Why Study Math?
There are a few answers to this question, some more obvious than others. We study and practice mathematics because it is useful for everyday activities like calculating the tip based on the percentage of the bill, or measuring the length of wood before cutting it. But there is also a deeper reason why we study mathematics, and that is because it is an activity inherently worth doing, just like playing the violin or drawing in a sketchbook.
Francis Su, the former president of the Mathematical Association of America, wants to convince us that studying and practicing mathematics is a path to building virtues, which lead to a flourishing life. In a series of speeches and publications, Su draws from ancient philosophers like Aristotle who understood that “people flourish when they exercise virtue.” Su invites us to see how mathematics, as a core component of a liberal arts education, can foster growth in virtue, which is a benefit to ourselves and a benefit to everyone around us.
Su always begins his reflections by introducing his audience to his friend Christopher, an inmate at a federal prison serving a 30 year sentence. The two became pen pals, and over the years, Christopher has sought Su’s guidance as he studies increasingly advanced mathematics in prison. For Christopher, math is not simply a distraction or something to fill up the time. Instead, math provides him with a source of profound meaning, allows him to achieve goals, and helps him develop as a person. In other words, math is helping Christopher to become a better person.
How Can Studying Math Build Virtue?
Francis Su’s friendship with Christopher has led Su to reflect concretely on how studying math builds virtue. The process of struggling with a problem, while trusting that there is a knowable answer, leads us to exercise hope that truth is attainable and strengthens the perseverance and grit required to solve the problem. Because mathematics is external and (mostly) objective, it requires us to submit to the discipline itself in order to progress, and that fosters both honesty and humility. As we advance in our understanding of mathematics, we can begin to see all kinds of unexpected patterns. This attentiveness can lead us to make all sorts of connections to the world around us, for example, seeing the Fibonacci sequence in flowers and seashells. In making these connections, the beauty of math can foster gratitude for the intelligibility of the world.
Math and Human Desires
Su agrees with classical thinkers like Plato and Augustine that both genuine learning and virtue are powered by desire. We act according to what we love, and what we love in turn shapes the kind of person we become. Su highlights five core human desires that mathematics can tap into: the desire to play, to perceive beauty, to understand truth, to render justice, and to express love. The best education helps to cultivate these desires while channeling them away from ignoble ends (like feeding the ego by winning competitions) and toward noble purposes such as using our knowledge to serve others. Christopher exemplifies this by using his math knowledge to tutor his fellow inmates and help them earn their GEDs.
Mathematics is useful for all sorts of practical goals. Su helps us remember that beyond its usefulness, the study of mathematics invites us into that deeper, sacred work, known as contemplation. Plato famously said that all philosophy is born in wonder, and mathematics shows us that the world truly is a wondrous place.
Here’s a 5-minute speech from Francis Su that outlines his thinking on math and virtue.
Su has also written an excellent book on this subject, titled Mathematics for Human Flourishing. Each chapter considers a different virtue, and Su interweaves his reflection with insights from personal experience as well as insights from thinkers like Simone Weil. At the end of each chapter, Su provides an optional mathematical puzzle that loosely connects to the theme of the chapter. Some of these puzzles are harder than others, and if you get stuck, there are hints as well as the solutions in the back of the book.
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I recently read a sobering cover story in The Atlantic on the rise of anxiety in children. The article’s author Kate Julian begins by looking at the grim statistics from PEW Research on the growing percentage of kids who are diagnosed with anxiety or other related disorders. There has been a steady uptick since the early 2000s, and there is also preliminary research that suggests each generational cohort is more at risk than the preceding one.
After this survey of research, Julian seeks to understand why anxiety has increased, and how to deal with it. One sentence from the article really jumped out at me. Julian writes:
Anxiety disorders are well worth preventing, but anxiety itself is not something to be warded off. It is a universal and necessary response to stress and uncertainty.
In fact, she goes on to note that trying to protect kids from any feeling of anxiety or shielding them from any risk of suffering can undermine the resilience we all need to deal with the curveballs of life.
Can Reading Aloud Help Children with Anxiety?
I’m not an expert, and the question of how to fully deal with the rise of anxiety in today’s kids is above my paygrade, but I do believe one source of help is found in parents reading stories aloud to their kids. I have increasingly grown to realize how important this was in my own life, in helping me to cope with early childhood struggles, and in giving me language to understand and express my own anxieties. My experience of reading aloud fits with the empirical data. In an article for PBS, Deborah Farmer Kris writes about the immense power of reading aloud. She cites several studies that have found clear cognitive and emotional benefits associated with reading aloud to kids, especially when it is the parent who is doing so.
In one such recent study cited in the PBS article, the researchers write that when parents read aloud, their children “learn to use words to describe feelings that are otherwise difficult and this enables them to better control their behavior when they have challenging feelings like anger or sadness.” This makes intuitive sense: stories provide us with language and imagery to make sense of our own experiences, desires, and anxieties. And when parents and children direct attention to the same story, the language and imagery can be a shared basis for dialogue about what children are experiencing.
As it turns out, even the very act of reading can help us (adults and children) to destress. The Telegraph reports on a British study from 2009 that indicates that even six minutes of reading a day can lower stress levels by 68%. Reading is a calming activity, both physiologically and mentally. And I think even just devoting the mental space and time is a helpful way of lowering anxiety. In my opinion, the content of our stories matters too. I believe stories that feature children acting bravely and with integrity and purpose can be an especially profound source of empowerment for kids. And indeed, such stories are able to delve deeply into heavy themes like death in ways children can respond to, which is far more helpful for their development than shielding them from these topics altogether.
In my own life, stories like Where The Wild Things Are, Charlotte’s Web, and To Kill A Mockingbird were all formative. These stories, and so many others, provided me with protagonists I could identify with, who wrestled with emotions I wrestled with, and who learned to face their world with courage and responsibility. And these stories provided my whole family with a shared reference point for our own family culture, helping us all to better communicate with each other.
In the end, reading aloud to your kids will not fully eradicate all anxiety, and to Julian’s point, banishing all anxiety probably isn’t best anyway. But stories are powerful; they inspire us, give us tools to name our fears and process our emotions, and provide a common foundation for dialogue with the people in our life who stand ready to love and support us, come what may.
Harvard University’s Center on The Developing Child has an excellent introduction to the science of resilience, that includes practical advice for how to deal with particularly stressful times.
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As a 90s kid, my introduction to the world of high stakes negotiation was trying to convince my parents to let me play the latest violent game. While I rarely prevailed in these conflicts, (yes to Star Wars, a resounding no to Grand Theft Auto), my parents were hardly the tyrants I felt them to be at the time. And in a surprising turn of events, some of the games I remember most fondly now were the games my parents were most enthused about: educational computer games that were more about creative thinking and problem solving than the shooting and slashing games my friends wanted me to play.
In this post, I’ll share some of the games that I played, and that I recommend because they are both genuinely fun and actually educational. Of course, we at Demme Learning always encourage you to research any game for yourself before deciding to let your child play it. And we also encourage you to decide with or for your child how best to balance screen time with other activities including outdoor play. Having a conversation with your child about not only the amount of time spent playing computer games, but which games can or cannot be played is a great opportunity to explore your family values together.
History: Oregon Trail
In this award-winning classic for kids of all ages, your student will choose a character who will venture out in a wagon with American pioneers to Oregon. Along the way, your student will need to keep track of how much money they have to spend on needed supplies, while making key decisions like how best to cross a river, and dealing with unexpected catastrophes like a venomous snakebite.
You can play the retro version of the game online for free.
Suggestions for Older Students
Consider games like Civilization, CivCity: Rome, and Crusader Kings II which are all turn-based strategy games that teach a wealth of history. Please note game ratings, and decide what is appropriate for your family.
Geography: Where In The World is Carmen Sandiego
The notorious art thief Carmen Sandiego has just stolen a valuable jewel, and the whole world is looking for her. Your student will need to sharpen their geography skills to track Carmen as she galivants around the globe. Your student will be so caught up in the adventure, they won’t even realize how much geography and history they are learning!
Science: Zoo Tycoon II
It’s time for your student to put on their small business owner cap, and design and run their own zoo. This game is a blast to play, and the learning opportunities are rich. To successfully run the zoo, your student will need to do in-game research about what each of their animals need in terms of living environments and diet, while making sure those tigers can’t escape their cage! This game also functions as a crash course in business, letting your student intuit principles about supply and demand, pricing, and leveraging savings to slowly expand infrastructure.
Civics: Democracy 3 (suggested for older students)
In this turn-based strategy game, your student is the newly elected leader of the nation of their choice. Your student will have a budget to maintain, and will need to use a slider bar of policy outcomes to keep enough voter bases happy to prevent being assassinated and to ensure reelection. In the midst of governing, your student will have to deal with random events like natural disasters and make tough split-second decisions about everything from labor disputes to new trade agreements.
Parental Note: Policy decisions can include controversial social issues. This can provide you with great opportunities for discussion with your older students.
Creative Play: Minecraft (suggested for older students)
Let your student build a world of their own imagination, using blocks as the primary resource. Minecraft is a completely open-ended game that allows for maximal creativity.
Here’s a short trailer that gives you a feel for Minecraft’s unique visuals.
Strategic Thinking: Chess.com
Whether your student is a chess novice or a grandmaster, chess.com will provide plenty of opportunities to grow. You can choose to play against the computer or a live human being (including your friends!). You can also watch tutorials or read articles to help you improve your game.
Chess.com is free, but you do need to sign up using an email address or by linking to a Facebook or Google account, etc. You can also pay for more extensive features, like a comprehensive analysis of your games to pinpoint strengths and weaknesses.
Parental note: Because chess.com lets you play against other humans online, you’ll need to decide whether or not you want your student to disable the optional chat window (our recommendation).
(Disclaimer: Demme learning does not own, benefit, or profit from the links provided in this post. Recommendations are the opinion of the author, and do not necessarily reflect the views of Demme Learning. Linked site owners are responsible for information and content on their webpages. We hope to provide resources to parents but encourage parents to do their own research and have family conversations about online safety as well as finding an appropriate balance with screen time and other activities.)
(If your student is struggling to feel motivated studying algebra or geometry, have them read the following about the exciting ways mathematicians aid healthcare professionals to keep us healthy.)
“Ugh! Not more lines on a graph! How will I ever use all this math I am learning?”
Friend, I totally get it! Throughout high school, I would constantly wonder why I needed to study abstract ideas that seemed so far removed from daily life.
Learning math can sometimes feel impractical and unrewarding. But did you know that public health scientists are at this very moment using math to figure out how to protect us during this coronavirus epidemic?
In fact, there’s a whole field in public health called mathematical epidemiology in which researchers use the kinds of graphs you’re learning about to read to answer questions like, “How long before the number of people infected doubles, and how long before that number doubles again?” Answering questions like these can be a matter of life and death, and by providing this data, researchers are able to help everyone from local governments to hospitals prepare for and respond to challenging situations.
What Does It Look Like to Be a Mathematical Epidemiologist?
In this short video, Dr. Lauren Meyers talks about her job, and how her nerdy childhood science camps and college education prepared her to tackle the complex challenges of public health.
One major job of a mathematical epidemiologist is creating mathematical models to provide hypothetical scenarios that can help us make key decisions. In the short video, the
Society for Industrial and Applied Mathematics, high school students talk about how they’re using math models to study disease, decide which recycling program is most cost effective, and even figure out what rollercoaster is the most thrilling!
So, Are You Excited About Math Yet?
Can you picture yourself as a mathematical epidemiologist, fighting the spread of disease? Try developing a math model for yourself – start by figuring out what question you want to answer, then decide what the variables will be for your model, and then determine what mathematical concepts you’ll need to find the solutions.
For more on developing your own math models, watch these short videos:
Note for Parents and Teachers
The Society for Industrial and Applied Mathematics has helpful resources on teaching and evaluating mathematical models.
The CDC has put together some online resources for teaching kids about epidemiology.
Karen Swallow Prior has been teaching literature at the collegiate level for nearly three decades. During that time, she says she’s noticed that
Many readers have been conditioned to jump so quickly to interpretation and evaluation that they often skip the fundamental but essential task of comprehending what the words actually mean.
She notes that this failure to attend properly to the text is even reflected in bodily posture: “Often their first response is to turn their eyes upward in search of a thought or an idea, rather than to look down at the words on the page in front of them where the answer actually lies.” Fortunately, while “attending to the words on the page requires deliberation,” the ability to do so “improves with practice.” Prior’s new book On Reading Well: Finding the Good Life Through Great Books seeks to convince you that “It is not enough to read widely. One must also read well.” And to make her case, Prior weaves together philosophy (particularly Aristotelian virtue-ethics) and close-readings of great books, including well-known works like Jane Austen’s Persuasion and lesser-known masterpieces like Shusaku Endo’s Silence. But Prior does not just seek for us to be good readers, she also wants us to become good people and she believes that good literature is essential in achieving that goal.
Virtue and Storytelling
Discussing virtue in connection to stories might call to mind the kind of overly didactic fables told to kids in an attempt to teach them some “moral” or lesson. This is not at all what Prior has in mind. First, Prior thinks that the very activity of reading is connected with the cultivation and expression of virtue.
There is something in the very form of reading – the shape of the action itself – that tends toward virtue. The attentiveness necessary for deep reading…requires patience. The skills of interpretation and evaluation require prudence. Even the simple decision to set aside time to read in a world rife with so many other choices competing for our attention requires a kind of temperance.
Second, when Prior describes a book as virtuous, she means that it functions as a “vision of the good life,” which means the goodness is found in the world of the book, inseparable therefore from the characters, the plot, maybe even the very literary form of the book, and thus not found in some lesson that can be extracted out of the book. And so her argument is less that reading good books can teach good lessons and more that reading good books can cultivate “knowledge of and desire for the good.”
Literary Criticism and Finding Meaning
The value of literary criticism is that it can help us put into words the various intuitions we often have about the deep meanings of a story. Prior spends the bulk of the book sharing reflections on some of her favorite literary works, helping to tease out the various ideas and insights she sees embedded in those stories. One particularly notable chapter is her discussion of Mark Twain’s beloved and enduring novel Huckleberry Finn. For Prior, Twain’s novel is a rich exploration of the importance of courage in our lives. She writes that “Huck finds his courage, albeit accidentally, through circumstances that come partly from his own doing and partly from sheer bad luck.” The beauty of this story is that it “reflects the way life falls out for most of us most of the time: some choices we face are the result of our own doings, others completely outside of our control, most some combination of the two.”
Twain’s novel also gives us characters who subtly show us what counterfeit courage looks like. For example, The King and the Duke “display ample boldness” but “gall is not the same as courage. Men who swindle, cheat, and steal their way through life, no matter how brazenly, are far from virtuous, and therefore do not have virtuous courage.” Similarly, as loveable a character as Tom Sawyer is, he isn’t an exemplar of this virtue either.
If facing difficulty were the only thing required of courage, then all a would-be hero would have to do is create obstacles to overcome, and voila! – courage would be born. This is exactly what the lovable but foolish Tom Sawyer does.
Courage requires prudential judgment: it doesn’t embrace risk for the sake of having an adventure. But that isn’t to say that courage avoids risk altogether. Prior draws attention to the willingness shown by Jim to risk becoming enslaved again in order to rescue Tom. She writes: “recognizing the risk and facing it for a greater good – a boy’s life rather than his own freedom – Jim embodies the virtue of courage,” and further, that “Jim’s courage is rooted in both reason and conscience.” Thinking through the moral complexity in the novel can be a helpful aid but the key is reading the novel itself, which is ultimately what Prior is hoping her chapter will entice you to do. After all, you can drill a student on the dictionary differences between courage versus bravado, but if you want to inspire that student to want to be or become courageous, nothing beats reading the novel aloud, and allowing her to judge for herself which characters she wants to emulate.
In the end, Prior’s book does two things for the reader. First, it reminds the reader that literature really does matter in cultivating our interior life. She writes that “reading well adds to our life – not in the way as a tool from the hardware store adds to our life, for a tool does us no good once lost or broken, but in the way a friendship adds to our life, altering us forever.” The second thing that Prior does for her readers is, of course, to introduce them to twelve great books that we can read and love as friends who add to our life.
In an article in The New York Times entitled “The Digital Gap Between Rich and Poor Kids Is Not What We Expected” Nellie Bowles argues that “America’s public schools are still promoting devices with screens — even offering digital-only preschools” while “the rich are banning screens from class altogether.” Bowles reports on a study from Common Sense Media which found that “lower-income teenagers spend an average of eight hours and seven minutes a day using screens for entertainment, while higher income peers spend five hours and 42 minutes.”
Parents say there is a growing technological divide between public and private schools even in the same community. [. . .] While the private Waldorf School of the Peninsula, popular with Silicon Valley executives, eschews most screens, the nearby public Hillview Middle School advertises its 1:1 iPad program.
Nellie Bowles reminds us that “it wasn’t long ago that the worry was that rich students would have access to the internet earlier, gaining tech skills and creating a digital divide.” She writes that now “it could happen that the children of poorer and middle-class parents will be raised by screens, while the children of Silicon Valley’s elite will be going back to wooden toys and the luxury of human interaction.”
At Demme Learning, we fully encourage hands-on learning and play structured around “old-fashioned” toys like lincoln logs and LEGO.
In an earlier post, I reviewed The Design of Childhood (Alexandra Lange) which explores this kind of play in detail.
One of the reasons that Lange is such a fan of kids playing with blocks is that this kind of play provides opportunity for imagination and creativity. In lovely prose, she explains that ‘many of our longest-serving toys have no baked-in narrative. Simple shapes and sturdy materials encourage free play and meet the child at her level. She may get in the box, color the box, cut the box, stack her box with a friend’s.’ I really like this language of toys that do not stifle the imagination with “baked-in narratives:” I get the sense that when parents bemoan “electronics” what they are really rebelling against is the (very wrong) idea that kids can only entertain themselves when the toys they are playing with give them explicit parameters for that play.
Nevertheless, we also love technology, which is why we are really excited about our math manipulatives app and our new digital toolbox. Likewise, Lange is not opposed to video gaming. As I noted in my review: “Lange sees games like Minecraft, which is literally a block-building game, as being analogous to physical block play. For example, she writes that ‘today the sandbox is as likely to be the rectangular space of the computer screen, where digital sand, in the form of Minecraft cubes or Scratch block commands, are used to explore building, civilizations, and geography.’”
One of the more lighthearted portions of the New York Times article I quoted above is the story of the mom whose son’s Christmas list was “a Wii, a PlayStation, a Nintendo, a MacBook Pro and an iPhone.” That mom responded, “Kiddo, you’re not gonna get one of those things…Yeah, I’m the mean mom.” This reminds me of the times when my parents would make me put away my Game Boy Advance SP (nineties kids know what I’m talking about, lol) to play outside or read a book. Speaking of “mean” parents, check out this funny parody that the Holderness family made about unplugging the video game consoles in preparation for going back to school. (And honestly, why would you play Fortnite when you could play Super Smash Brothers Melee instead???)
In my blog post Risky Play: A Need of The Soul I explore the insight of the French philosopher Simone Weil on our need for risk, the American Academy of Pediatrics on the importance of childhood play, and CityLab on the emergence of “adventure playgrounds.”
Ethan Demme, CEO of Demme Learning, has a helpful review of the book The Tech-Wise Family by Andy Crouch. Ethan explains that “Crouch isn’t afraid of technology, but he is concerned about potential pitfalls.”
Hey, Mom and Dad! We’re doing the best we can!
Being myself one of those dreaded “millennials” who has been the subject of a seemingly endless popular discourse, I was eager to read Malcolm Harris’ new book Kids These Days: Human Capital and the Making of Millennials. Harris is himself a millennial; the cover of his book proudly marks his birth year: 1988. More importantly, Harris is a well-read and rather attentive cultural critic, and he’s able to deftly weave personal experience with hard data into a compelling description of the challenges that face me and my peers. I want to dig into Harris’ insights and then end the review with some of thoughts of my own.
Harris begins his critique with a depressing view of childhood culture. He writes that we have created “a culture in which children are taught that the main objective while they’re young is to become the best job applicant they can be.”
Here is Harris’ bracing description of childhood in 2018 America:
If they track into the right classes, and do their homework, and study, and succeed in the right extracurriculars, and stay out of trouble, and score well on standardized tests, and if they keep doing all that from age five to eighteen, they’ll have a good chance at a spot in a decent college, which is, as far as you can plan such things, a prerequisite to ‘better life outcomes.’ Of course, the more kids who can do all that, the harder everyone has to work to stay on top.
Two quick notes on that description.
First, Harris’ description of this culture most aptly describes public and private school settings, and yet I’d argue that homeschoolers are not immune to the underlying anxieties and thus to the corresponding conformity of behavior we are tempted toward.
Second, you might have heard about the problem of grade inflation, likely presented as another sign that Millennials are rewarded for little effort in an attempt to boost our self-esteem. Harris rips that explanation apart in one pithy sentence: “It’s a twisted system that aspires to train every student for “A” work, then calls it a crisis when the distribution shifts in that direction.”
Myth-Busting in Kids These Days
One way to approach the book is to focus on the myth-busting.
For example, as an age cohort, we millennials have been labeled lazy: Harris retorts: “no one puts their whole self into their job like a Millennial who never learned to separate work and life enough to balance them.”
Here’s the substance behind that retort:
Technological development leads to increased worker productivity, declining labor costs, more competition, a shift in the costs of human capital development onto individual competitors, and increased productivity all over again.
In plain English, Harris is describing a reality in which we have spent our childhood working our tails off in academics, extracurriculars, and volunteering, in order to get into a college where we can continue that same work, while perhaps picking up an unpaid internship (“students are paying their colleges and working for companies [or the state or nonprofits], and in return both will confirm for anyone who asks that the student indeed paid for the credits and performed the labor”), all in the hopes that we’ll land a good enough job to pay off student loans that we can’t default on. We’re taking out those loans, by the way, because given the price of tuition we literally can’t work our way through school: we know, because despite it being impossible, we are still trying.
Harris has the exact numbers: “In 1960, 25% of full-time college students between the ages of sixteen and twenty-four worked while enrolled. Now it’s over 70%, and 20% of these undergrads are working full-time hours.” It’s sobering to see the statistics and realize that “for all the jokes about students living off ramen, undergraduates are significantly more likely to experience high levels of food insecurity (in technical terms: ‘hunger’) than to live in a dorm.” Anyway, a full two-thirds of us college students have taken out loans because “succeeding at contemporary American childhood now means contracting out hours, days, years of future work to the government, with no way to escape the consequences of what is barely a decision in the first place.”
Another favorite disparagement of the millennials is that we are entitled, largely due to all those participation trophies. Harris observes that “no AYSO-playing Millennial in fourth grade ever owned a trophy factory – we’re not giving trophies to ourselves.” Participation trophies do tell us a lot about the state of our culture, says Harris: specifically “the market for plastic awards has grown with the level of competition, organization, and anxiety about success.” And to be clear, that anxiety begins with parents who are understandably concerned about their children’s increasingly precarious economic future. That same parental anxiety, by the way, likely explains why so many school-kids are over-medicated. Harris writes of this that:
Once again, we’re confronted with the conflict between what nearly everyone will recognize as a social problem (‘too many kids are being medicated to improve their academic performance’) and the very material considerations that weigh on any particular decision (“but my kid is having a really hard time focusing, and the PSAT is only a year away.’)
Speaking of sports, Harris is also no fan of how lighthearted childhood play has been professionalized, becoming just another tool for application-building: “Organized sports have taken the place of self-organized play, and though league games count for their college applications in a way that sandlot ball doesn’t, kids are missing out on the important experience of following and enforcing their own rules.” He also wryly observes that “in the age of rationalized training regimens, autonomy gets in the way of labor development.”
By the time we get to Harris’ review of the research on mental health, we as readers already know the picture will be bleak. Even anticipation, however, can’t soften the blow of a sentence like this: researcher Jean Twenge’s “meta-analysis suggests that depression has increased 1,000 percent over the past century, with around half of that growth occurring since the late 1980s.” We likely all have our own anecdotes about the young people in our lives who struggle with mental health: the jarring thing is to recognize the pervasiveness of this phenomenon and to connect it to the context which arguably creates or at least contributes to poor mental health.
Reflecting on Kids These Days
Harris’ book is, itself, rather depressing, in case you hadn’t noticed, haha. I want to briefly reflect on why I have less of a fatalistic perspective than he does. Unlike Harris, I don’t think we’re doomed to just suffer under the system as it is: we have agency and our choices are meaningful.
As a homeschooler, my childhood was much freer and playful than that of so many of my peers. I spent hours playing outside (remember when kids did that??) or reading novels of my own choosing. Looking back, I can see how privileged my childhood really was. I know that homeschooling isn’t an option for every family – but I think Harris’ book is a good reason to at least consider it. Of course, with the school choice movement, we are also seeing other education alternatives being made more widely available and accessible, choices that challenge the status quo. For example, public charters designed for creativity and the arts, Waldorf schools that seek to nurture the social lives of kids as much as their academic abilities, etc.
Regardless of what schooling option you choose for your kids, I only ask that you give them as much time and permission for unstructured play as possible. Seriously. The System is sucking the life out of kids: fight back with every breath. (I say unstructured because structured play easily lends itself to the taxing schedule of dance on Monday, piano on Tuesday, playdate on Wednesday, etc., and no time for genuine play.) And let that play be filled with risk: the stakes in the real world are high, and risky play is not only more fun (generally speaking), it’s also good, organic preparation for life in general.
The other reason I am less fatalistic is because my college experience has been rooted in the formative liberal arts tradition. I think that choosing to study the liberal arts (English and History in my case) is a subversive act of cultural rebellion. In a society that says education, at all levels, is all about becoming a productive worker, my professors have helped me see time and time again that career preparation is a secondary purpose: the primary purpose of education, like the primary purpose of the family, is to cultivate and form us as human persons, preparing us to live lives of virtue, love, imagination, and service. And don’t worry: my college education has left me well-prepared for work: I’ve helped do research for a published book on mass incarceration, helped teach grade-school and high school students, organized and led summer programming at my local library, and am now working in a salaried marketing job. But even if I were struggling to find gainful employment, I think choosing the liberal arts would still be worth it, just for the chance to remember that the 9-to-5 and the 401k are not all there is to life, that human flourishing is found in relationships and experiences that exist in a realm outside materialistic metrics and managed markets. In short, Harris’ book might tempt you to dissuade your student from studying open-ended subjects that don’t track them into specific careers: I think such efforts would be a huge mistake. Now is certainly not the time to conform. We gotta fight the system!
(content note: Harris’ frustration is often palpable, and consequently his book contains a sprinkling of profanity. I should probably also mention that Harris’ political disposition, inasmuch as it bleed through on occasion, might best be characterized as…revolutionary?)
The Design of Childhood is the kind of book that brings sunshine to your heart on rainy day. The author, Alexandra Lange, is an architecture and design critic, a historian, and a mother. In her book, she draws from each of these core aspects of herself in an illuminating exploration of the material world that children inhabit.
As she writes in the first few pages of the book, “to have a child is to be thrown suddenly, and I found rather miraculously, back into the world of stuff. Dirty stuff, clean stuff, sleepy stuff, heavy stuff.” Lange is the kind of adult who pays close attention to children and who takes children seriously as persons and citizens. You can see this attentiveness present even in Lange’s description of how the book developed: “I studied the landmarks of my son’s territory as it grew from rug to house, school to playground to the whole city (under my supervision).”
The Opportunity of Play
Loving attention toward a child engaged with the material world is the origin and bedrock of education, according to Lange. (Here I am reminded of that stunning line from the philosopher Simone Weil that “attention is the rarest and purest form of generosity.”) Lange writes that “Progressive education in the United States and Europe – education not based on the primer and the lash – begins when a teacher places a block before a child and watches what happens.”
Lange explains the significance of the child playing with blocks, calling this play an opportunity to learn the “elements in the grammar of nature,” elements that need to be “touched, stacked, dangled, and rearranged in order to learn about geometry, gravity, time, and symmetry.” Lange quotes Ann Hulbert, literary editor, who describes the child as “an independent experimenter investigating a world of objects, solving the epistemological problems of space, time, causality, and categorizing,” which is as great a description of the child as budding philosopher as I’ve encountered.
Imagination & Creativity
One of the reasons that Lange is such a fan of kids playing with blocks is that this kind of play provides opportunity for imagination and creativity. In lovely prose, she explains that “many of our longest-serving toys have no baked-in narrative. Simple shapes and sturdy materials encourage free play and meet the child at her level. She may get in the box, color the box, cut the box, stack her box with a friend’s.” I really like this language of toys that do not stifle the imagination with baked-in narratives. I get the sense that when parents bemoan “electronics” what they are really rebelling against is the (very wrong) idea that kids can only entertain themselves when the toys they are playing with give them explicit parameters for that play.
Treat Children as Citizens
Likewise, Lange warns that “our built environment is making kids less healthy, less independent, and less imaginative. Instead of toys that tell kids what to do with them, Lange says that “what those hungry brains require is freedom,” and that requires the rest of us to treat children “as citizens, rather than as consumers.” To treat children as citizens means to make available to them “elements children can pick up and transform into environments themselves” with the understanding that “children are the designers here.”
As a brief aside, it’s worth mentioning that the critique of electronic toys and overly built play environments also has implications for social class structures. Throughout Lange’s book, she sneaks in commentary on how parenting fads, which often involve increased expenditure on kids, tend to originate in upper classes before becoming normative for everyone else. The downside to this, of course, is that families which can’t afford to ‘keep up with the Jones’ can feel guilty, as though they are failing their kids. Lange’s book should help to assuage that unnecessary guilt. And if her book isn’t enough, consider this statement from the American Academy of Pediatrics’ report “The Power of Play” “children’s creativity and play is enhanced by many inexpensive toys (eg, wooden spoons, blocks, balls, puzzles, crayons, boxes, and simple available household objects) and by parents who engage with their children by reading, watching, playing alongside their children, and talking with and listening to their children. It is parents’ and caregivers’ presence and attention that enrich children, not elaborate electronic gadgets.”
Is There Worth in Video Games?
Nevertheless, while the above paragraphs might suggest that Lange is opposed to digital games, nothing could be further from the truth. In fact, Lange sees games like Minecraft, which is literally a block-building game, as being analogous to physical block play. For example, she writes:
Today the sandbox is as likely to be the rectangular space of the computer screen, where digital sand, in the form of Minecraft cubes or Scratch block commands, are used to explore building, civilizations, and geography. [. . .] video games played in sandbox mode, or purpose-built sandbox games, allow the player access to the whole world (the box) at once, and allow her to change that world at will (the sand). There is no preset narrative to force the player to run, hide, or shoot, and no marauders to destroy what she has built. Time is her own. The pleasure is in the creation. [. . .] just as you shouldn’t assume all blocks are the same, you can’t assume all digital games are the same. [. . .] the material is only one aspect of a larger play experience, which may or may not be moderated, scaffolded, or undermined by adults.
Here’s the advice Lange gives on evaluating all play, digital or physical: “To understand the roots of a toy – wood, plastic, pixels, or a hybrid thereof – you have to see its potential in a child’s hands. To understand what children can do, you need to give them tools and experiences that are open-ended, fungible: worlds of their own making.” In addition to Minecraft, another series of digital games that arguably fit Lange’s description are the SimCity games which allow players to design and build cities from scratch. (Here’s a really cool article on what happens when a real city planner plays the game and innovates using his math skills.)
Building Toy Recommendations
At the end of her chapter on blocks, Lange mentions that when she was researching for the book, people often asked her recommendations for building toys. She writes:
“my short list includes Duplo, LEGO’s younger sibling…Tubation, a set of straight, L-, T-, and X-shaped tubes that can be connected into marble runs, musical instruments, and animal skeletons; Magna-Tiles; and Zoob.”
My student is telling me that the Math-U-See curriculum is too repetitive; I’m not sure what to do.
A key component to mastering any new skill or concept is sufficient amounts of practice. But often practice can feel dull and unexciting when there are all sorts of new things out there waiting to be learned. Fortunately, even small tweaks to a routine can help make math feel fresh and exciting again.
Here are three quick tips to keep math engaging.
1) Skip Lesson Practice Sheets
The goal of using Math-U-See is mastery not drudgery. If your student can demonstrate mastery of a new concept, you can adjust the number of problems you assign or skip any or even all of the Lesson Practice worksheets for that lesson. We do still highly recommend doing at least one Systematic Review sheet in order to apply new concepts in the context of previously learned material and to keep skills sharp.
2) Let an Older Sibling Tutor
In addition to this being a fun opportunity for sibling interaction, research suggests it can also be a great way for your students to sharpen their math skills! When students engage in peer tutoring they organize their knowledge improving their own understanding of the material. As a result, they recall it more accurately and apply it more effectively.
3) Supplement with Activities
Instead of doing a worksheet on a particular day, have your student help you bake a cake and have them double a recipe to sneak the math skills in.
I’m considering switching to the Math-U-See program, but I’m worried that your curriculum’s unique sequence will prevent student from having a smooth transition. Can you help?
Depending on what skills your student has developed, this may or may not be a concern. As a first step, we have a free placement tool that will help you determine the most appropriate level for your student.
If there are a few gaps (missing skills or concepts) prohibiting a seamless transition into that level, our customer service team would love to help you figure out how to address that obstacle. They are trained to provide resources and strategies for helping your student get ready for the level that best fits their need.
You can contact them here via email, phone, or live chat.
I don’t understand why the Math-U-See curriculum teaches concepts in the sequence that it does. Can you explain the value of your approach?
The short answer to this is that we want your student to develop a robust foundation of conceptual understanding of basic skills and problem solving first in order to prepare them for the challenges of higher-level math like Algebra 1 and Algebra 2.
For example, we’ve heard countless stories from parents who say that when their student revisited conceptual skills, they were able to master the algebra that had been so difficult for them before.