Room for Debate about Homework

I'm honored to appear in The Room for Debate at the New York Times today, on the topic of "Should Parents Help Their Children with Homework?"

The timing is great, as I'm headed out to the East Woods School in Oyster Bay, NY in about fifteen minutes to talk about that very topic this evening. That event, by the way, is free and open to the public, at 7:00 PM, so come on down! 

 

 

Hope is the Thing with Feathers

I made my annual pilgrimage to the Albert Schweitzer Fellowship Leaders in Service Conference this weekend, and as happens every year, I'm feeling energized, hopeful, and optimistic in its wake. I became an Albert Schweitzer fellow in 1998 (Tim became a fellow in 1997) and we've continued attending these conferences, interviewing and mentoring fellows, and generally supporting the Albert Schweitzer Fellowship, mainly because it makes us feel good. It gives us a regular great reminder that no matter what the bobbleheads on the news say, there are still many people out there who are set on doing good in the world. 

I was there to give a talk on raising motivated, yet caring, and empathetic kids, and I told the story of Mother Mallard, a duck who unwittingly helped the entire faculty at Crossroads Academy teach a few lessons in character, temperance, and kindness in the spring of 2013. I'm telling her story again, as it originally appeared at The Atlantic, both because I promised I'd post it for my session attendees, and because I'm always a fan of a good tale about a duck. 

When I signed on to teach English at a core virtues school, I had no idea what I was in for. I nodded and smiled in my interview when the Headmaster explained the virtues curriculum, and I parried back with everything I thought she wanted to hear; how I could infuse my lessons on To Kill a Mockingbird with discussions about empathy and courage. I may have even quoted Atticus’ line about walking around in someone else’s skin. I figured I could tack on some of that quaint “virtue” stuff before getting to the real meat of the lesson, the academic stuff.

And for the first year I taught at Crossroads Academy, that’s pretty much what I did. I made some empty gesticulations toward the core virtues bulletin board in my classroom and made some token mentions of fortitude at obvious moments in our reading of The Illiad and The Aeneid. I was teaching literature, but I certainly wasn’t doing Aristotle proud.

I mean come on. Character education? Core virtues? I teach English, not Sunday school, and besides, I teach middle school. If I were to walk into my eighth grade English class and wax rhapsodic about prudence and temperance, those kids would eat me alive. It’s hard enough to keep the attention of a classroom full of middle school students without coming on like an 18th-century schoolmarm.

Somewhere along the way, someone must have started dosing me with the character education Kool-Aid, because five years in, I have come to understand what real character education looks like and what it can do for children. I can't imagine teaching in a school that does not have a hard-core commitment to character education, because I've seen what that education can mean to a child's emotional, moral, and intellectual development. Schools that teach character education report higher academic performance, improved attendance, reduced violence, fewer disciplinary issues, reduction in substance abuse, and less vandalism. At a time when parents and teachers are concerned about school violence, it is worth noting that students who attend character education schools report feeling safer because they know their fellow students value respect, responsibility, compassion and hard work. From a practical perspective, it's simply easier to teach children who can exercise patience, self-control, and diligence, even when they would rather be playing outside - especially when they would rather be playing outside.

American schools used to focus on character education and civic virtue. The founders of this country, including John and Abigail Adams, Thomas Jefferson, James Madison, and Benjamin Franklin wrote about the importance of character education in maintaining the new republic. Those founders would likely be horrified by the loss of this goal, as they all cite character education as the way to create an educated and virtuous citizenry. As Gallup polls show that over ninety percent of American adults support the teaching of honesty, democracy, acceptance of people of different races and ethnic backgrounds, patriotism, caring for friends and family members, moral courage, and the Golden Rule in public schools, it seems odd that this facet of American education has disappeared from public debate over curriculum and academic content. The core virtues -- prudence, temperance, fortitude, and justice -- make it into nearly every lesson we teach at our school and every facet of our daily lives on campus. The curriculum we use, designed by Mary Beth Klee, is a non-sectarian education in intellectual, moral, and civic virtues through literature, and can be used in conjunction with any academic curriculum.

This week, I gained a fantastic teaching assistant who has raised my character education skills to the next level, a wise teacher who has illustrated the importance of temperance far better than I -- or Achilles or Macbeth -- ever could.

As the core virtues program uses examples to literature in order to illustrate character, I choose my texts accordingly. In my middle school Latin and English classes, we explore the concept of temperance through discussions of Achilles' impulsive rages, King Ozymandias' petulant demand that we "Look on my works, ye Mighty, and despair," Macbeth's bloody, "vaulting ambition, which o'erleaps itself and falls on the other."

A Mallard duck (Mother Mallard to our students) took up residence on our campus this week. Mallards, or anas platyrhynchos, are also known as "dabbling ducks," and this particular duck has apparently been dabbling in Aristotelian philosophy, because she's presented our students with a real-life lesson in the core virtue of temperance.

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Her nest, made from feathers she's plucked off her own breast and filled with ten eggs, lies about eighteen inches from the entryway to our main building, a path our students take in out of school at least six times a day. Mother Mallard doesn't seem too worried about our students' feet...as long as they keep moving. However, the second those feet stop and one of the children pauses to take a good, long, look, she quacks angrily and abandons her nest. Her first day in residence, she spent more time off the eggs than she did on them, and we realized we were going to have to find a way to teach our students some self-control.

It just so happens that this month's virtue is temperance; stopping to think about our actions before we enact them, giving the best of ourselves, and saying "no" to our weaknesses. The middle school students use the term "temperance," and the lower school kids use the term self-control, but tomāto, tomăto, it's all the same idea.

In Stanford's oft-repeated experiment on self-control, children were faced with the immediate reality of one marshmallow versus the promise of two marshmallows if they can just wait for fifteen minutes. The children who were able to resist temptation and wait fifteen minutes for that second marshmallow had better life outcomes in the form of lower obesity rates, higher SAT scores, and higher levels of education. Self-control itself does not make a kid smarter, or fitter, or more proficient at test-taking, but it's the essential skill hidden within all of these positive outcomes.

Character education is not old-fashioned, and it's not about bringing religion in to the classroom. Character education teaches children how to make wise decisions and act on them. Character is the "X factor" that experts in parenting and education have deemed integral to success, both in school and in life. Paul Tough, author of How Children Succeed, calls that character-based X factor "grit," while educational consultant Dr. Michele Borba calls it "moral intelligence."

When I asked parenting expert Borba to explain why she thinks character education is so overlooked as a vital part of children's success, she wrote, "That's what parents don't seem to get, the hidden values of character traits for success. They see character education as fluff, because that's often how it's taught -- posters and worksheets. Character education needs to be relevant. It needs to be woven in curriculum, not tacked on. We are such a trophy-, SAT-obsessed society, but if parents would recognize the value beyond the humanness, civility and ethics, they might get it."

Here on our campus, our marshmallow is a duck. Our students must weigh their desire for a quick peek at Mother Mallard with the promise of ten ducklings waddling around our playground in 28 days. If everyone, even the youngest, most impulsive kindergarteners, can learn to exercise self-control, we will all benefit.

Next week, Mom Mallard will catch a bit of a break from our students, because they will be confined to their classrooms for a week of standardized testing. Our character education curriculum may not show up as an increase in this year's test scores -- but then again, it could: self-control, after all, is exactly what's needed to put off a video game or a TV show for another 20 minutes to finish reading or studying. Though temperance isn't easily measured with number two pencils and bubble forms, it has the capacity to foster and reinforce the skills those bubble forms do test.

Update: 28 days later, the students' patience was rewarded. We mis-counted, because eleven healthy ducklings were born, and the kids had a day or two to enjoy their company before Mother Mallard led them off to the nearest body of water in the early morning hours. I read somewhere that nesting spots can repeat in subsequent generations, so here's hoping she told her offspring about the kindness of the strangers she met at Crossroads Academy.


Helping Adolescents Who Self-Injure

My most recent "Parent-Teacher Conference" column has been nearly a year in the making. It wasn't until I'd read Dr. Michael Hollander's book, Helping Teens Who Cut: Understanding and Ending Self-Injury, and started spending time with Sarah, who agreed to tell me her story, that it came all came together. I've taught plenty of kids who cut themselves, but I've never felt as if I understood their behaviors and my role in their recovery adequately. Thanks to Sarah and Dr. Hollander for helping me find the words to describe what is too often an unspeakable act. 

You can read the article here

This is Twelve

Oh, dear. This one made me tear up. I don't know if it's because I'm overtired from a hectic week of travel and speaking, or because my copyedits came in last night for The Gift of Failure and I'm kind of afraid to look...it's more likely just that Allison Slater Tate is a lovely, lovely writer.

So without further ado, I present, for your clickthrough and reading pleasure, "This is Twelve." 


This is Eleven

Welcome to the first in our series, This is Adolescence. "Eleven" comes from Lindsey Mead, who writes at A Design So Vast, "One woman's journey to right here." Follow her on Twitter at @lemead.

Enjoy!

Eleven



In the last week of each summer, we traditionally spend a day at a beach north of Boston. Lately, these outings have felt like encounters with the tide. Last year we stood on a sand bar, marveling at the way it shrank under our feet as the tide came in. This year my children built a sand wall and watched it disappear under the onslaught of the rising tide.

Eleven is like this. It is the last visible piece of childhood’s sand as the tide of adolescence comes in, inexorable, welcome, but bringing anxiety in its wake, too. That tide whose approach we watch with both wonder and fear will change the landscape forever. It will dismantle many things even as it makes space for new ones.

Eleven oscillates between closeness and the distance I know she is supposed to be pushing for. Mothering an eleven year old is bringing to life all the academic study I did years ago about the mother-daughter relationship. I’m living that which I studied so closely, and though I understand what’s happening intellectually, it is still emotionally difficult.

Eleven walks a neighbor’s puppy by herself. She is responsible and organized, and lets herself into the house I have never seen, collects what she needs, and returns the same way. It is a small universe that she controls by herself. She also sleeps with four stuffed animals, all of which are dogs. She wants to be a vet.

Eleven can beat me in a set of tennis and can always, every single time, get a soccer ball past me. This summer we went for a run together for the first time and she left me in the dust.

Eleven can wear my flip-flops and is almost my height. She runs a six minute mile and is fluent with technology in a way I will never be. She doesn't have her own phone yet but I know that’s coming soon. She still sleeps with the two teddy bears she’s had since infancy. She likes to snuggle before bed and still says prayers that include “thank you for giving me everything I need and most things that I want.”


Eleven started running cross-country for her school this year, and I can’t watch a race without tears in my eyes. There’s something about watching her go, seeing her take flight, cheering for her sprinting towards the finish line, that makes me cry. A wise reader pointed out the metaphor that I can’t stop thinking about: she’s running away from me, and I’m cheering for her, on her team no matter what, even when I can’t see her.  Though I can’t see the part of the race that happens in the woods, I can imagine it, based on my own experiences (of running cross-country as a high schooler, myself, but also of being an adolescent girl).  Her path and my own feel interwoven, but that identification is largely in my head.  The woods she’s running in, and the tracks she makes through them, are hers and hers alone.

More and more, Eleven is in the woods.  Her world is her own. I have less visibility into what she is doing at school and the use of email and instagram has allowed her to develop friendships I don't know as much about. I trust Eleven and we still have a lot of rules about internet access and social media, but I’m aware of her autonomy and growing privacy. This is just another manifestation of the separation that I know is healthy and right.

This was Eleven’s fourth year at sleepaway camp but the first she was homesick. In the sagging middle week of her 3.5 weeks at camp, there were tearful phone calls and sad letters. Then, as the days towards pickup shortened, the mood brightened, and equilibrium was restored. I can't help thinking this was the last gasp of attachment before eleven pushes off for the other shore, for adolescence and young adulthood, for good.

For now, I will curl up next to Eleven at bedtime and listen to her stories about her day and cherish every minute of time she wants to spend close to me, both physically and emotionally. I can see the tide coming in, and I know what it will bring with it. I’m still looking forward to what is ahead and trying to trust, that like on the cross-country course, though she’s about to disappear into the woods, she will circle around and come back towards me.  She will have a smile on her face as she sprints towards the finish line, and she'll see me standing there, and I hope that will make her glad.

This is Adolescence


A year or so ago, a fantastic series of essays called This is Childhood was published in book form and at the Brain, Child website. I adored these essays, so was thrilled when Allison Slater Tate and Lindsey Mead asked me to be a part of a new series called, appropriately, This is Adolescence.

The first installment, "Eleven," by Lindsey Mead, will go live on Wednesday, October 22, and each week after that, a new essay will appear here and at the websites of the other contributors. Come on by, or visit the other authors' sites, and join us in a celebration of the insanity and wonder of adolescence. 

Eleven – Lindsey Mead
Twelve – Allison Slater Tate
Thirteen – Bethany Meyer
Fourteen – Catherine Newman
Fifteen – Jessica Lahey
Sixteen – Marcelle Soviero
Seventeen – Shannon Duffy
Eighteen – Lisa Heffernan

Remainders: The Rest of My Interview with Steven Strogatz



Response to the Atlantic article, "Teaching Math to People Who Think They Hate It," a look into Steve Strogatz's adventures teaching math to liberal arts majors at Cornell, has been lovely. I've received a couple of emails asking for more information about Discovering the Art of Mathematics, Julian Fleron and his team at Westfield State, so Steve and I thought it might be fun to post the rest of our interview, as well as a link to the scalene triangle straight-cut origami exercise described in the article (Chapter 3 of Discovering the Art of Mathematics: Art and Sculpture).

Steve is a great interview; he loves what he does, and has a knack for explaining the details of that love to other people. I hated having to cut anything he said, but in order to make my word count, I had to chop, chop, and snip, snip.

If you'd like to read Steve's work, and you have not read his "Elements of Math" series in the New York Times, I highly recommend that series of essays as a starting place. Be sure to start with the first one, "From Fish to Infinity." You can also hear him in his regular appearances on Radiolab.

And with that, here's the rest of our interview, with a few liberties made for the sake of clarity.
  


Lahey: What prompted you to teach mathematics to liberal arts majors?

Strogatz: For the past few years I've been growing dissatisfied with the results of my usual way of teaching, which is lecturing. Although quite a few of my students seemed to enjoy my lectures, many of them weren't engaging with the material deeply. Just watching a performance, a lecture, and then doing homework, wasn't enough to get them to learn the subject properly, to master it.

So I’d been toying with the idea of trying some more active form of teaching and learning, but I wasn't sure how to start. One day when I was at the big annual math meeting – the “Joint Mathematics Meetings” where the major mathematical societies come together in January – I was wandering around in the exhibition hall and came across an exhibit that caught my eye. There were three or four young professors from Westfield State who were encouraging people to play math games. They were handing out Rubik's cubes, getting people to play a game called hex, or tying knots, or even dancing and making knots with their own bodies in groups. When I took a closer look I noticed that they had workbooks strewn over their table. These were workbooks that they themselves had written for a "math for liberal arts" course that they'd been teaching for the past few years at Westfield State. These workbooks were so attractive, and so filled with interesting activities for students to do, that I started to think this could be a way for me to try teaching in a style where my students would be more active.

When I talked with these faculty from Westfield State, I was struck by their passion for what they called inquiry-based learning. I found myself coming back to their exhibit, over and over again, over the next few days. I kept bringing other colleagues over to their booth to show them what was going on, to show them how cool and exciting it was. Something about it grabbed me.

And I guess what really clinched it was when Julian Fleron, one of the faculty from Westfield State, told me that they had a grant from the National Science Foundation to spread their ideas widely through the math community, and that they would be delighted to come to Cornell to give us a workshop, to show us how to make this style of teaching a reality in our courses. That was an offer I couldn't refuse. So when the time came to choose courses for this year, I asked to teach a course that was already on the books at Cornell called "Mathematical Explorations." It turns out that a course in this active style of learning, this inquiry-based learning, already existed at Cornell and had been taught for a number of years. But I had only recently joined the math department, having spent the first 20 years of my career at Cornell in engineering. So the course was new to me. I asked to teach it.

In mid-August the Westfield State folks came to visit us and give us that workshop. They showed us how to teach in this style, and how to assess our students’ performance, and also how to approach some of the psychological issues that come up with this population of students, issues like math anxiety and math phobia. They also showed us what it would feel like to be a student in such a class. My Cornell colleagues and I were the students, doing a paper-folding-and-cutting game; the Westfield State folks were our teachers. That was important since none of us had ever been students in an inquiry-based learning classroom. We needed to know what it felt like, to have the right kind of empathy for our students.


Lahey: Your usual fodder, as evidenced by your Twitter feed, is higher math. Do you find teaching a more...elementary level of math interesting? 

Strogatz: Yes, I find it fascinating and thrilling. This population of students is unlike any I've ever taught before. The course I’m teaching fulfills our "mathematics and quantitative reasoning" requirement at Cornell. That's a requirement to ensure that all students in the College of Arts and Sciences are exposed to some minimal amount of mathematical thinking. As it turned out more than half of the students in my class of about 36 are seniors. In other words, they have been putting off this requirement for as long as they possibly could!

It's what you might imagine – these are students who have had some unpleasant experience with math at some point in their education. For the first assignment I asked them to write their mathematical autobiography, detailing experiences that they had both good and bad in their math education up to this point. I also wanted to hear about any teachers who made an impression on them, positively or negatively, and what other subjects they're interested in and so on. I'm still reading through some of those autobiographies now but what's emerging is that many of the students liked math for several years. These are all very bright students but somewhere along the line they got discouraged. Sometimes it was because of a certain teacher or subject. In other cases everything was fine through high school, but when they took calculus at Cornell, something about that class turned them off.

As for teaching at a more elementary level, well, first of all, math is interesting at every level. Elementary school math is just as interesting as middle school, high school, college, or graduate level math. I love thinking about the fundamentals! So the elementary nature of the subject is not an issue.

Besides, what we’re exploring in this class is not particularly elementary! This week, for example, the week that you're visiting, we’ll be investigating ideas in abstract algebra (in the particular, the subject known as group theory) but we’ll be doing it in an unusual way (at least, unusual for a math class): we'll use dance to explore symmetry. Dance may be a bit of an inflated word for what we’re doing (in fact, I was a little intimidated to start teaching about dance, since I'm such a lousy dancer myself). What we’re doing is more like striking a pose. Or moving very slowly from pose to pose, while a partner tries to follow the leader in mirror-image symmetry, or rotational symmetry, or some other type of symmetry.

I have to say that teaching this class has been a joyful experience in a way that no other class I've ever taught has been. I love teaching, and I certainly love teaching students who already enjoy math – don't get me wrong. But there's something remarkable about working with a group of students who think they hate math or find it boring, and then turning them around, even just a little bit.

For example, the first activity that we worked on was what's known as “straight-cut origami.” Imagine a simple shape, say an equilateral triangle, drawn on a piece of paper. The goal is to cut out the triangle with scissors. Except that you're not allowed to cut out the triangle in the obvious way. Instead you have to fold the paper in such a way that you can cut out the triangle by making a single straight cut. For an equilateral triangle this turns out to be pretty easy and everyone can do it. But if you pick a general triangle – a scalene triangle, meaning one where all three sides are different lengths – then figuring out how to fold the paper in such a way that you can cut out the triangle with a single straight cut turns out to be very difficult. Or, at least, not obvious. I had trouble with it myself for quite a while the first time I tried it.

So while we were working on this in class, with the students seated at tables of four, all discussing the problem, showing each other their ideas, things that had worked or not worked, after they struggled with this for about a half-hour it turned out that only one student out of 36 was able to do it. So at the end of the class, when I noticed that there were only about five minutes left I asked "Would you like a hint?" A few students immediately said yes, but then they were drowned out by the rest of the class, which said no!

I was so proud of them. They were having a true mathematical moment. That is, they were deeply engaged with a puzzle that made sense to them, and they were enjoying the struggle, and no, they did not want a hint! They were feeling what anyone who loves math feels, the pleasure of thinking. The pleasure of wrestling with a problem that fascinates you. No one in the class was asking, “what is this good for?” Or "where will I ever use this?” Those are questions that students ask only when they are not engaged.

I told the students to think about the scalene triangle over the weekend and to try it in their dorm room. Over the weekend I started to get emails from some of them expressing the excitement they felt when they solved it. One student wrote: “I am feeling exceptionally accomplished. I have to admit: this math assignment has made my day. I never thought I would ever be saying this.”

Lahey: There has been a lot of talk lately about approaches to teaching math, particularly as it relates to the Common Core State Standards. Do you have any thoughts about the "critical thinking" approach versus the traditional route toward mathematical fluency via math facts and rote execution of concepts?

Strogatz: On the whole I think we usually go too fast in our teaching of math. There's a big rush to cram all kinds of information into the students’ heads, and get them fluent with certain procedures, at the expense of their understanding what they're doing.

But let me be careful here. It's so easy to cast this discussion in black and white terms, to make one point of view seem ridiculous and the other obvious. I don't want to do that, because of course you need to memorize certain things and of course you need to have an understanding of what you're doing.

It'll probably sound like a wishy-washy answer, but I really want both. I want my students to memorize and know basic facts, and I want them to understand what those facts mean, why they're important, where they come up in the real world, how to calculate efficiently and easily with them, how they developed historically, what their connections are to the arts and humanities and sciences and engineering, where they pop up in daily life and in the universe. I want it all and I think students want it all too.

If we just stick to teaching them rote procedures, math becomes meaningless. That's how it's experienced by many people. So I'm definitely against that.

But likewise if we only teach conceptual approaches to math without developing skill at actually solving math problems, students will feel weak. Their mathematical powers will be flimsy. And if they don't memorize anything, if they don't know the basic facts of addition and multiplication or, later, geometry or still later, calculus, it becomes impossible for them to be creative. They can't take the first step, because they have to rely on their graphing calculator, or look something up in a book. That makes for a student who can never achieve the greatest pleasure or success in math, which is to be inventive, to think of things for yourself. It's like in music. You need to have technique before you can create a composition of your own. But if all we do is teach technique, no one will want to play music at all.

Nothing I'm saying here is very radical or surprising to anyone who actually understands mathematics (or any other creative endeavor). If you want to be a great soccer player, you can't just do drills. You won't even want to play soccer if you're just doing drills all day. You have to get out there and play the game, and learn from your mistakes and then practice. Drills have their place, and so does playing the real game.

We do too much drilling in school, and not enough playing of the real game of math. And as with any game, or playing music or making a piece of art, it's doing the real thing that's inspiring. We need to give students more of a chance to do that. And that’s what I'm trying to do in this class. They are actually making mathematics -- in many cases, for the first time in their lives. And they’re loving it. And why wouldn't they? It’s a joyous, glorious experience. At every level. Little kids can make math. It may be the mathematical equivalent of fingerpainting, but it’s still math. Genuine creativity is required at every level.