Rebecca Zook - Math Tutoring Online

“It has been a long trip,” said Milo, climbing onto the couch where the princesses sat; “but we would have been here much sooner if I hadn’t made so many mistakes. I’m afraid it’s all my fault.”

“You must never feel bad about making mistakes,” explained Reason quietly, “as long as you take the trouble to learn from them. For you often learn more by being wrong for the right reasons than you do by being right for the wrong reasons.”

-Princess Reason in The Phantom Tollbooth by Norton Juster; illustration by Jules Feiffer

I’ve recently been working with a student who frequently beats herself up for making mistakes. Today I paraphrased this quote to her and explained that it’s okay to make mistakes as long as you learn something from them. She listened, but I wasn’t sure if it had sunk in.

Later in the session, *I* made a mistake, and I jokingly berated myself about it. She matter-of-factly responded: “it’s okay to make a mistake as long as you learn from it,” and smiled at me.

That’s when you know they get it. When they tell you what you told them.

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A while back, I was working online with a younger student on a math problem that was challenging for him. He was getting frustrated.

“Look, kiddo,” I said (or words to that effect), “when you’re doing something and it feels hard, it doesn’t mean anything is wrong with you. It just means that you’re learning something challenging. Everyone feels that way when they’re learning something new that’s hard. You’re not alone.”

My student got really quiet. There was a long pause.

“Thank you for that,” he said quietly.

I wasn’t expecting such a solemn response, and I wasn’t expecting gratitude, either. But then I realized—maybe no one had ever told him this before! Maybe every other time he had struggled over something new, he’d thought he was defective or inadequate.

I brought this up when I was talking shop with a friend who also teaches. She shared a similar story about having a new piano student break down in tears at his first lesson with her. When she mentioned this to the kid’s mother, the mother brushed it off and just said, “Oh, yeah, he’s been crying through all of his piano lessons for at least a year.”

But when the kid cried, my friend took it upon herself to ask him why. He talked to her about how he was frustrated and talked about what he’d rather be doing than playing piano. They had a whole discussion about stuff that, apparently, everyone else had ignored or glossed over.

Coincidentally, after that talk, he never cried again in a lesson with my friend, and ended up being one of her best students.

How can we make kids okay with things being hard? I think it helps to state the obvious, even if it seems … too obvious. It’s normal if something feels hard. Or, If you’re crying, something’s wrong and maybe we should talk about it.

As adults, it’s easy to forget that things that now seem obvious to us were not always so clear. But at some point, someone explained these things to us, or we figured them out the hard way, on our own.

Sometimes I’m afraid to tell my students these obvious things because I’m worried they might think I’m being cheesy or meddling in their emotions. But it hasn’t happened yet, which leads me to believe that they really need to hear this stuff.

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I was really struck by Oliver Sacks‘s description of a recovering stroke victim in his June 28th New Yorker article, A Man of Letters.

Sacks describes a letter he received from writer Howard Engel in early 2002. One morning, Howard woke up feeling fine. However, the newspaper now appeared to be printed in a foreign language.

After determining that what he was experiencing wasn’t actually a practical joke, Howard realized he had suffered a stroke. The diagnosis was “alexia sine agraphia”: Howard could still write just fine, but he couldn’t read.

The article insightfully explores how, even though we think reading and writing are part of one seamless whole, they actually involve very different neurological processes. But my favorite part of the article describes Howard’s rehabilitation, which involved keeping a journal of his life in the rehab hospital:

Occasionally, with unusual words or proper names, Howard might be unsure of their spelling—he could not “see” them in his mind’s eye, imagine them, any more than he could perceive them when they were printed before him. Lacking this internal imagery, he had to employ other strategies for spelling. The simplest of these, he found, was to write a word in the air with his finger, letting a motor act take the place of a sensory one.

Increasingly and often unconsciously, Howard started to move his hands as he read, tracing the outlines of words and sentences still unintelligible to his eyes. And most remarkable, his tongue, too, began to move as he read, tracing the shapes of letters on his teeth or on the roof of his mouth. This enabled him to read considerably faster… Thus, by an extraordinary metamodal, sensory-motor alchemy, Howard was replacing reading by a sort of writing. He was, in effect, reading with his tongue.

First, Howard’s determination to regain his ability to read, even through seemingly strange methods, is totally inspiring. But his experience also made me wonder if multi-sensory learning is hardwired into our humanity.

We’re socialized to learn primarily by sitting, listening, reading, and writing with a pen or pencil. Other ways of learning—through song, dance, movement, or writing words in the air with your finger, are frequently regarded as kids’ stuff.

Sure, it’s fine to rap about the multiplication tables, but rapping or singing to remember material isn’t encouraged in during medical or law school! Adults are supposed to learn quietly, politely—invisibly.

Or multi-sensory learning methods are viewed as a back-up plan—something to try when nothing else works, even though active, multi-sensory learning seems to work a lot better than the passive kind.

The relative ease with which Howard, in his late 60s or early 70s, found multi-sensory ways to read again—by tracing words in the air with his finger or moving his tongue as he read—suggests that the instinct to use all of our senses to learn is somehow essential to who we are as human beings.

Three months ago, I acted out what the different parts of the brain cell do with one of my students to help her remember. I still remember the roles of the dendrites, axon, and synapses. If it had been written on a flash card, I probably wouldn’t remember any of it.

What if multisensory learning is actually plan A, and it’s just been socialized out of us?

Image by Lev Yilmaz for NPR.

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I love this example of a growth-mindset message!

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A few years ago, I was tutoring a ninth grader who was struggling in her geometry class. Her teacher’s teaching style didn’t mesh with her own learning style, and she also had a lot of test anxiety, so even when she began to master the material, it wasn’t yet showing through on her tests.

As we worked together, I observed my student slowly replacing her overwhelmedness with genuine interest and enjoyment. She started tackling difficult proofs, and her eyes would light up with excitement and understanding when all the pieces fit together. We were a few months into the long-term project of slowly building up her understanding when her dad made a decision, without my input, to pull her out of her geometry class because she was “in danger of failing.”

Even though my student understood the material, she got so nervous on the tests that if you just looked at her test scores it looked like she couldn’t do geometry. But she could! She consistently did it perfectly, by herself, in our tutoring sessions! When we reviewed her tests, the material made sense to her once she was outside the testing environment. And I was confident that she could pull up her grades if we continued working together.

In the sessions before her dad switched her math classes, I asked my student what she wanted to do. She told me that her choice would be to switch to another geometry class at the same level, but just with a different teacher. But for whatever reason, she didn’t perceive this option as being available to her—I’m not sure if it was a scheduling issue, a political issue, convenience, parental pressure, or something else.

What her dad decided to do was switch her into a “problem solving” class. My student and I met one last time after she switched into this class. Her book made me want to cry—it was a bunch of reasoning problems about things like Corey the Camel carrying bananas across the desert. (I’m serious. It really had problems featuring Corey the Camel.) The material was basically elementary-school level—no algebra, no geometry. Just simple word problems. Maybe the geometry class was 15% too hard for her, but this “problem-solving” class was about 100% too easy for her.

After that session, I did something I’d never done before. I wrote an email to the dad, explaining as diplomatically as possible and at great length that I really didn’t think this new class was appropriate for his daughter. I explained how much his daughter loved working on Geometry and was learning a lot even if she wasn’t yet testing well. And I expressed my concern that this class would limit her in the future, since basic algebra and geometry were prerequisites for so many other disciplines.

I wrote, wouldn’t it be better for her to take geometry and learn some geometry, even if she got a “failing” grade, than for her to take a class where she would learn nothing at all?

Her father’s response was vituperative. How dare I suggest that he allow his child to “fail!” And I never saw either of them again. I honestly don’t know how I could have handled this differently, but my heart still breaks for that student.

In comparison, another student’s family handled the perceived threat of failure very differently. I was working with a ninth grader who was struggling with Algebra 2 because her elementary school had failed to teach her basics like long division (she was supposed to “figure it out for herself”.) I believe when we started working together she was failing the class.

I was extremely proud of how hard this student worked, and she finished the year with either a low B or a high C. At the end of the year, her algebra 2 teacher suggested that she consider voluntarily repeating the class, just to strengthen her skills before moving on to more advanced math.

My student chose to repeat the class, even though she felt at least a little bit embarrassed to be the only sophomore in that class full of freshmen (at least I figured this was the case since she joked about it). She chose to learn instead of to look good. And her parents supported her. I was so impressed with her integrity.

By the end of her second time through algebra 2, the material that had brought her to tears the previous year did not phase her at all. But I think about the other family,
and how they didn’t want to let their daughter fail. Did that student ever get another chance to love geometry? Was she stuck in remedial math classes for the rest of high school? What did she did she do for her math requirements in college? I wish I knew. I hope she got another chance, instead of internalizing a message that she “couldn’t do math.”

Why do we protect our kids from failure, even to the detriment of their own learning?

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I’m super excited about this New York Times Magazine article about building a better teacher.

In it, the author explores a paradox. Having a great teacher maximizes a kid’s academic success more than any other factor. No other policy or practice—rigorous standards, standardized testing, phonics, smaller class size, more parental involvement—even comes close.

However, the current debate about education policy seems to completely ignore this fact. The logic goes, if teachers aren’t up to snuff, they should be fired, because teachers are either good or bad, and a bad teacher can never become a great teacher.

Doug Lemov, one of the main subjects of this article, shows that being a great teacher is not a function of one’s charisma; it’s not a fixed, intrinsic trait. Anyone can learn how to become a a great teacher.

Lemov has spent years studying superstar teachers, breaking down their technique like a football coach analyzing effective plays. He’s dedicated his life’s work to identifying the superstars’ common practices, creating a language to describe these practices, and helping both new and veteran teachers adapt these practices of champions.

For years, “Lemov’s taxonomy” was primarily available in xeroxed, samizdat-style copies passed around the educational community. But now his work is finally available to everyone. His new book, Teach Like a Champion, clearly explains how to immediately start implementing the techniques of these superstar teachers in your own classroom.

I’m halfway through reading Teach Like a Champion and look forward to reviewing it here, so watch this space!

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Community facing a protracted, draught-induced famine? Family struggling to subsist on one meal a day? Forced to drop out of school because your parents can’t afford the $80/year school fees?

Build a windmill.

That’s what William Kamkwamba did at the age of fourteen.

After surviving a five-month famine, Kamkwamba was determined to find a solution. Inspired by a picture on the cover of a library book, Kamkwamba built a windmill out of trash and scrap metal–even though he had barely any resources, his community ridiculed him as a crazy man, and there wasn’t even a word for “windmill” in his language. His windmill brought electricity to his village and powered an electric pump, allowing his family to consistently irrigate their fields and squeeze and extra growing season—and an extra harvest—in every year.

What makes Kamkwamba’s story so exciting is how he figured out his windmill totally by himself. But I wish we all learned in school how to make sustainable energy sources out of trash!

On the other hand, I wonder if Kamkwamba would have built his incredible windmill if he hadn’t had to drop out of school. It seems like that period of “empty time” really gave him space and drive to explore his dream.

That said, I am thrilled that Kamkwamba is now getting an awesome education at the African Leadership Academy, a pan-African high school in Johannesburg.

You can read all about Kamkwamba’s truly awesome triumph of persistence, determination, and self-education in his book, The Boy Who Harnessed The Wind.

Also, Kamkawamba has a great sense of humor that doesn’t always come across on the printed page. You can get a little taste of how funny he is in this clip where Jon Stewart interviewed him on the Daily Show.

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A little while ago, I was working with a fifth grader on a problem that challenged her. In the middle of the problem, she looked up at me, smiled, and said, “I’m struggling, but that’s OK. My teacher told me that mathematicians struggle.”

What an exciting moment! I am so glad that my student has a classroom teacher who is teaching her that struggling doesn’t mean that you’re “stupid,” and to persist in the face of a challenge!

My student also told me that when she was eager to stand up and give the answer to a math problem, her teacher said, “I think I see a mathematician!” I’m thrilled that this teacher is encouraging her students to identify themselves as mathematicians—people capable of deeply engaging with mathematics!

Thank you to Choco Leibniz for creating and sharing this beautiful, inspiring image of mathmaticians! The Famous Mathematicians are from left to right, top to bottom: Euclid, Boole, Al-Kwarizmi, Newton, Leibniz, Turing.

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Self-Taught Hero: Pearl Fryar

A Man Named Pearl is one of the most inspiring documentaries I’ve seen in a long time. The son of a sharecropper, Pearl Fryar wasn’t able to buy a home in his small town’s white neighborhood because prejudiced neighbors believed he, as a black man, “wouldn’t keep up his yard.”

In 1984, Pearl decided he wanted to try to win the “Yard of the Month” award. With no experience, no training, and using plants that had been thrown in the garbage, Pearl taught himself topiary sculpture and created a spectacular, whimsical, and completely original three-and-a-half-acre garden in Bishopsville, South Carolina. Take that, Edward Scissorhands!

Since he began his garden in 1984, Pearl has become a leader in his own community and recognized throughout the international art world for his unique and compelling vision. Now in his late 60s, Pearl continues to maintain his elaborate plant sculptures and welcomes visitors from his garden from around the world.

I’m really interested in self-directed learning, and Pearl Fryar has got to be the ultimate example–teaching himself a brand-new skill to execute a huge solo project! As a tutor, I’m really trying to teach my kids how to direct and customize their own learning when I’m not around. Ultimately I hope this helps them to find their passions and pursue and create what they really want. Pearl Fryar’s example of self-directed learning is extremely inspiring to me.

Pearl also spoke passionately about encouraging kids, especially the ones who might not be doing so well in school. “If you tell a kid by third grade that they’re not going to achieve at a certain level—I think that’s terrible.” Pearl lives the message of, “There’s always gonna be obstacles. The thing is you don’t let these obstacles determine where you go.”

One of the things he said that really struck me was, “Horticulture people come to my garden and say, ‘You shouldn’t be able to do that.’ And I’d say, “I didn’t know that.” I love it when people come at something from a different angle and find new solutions!

As an artist, I was also really inspired to hear Pearl talk about why he started his garden—not just to express himself, but also “to inspire others to find their creativity to work hard at it.” His advice to others? “Be patient and work hard until you figure it out.” And also, “you can’t be too big.” An amazing example of the growth mindset at work!

Pearl’s own website is here with directions on how to visit (“You just have to come visit me!”) There’s a nice little Q & A with Pearl on amazon. And the DVD of A Man Named Pearl is available on Netflix. I hope someday I can meet this inspiring artist in person!

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Looking back at how I responded so insensitively to my student who cried during our tutoring session, I’m stunned by my in-the-moment lack of compassion. Because… I cried myself to sleep over my algebra homework throughout most of eighth grade! It’s still vivid in my mind: sitting on my twin bed with my algebra book in my childhood bedroom, with its pink hearts and flowers wallpaper, struggling to finish my homework and crying with sheer frustration.

I loved math as much as any other subject until I hit 6th grade and was introduced to pre-algebra for the first time. Isolating for a variable, balancing an equation, the order of operations—none of this made any sense to me. I would go to my teacher for help, and he would patiently try to explain it to me, but it still didn’t make any sense. I made the same mistakes over and over and over without gaining any understanding or insight.

I have absolutely no memories of seventh grade math, but eighth grade math burns in my memory: sitting in class, trying to do the problems, approaching my teacher’s desk, asking him to explain it to me, dutifully nodding even though I still really didn’t understand, returning to my desk, and feeling overtaken by numb despair.

I’m not sure if his explanations didn’t make sense to me because he always explained everything the same way, or if he had a variety of explanations but none of them clicked with my learning style. He was a sweet, patient man, but his explanations did not help me to learn.

Now that I’m a math tutor, when I remember all those eighth grade nights, crying myself to sleep over my algebra book, I ask myself, why didn’t I think of getting a tutor? I never thought about asking anyone but my math teacher for help. I didn’t ask my friends, I didn’t ask my parents, I didn’t ask other teachers. It never even crossed my mind to try to switch to another teacher, or get another book. Why?

Maybe I wasn’t aware that these options were available. Or maybe I felt somewhere deep inside that, as a student who had a passion for learning and a capable reputation, asking for a tutor would be an admission of defeat. Or maybe it seemed “easier” to think of those nights of algebra tears as isolated incidents instead of taking on the “larger project” of trying to find a better solution for myself.

But paradoxically, I think this experience made me a better tutor. Many of the students who come to me might be completely frustrated and far behind. Maybe they don’t have anyone else they can turn to for help. Maybe they’ve never found a textbook that works with their brain. Maybe they are crying themselves to sleep over their algebra homework. Just like I did.

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