adoptive parents. In that book, the authors write that “with compassion, you can look inside your child’s heart and recognize the impairments and deep fear that drive maladaptive behavior – fears of abandonment, hunger, being in an unfamiliar environment, losing control, and being hurt.” Like Malaguzzi, the authors of The Connected Child ask us to recognize the complex ways that interior grief can manifest itself in external behavior. They write that “a child’s grief can take many shapes. It might look like opposition, agitation, aggression, withdrawal, or obvious sorrow” and they caution that “unless adopted children can authentically express their losses, sadness, and emotions, they will never be able to connect to you or others in meaningful ways.”
In her groundbreaking book Grit: The Power of Passion and Perseverance, Angela Duckworth – a psychology professor and 2013 MacArthur Fellow – introduces us to David. She recounts how while taking a freshman high school algebra course, David’s first math test came back with a D. In her interview with David, she asked him how he dealt with that disappointing result. He said: “I did feel bad – I did – but I didn’t dwell on it. I knew it was done. I knew I had to focus on what to do next. So I went to my teacher and asked for help. I basically tried to figure out, you know, what I did wrong. What I needed to do differently.” Duckworth reports that “by senior year, David was taking the harder of Lowell’s two honors calculus courses.”
David’s story might seem rather surprising. Duckworth observes that “conventional wisdom says that math is a subject in which the more talented students are expected to excel, leaving classmates who are simply ‘not math people’ behind.” While we tend to think of riding a bike as something anyone can learn with dedication, effort, and time, we are also used to thinking that math comes naturally to those who are good at it, and that if it doesn’t come naturally, it cannot be learned. But the more Duckworth paid attention to both her teaching and the research she was conducting, the more she realized that talent isn’t a good guide and that instead it was an attitude of grit and a willingness to grow that predicted student success. Duckworth says that initially she too had been “distracted by talent” but she slowly learned that “aptitude did not guarantee achievement.” She further writes that “during the next several years of teaching, I grew less and less convinced that talent was destiny and more and more intrigued by the returns generated by effort.”
Duckworth is quick to stress that “talent – how fast we improve in skill – absolutely matters.” But she also points out that “effort factors into the calculations twice, not once. Effort builds skill. At the very same time, effort makes skill productive.” Duckworth says talent can be a helpful boost at the beginning of the learning process, but she also notes that the best way to develop any skill is to focus on practicing at the edges of current ability, and that means embracing failure. Duckworth also warns about the danger of overemphasizing talent because it can easily lead to a fixed mindset, the kind of mindset that says “I’m not a math person so I can’t learn this” rather than allowing a growth mindset that says “I don’t know how to do this yet, but I can learn!” (You can read more about the difference between these two mindsets by reading this article.)
It isn’t just in the discipline of mathematics that grit matters. Duckworth reports on her research on competitive spellers, “Measurements of grit taken months before the final competition predicted how well spellers would eventually perform. Put simply, grittier kids went further in competition. How did they do it? By studying many more hours and, also, by competing in more spelling bees.” Duckworth also studied the military students at West Point to answer the question, “what matters for making it through Beast,” the grueling program that separates West Point grads from the dropouts. She found that the answer to that question is “not your SAT scores, not your high school rank, not your leadership experience, not your athletic ability.” Instead, “what matters is grit.”
Parenting for Grit
Duckworth devotes a whole section of her book to providing ideas for parents who want to cultivate grittiness in their children. “First and foremost,” she stresses, “there’s no either/or trade-off between supportive parenting and demanding parenting.” She notes that “it’s a common misunderstanding to think of ‘tough love’ as a carefully struck balance between affection and respect on the one hand, and firmly enforced expectations on the other” and argues that “in actuality, there’s no reason you can’t do both.”
Another piece of advice to parents is to encourage their children to play. She writes, “before those who’ve yet to fix on a passion are ready to spend hours a day diligently honing skills, they must goof around, triggering and retriggering interest.” One way to help children in this process is to encourage them to sign up for extracurriculars and also pushing them to stick with their chosen activity. Duckworth writes, “If I could wave a magic wand, I’d have all the children in the world engage in at least one extracurricular activity of their choice, and as for those in high school, I’d require that they stick with at least one activity for more than a year.” The reason for this this desire is her recognition that “kids thrive when they spend at least some part of their week doing hard things that interest them.”
The point about sticking with activities is crucial. Duckworth notes that passion has less to do with intensity and more to do with consistency: “Enthusiasm is common. Endurance is rare.” In order to foster grit, the Duckworth family created the “The Hard Thing Rule” which has three parts:
1. Everyone – including Mom and Dad – has to do a hard thing, something that “requires daily deliberate practice.”
2. “You can quit. But you can’t quit until the season is over, the tuition payment is up, or some other ‘natural’ stopping point has arrived…In other words, you can’t quit on a day when your teacher yells at you, or you lose a race, or you have to miss a sleepover because of a recital the next morning.”
3. “You get to pick your hard thing. Nobody picks it for you because, after all, it would make no sense to do a hard thing you’re not even vaguely interested in.”
Earlier in the review, I mentioned the problem of fixed mindsets. Duckworth cautions parents that “children develop more of a fixed mindset when their parents react to mistakes as though they’re harmful and problematic.” She instead recommends that parents try to model “emotion-free mistake making.” For example, she shares about a technique where teachers “commit an error on purpose and then lets students see them say, with a smile, ‘Oh, gosh, I thought there were five blocks in this pile! Let me count again! … Great I learned I need to touch each block as I count!” If you’re anything like me, daily life provides plenty of opportunities for me to own up to honest mistakes and model a growth mindset. (For more tips on cultivating a growth mindset in yourself and your children, check out this article.)
While Duckworth believes that grit is essential for success, she thinks there are other traits that need to be cultivated alongside grit. She writes, “In assessing grit along with other virtues, I find three reliable clusters. I refer to them as intrapersonal, interpersonal, and intellectual dimensions of character. You could also call them strengths of will, heart, and mind.”
1. Intrapersonal character: this cluster includes grit as well as “self-control, particularly as it relates to resisting temptations like texting and video games.”
2. Interpersonal character: “includes gratitude, social intelligence, and self-control over emotions like anger. These virtues help you get along with – and provide assistance to – other people.”
3. Intellectual character: “includes virtues like curiosity and zest. These encourage active and open engagement with the world of ideas.”
(As a brief aside, Duckworth’s cluster of virtues is very similar to the skillsets commended by Joseph E. Aoun, president of Northeastern University, in his book on robot-proofing education.)
Finally, Duckworth warns that while grit is good, too much effort without enough rest can lead to burnout. She explains that the cardinal feature of burnout is “the feeling of exhaustion” usually accompanied by “depersonalization – the sense that you’re unconnected to the people you’re serving or working with – and also helplessness – the sense that no matter what you do or how hard you try, you’re not making progress.” The concern about burnout is real; we sometimes recommend our customers take a math break. Amanda Capps explains that a math break can be full break and other times it can mean “taking a break from the current curriculum and focusing more on math games, math apps, reading math-related literature, or reviewing concepts.” She notes that a math break “could also include applying math to real-world applications such as cooking, budgeting, or building that occur outside of a workbook!”
To conclude the review, I want to revisit the story of David. Remember that David was the high school freshman who got a “D” on his first math test, and who went on to take advanced math as a senior. As it turns out, David went on to earn a PhD in mechanical engineering and is now working at the Aerospace Corporation. Duckworth writes: “quite literally, the boy who was deemed ‘not ready’ for harder, faster math classes is now a ‘rocket scientist.’”
Did you know that Iceland is the leading European country for cleanest-living teens? The World Economic Forum reports:
The percentage of 15- and 16-year-olds who had been drunk in the previous month plummeted from 42 percent in 1998 to 5 percent in 2016. The percentage who have ever used cannabis is down from 17 percent to 7 percent. Those smoking cigarettes every day fell from 23 percent to just 3 percent.
And also reports on a study that:
…revealed clear differences between the lives of kids who took up drinking, smoking and other drugs, and those who didn’t. A few factors emerged as strongly protective: participation in organised activities – especially sport – three or four times a week, total time spent with parents during the week, feeling cared about at school, and not being outdoors in the late evenings.
The push for parental engagement proved essential in Iceland’s campaign to reduce substance abuse.
Links between parents and school were strengthened through parental organisations which by law had to be established in every school, along with school councils with parent representatives. Parents were encouraged to attend talks on the importance of spending a quantity of time with their children rather than occasional “quality time”, on talking to their kids about their lives, on knowing who their kids were friends with, and on keeping their children home in the evenings.
In addition, the national umbrella organization Home and School has introduced agreements for parents to sign. “The content varies depending on the age group, and individual organisations can decide what they want to include. For kids aged 13 and up, parents can pledge to follow all the recommendations, and also, for example, not to allow their kids to have unsupervised parties, not to buy alcohol for minors, and to keep an eye on the wellbeing of other children.”
The director of Home and School Hrefna Sigurjónsdóttir argues that “these agreements educate parents but also help to strengthen their authority in the home.” Researcher Inga Dóra adds that “we learned through the studies that we need to create circumstances in which kids can lead healthy lives, and they do not need to use substances, because life is fun, and they have plenty to do – and they are supported by parents who will spend time with them.”
One reason that Iceland’s reliance on parental engagement is so effective can be explained by recent research in the field of social neuroscience. An article in Scientific American explains that while we have known for some time now that the brains of adolescents are still developing in areas related to risk assessment, self-control, emotional regulation, etc., what this newer research is showing is that social factors affect the teenage brain and thus play a significant role in teen decision making. The simple version is that when teens are around their peers, their ability to accurately assess risk diminishes, whereas active parental engagement can help increase teens ability to self-regulate, assess risk, etc.
One of the most memorable memories recounted in Augustine’s Confessions is the story of how as a youth, he and his friends stole pears from their neighbor’s tree simply for the thrill of it. While this story reminds me of the kind of comically mischievous adventures of Tom Sawyer or Peter Pan, Augustine is not in the least amused by his earlier folly. In context, Augustine uses this story to diagnose our tendency to delight in sheer wickedness, a problem that can manifest itself in worse things than stealing a pear! But there’s another feature of interest in Augustine’s account: he mentions that he only stole the pears because his friends were doing it!
Augustine’s pear story illustrates something that parents know quite well: teens tend to take more risks in the presence of their peers. Recent research in neuroscience is helping us understand why this is the case. An article in Scientific American explains that while we have known for some time now that the brains of adolescents are still developing in areas related to risk assessment, self-control, emotional regulation, etc., what this newer research is showing is that social factors affect the teenage brain and thus play a significant role in teen decision making.
One study had teens play a video game version of “chicken” where they had to choose whether or not to drive their car through a series of yellow lights or wait for the green light. The researchers found that “when teenagers played this game alone, they took risks at about the same frequency as adult players.” But as soon as teens were told that their friends were watching from an adjacent room, they began to take significantly more risks. In contrast, when teens were told their mothers were watching, they took fewer risks.The article reports that “the scanner revealed greater activation in reward-sensitive brain regions, such as the ventral striatum, with the friend-influenced risky behaviours. Meanwhile, the mothers’ presence correlated with activation in the prefrontal cortex, an area known to be involved in cognitive control.”
This research points to the importance of our role as parents in helping our teens as they build their risk assessment skills and learn to act wisely. As fully developed adults with years of experience, our guidance is essential in helping our teens in this challenging phase of their development. Nevertheless, while it might be tempting, in light of this research, to hide your teen away in a tower until they’re 25, another dimension of this research shows why that would be a bad idea. The researchers found that “when they returned to the driving game after experiencing social exclusion, adolescents who said they were sensitive to peer influence took significantly more risks. Those who demonstrated this pattern also showed greater activation in a brain area involved in modelling the thoughts of others, the temporoparietal junction.” In another study, these researchers also found that “teenagers who were more socially excluded or victimized took more risks.” The key takeaway, then, is not that teens shouldn’t spend time with their peers, but rather that the time spent being influenced by peers should not supplant the primary attachment bonds of the teen to the family.
At the end of the Scientific American article, a neuroscientist named B.J. Casey pointed out that adolescence is a uniquely difficult transition period in our lives. Casey said, “I can’t think of a more challenging period of development. Every time I give a talk, I ask people to raise their hand if they want to go through adolescence again. And no one does.” Thankfully though, your teen doesn’t have to figure this stuff out on their own: they can look to you for guidance.
In his book, Hold on to Your Kids: Why Parents Need to Matter More Than Peers, Dr. Neufeld discusses the rise of youth culture and the shift from young people being mostly influenced by their parents to being mostly influenced by their peers. Dr. Neufeld outlines three negative effects of peer orientation:
1) Peer-oriented kids are more vulnerable.
2) Peer-oriented kids lose their natural shield against stress.
3) Peer-oriented kids become sensitized to insensitive interactions of children.
Neufeld advises parents to continue to nurture a bond with their teens and to recognize the vital role they have in their teen’s development. Here’s an article with four tips for cultivating healthy attachments with your kids, based on Dr. Neufeld’s research.
Joseph E. Aoun has been president of Northeastern University for twelve years. During his tenure, he has thought deeply about the role of education. In his recent book, Robot-Proof: Higher Education in The Age of Intelligence, Aoun asks “How should education be used to help people in the professional and economic spheres?” He notes that “as a university president, this is no small question for me…the university I lead, Northeastern, is explicitly concerned with the connections between education and work.”
Like many of our nation’s thinkers, Aoun is deeply concerned with how automation, artificial intelligence, and robotics will transform economies and displace workers. Thankfully, Aoun’s own rich academic background in linguistics and philosophy as well as his experience as a leader in higher-education have combined to give him a vision for robot-proof education. The education that Aoun recommends is a blend of the liberal arts and STEM, a mix of textbook and experiential learning, a balancing of the contemplative and practical.
Education is its own reward, equipping us with the mental furniture to live a rich, considered existence. However, for most people in an advanced society and economy such as ours, it also is a prerequisite for white-collar employment.
Aoun thinks there are two kinds of thinking that are uniquely human and that need to be emphasized in education. The first is critical thinking – something often talked about but not always well defined or understood. He defines critical thinking as “analyzing ideas in a skillful way and then applying them in a useful one.” Moreover, “to do this well, a person needs to be able to observe, reflect, synthesize, and imagine concepts and information and to communicate the results of the process.” Critical thinking goes hand-in-hand with the second model of thinking, systems thinking. This approach “involves seeing across areas that machines might be able to comprehend individually but that they cannot analyze in an integrated way, as a whole.” For example, even a well-coded algorithm can’t tell us “why certain hashtags on Twitter are trending, why the global commodities markets are rising and falling, why the Antarctic ice shelf is melting.” Aoun gives a concrete example of how humans and computers can work together: “…in the case of wind blow-over derailment, computers can help a team of engineers predict when it is likely to occur, but they cannot marshal the different talents needed for the project, give them direction, interpret the wider ramifications of the findings, and decide how to implement change.”
3 New Literacies
In order to develop the kind of thinking that will prepare us for careers in the digital age, Aoun proposes three new literacies. Just as today’s students are guided into mastering basic reading, writing, and math, tomorrow’s students will also need basic proficiency in technology, data analysis, and human literacy.
1) Technological Literacy
This means “Knowledge of mathematics, coding, and basic engineering principles.” Aoun explains that, “in much the same way as factory workers a hundred years ago needed to understand the basic structures of engines, we need to understand the elemental principles behind our devices. This empowers us to deploy software and hardware to their fullest utility, maximizing our powers to achieve and create.” In addition, “because coding is the lingua franca of the digital world, everyone should be conversant in it.”
2) Data Literacy
This is about knowing how to read and interpret data, particularly as it is reported in journalism. Aoun notes that “there is little use in accumulating massive amounts of data unless we can arrange it into useful information and thence into understanding. Data analysis allows us to do this by shifting through these giant sets of data to find the correlations in them that yield useful findings.”
3) Human Literacy
Human literacy equips us for the social milieu, giving us the power to communicate, engage with others, and tap into our human capacity for grace and beauty. It encompasses the humanities traditionally found in a liberal arts education but also includes elements of the arts, especially design, which is integral to much of digital communication.
In addition to basic training in ethics, human literacy is about forming human judgment. Aoun observes that “technology lacks the discernment to filter truth from deceit. And although human judgment can be grossly flawed, humans are also adept at sniffing out the truth by using context.”
In each of these literacies, Aoun identifies the same sequence of learning, and one that should be familiar to all of you who use our Math-U-See curriculum: “acquisition [of skills], integration, application” which leads to “high level of mastery,” otherwise known as “expertise.”
We can think of a student’s progress from ignorance to mastery as an advancement through four stages of development within the dimensions of consciousness and competence. In the first stage, students are unconsciously incompetent. They lack the knowledge to realize the extent of what they do not know. In the second stage, as the extent of this begins to dawn on them and they understand they have much to learn, they advance to a state of conscious incompetence. Further advancing, they reach a state of conscious competence in which they can perform well but must do so with deliberation and intent. At the final stage, they achieve the liberating state of unconscious competence, instinctively operating at the highest level of their domain.
Moreover, just as our math curriculum, Math-U-See, is both sequential and conceptual, so is the education model proposed by Aoun. Without conceptual mastery, Aoun warns:
[Students] may find themselves overly dependent on familiar contexts and inflexible to new applications. They also make lack a deep understanding of their domain, knowing the what but not the why. This blinds them from seeing how their knowledge could be utilized in a different setting.
Thus, the goal is to teach conceptual mastery, the “why” of education, not just the how, because that will allow students to “take the components they have integrated and apply them to complex, living contexts.”
Aoun also recommends the exciting work of Carol Dweck who coined the phrase “growth mindset” to describe ways of thinking that point to our potential to grow (“I don’t know how, but I can learn”) rather than to fixed mindsets (“I can’t do it, I’m just not a math person”).
The growth mindset is essential to nurturing the cognitive capacities of critical thinking and systems thinking because both demand that students cast the nets of their minds on wide, and often unexplored, waters. And it is the key to becoming the most robot-proof person of all – the self-directed, lifelong learner.
Aoun also reminds us that life-long learning isn’t just about picking up new skills. He writes, “by experiencing different situations and contexts, we trigger our emotions, challenge our beliefs, and test the fabric of our minds.”
While it may seem like the education model being proposed here is fixated on STEM and ignores the humanities, Aoun is deeply concerned about keeping the humanities front and center as well.
“[We need to] move beyond the canard that students must choose between an economically rewarding career and a fulfilling, elevated inner life. More than ever before, the capacities that equip people to succeed professionally are the same as the virtues espoused by Cardinal Newman in his paeans to ‘liberal knowledge’ – namely an agile mind, refinement of thought, and facility of expression.
Rather than replacing the liberal arts, Aoun thinks we need to add “an experiential component.” He explains that “this means combining the rigor of traditional academics with active participation in workplaces, laboratories, or volunteer opportunities. For example, an English major might intern with a media company, applying ideas encountered in a class on the technology of text to writing in new publishing formats.” Aoun further explains that “an experiential liberal arts model integrates traditional liberal arts skills with technological proficiencies…History students, for example, could compile digital archives of nineteenth-century black intellectuals in their cities or create networks of historical texts and maps.” The bottom line for all of us who love the liberal arts is this: “the humanities are expanding their digital toolbox. As we expand the scope of what they can do, we have to expand the scope of what we must teach.”
Aoun ends his book by saying: “I believe that when people are given education, they may still be astonished by the changes and mysteries that the future holds, but they will see these as opportunities rather than threats.” While the future is always an unknown, Robot-Proof is a great resource for thinking about how we can best prepare for the unknowns of tomorrow.
In his book, Actual Minds, Possible Worlds, the acclaimed social theorist, psychologist, and educator Jerome Bruner explores the power of literature as a pathway to this important ability to imagine new possibilities. Bruner asks us to recognize that the artist, whether the painter or novelist, “creates possible worlds” that we, the viewer or reader, can inhabit. Bruner says that the purpose of the humanities is to cultivate hypotheses about our world which can lead to new ideas, whether a new scientific theory or new business or even a new political order as seen in the founding of America.