Rebecca Zook - Math Tutoring Online

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 Think I See A Mathematician!”

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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Self-Taught Hero: Pearl Fryar

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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Algebra Tears

I recently posted about Po Bronson and Ashley Merryman’s recent report on the downside of always telling kids to try harder.

As someone who cried herself to sleep over her middle school math homework, I know that trying harder isn’t always the solution.

I believe the real solution is not to try harder, but to try again, differently: with a new tool, or with a different approach, or even just after taking a break to refresh your mind.

Perhaps the reason why some of the Chinese students discussed in the article (or students anywhere in the world) appear to have more of an “innate willingness to work hard” is just because they’ve learned how they learn most pleasurably and effortlessly. Maybe they’ve learned how to create flow states for themselves so they enjoy what they’re doing, instead of just grinding it out.

As a learner, I feel like the most useful thing I can do is examine how I learn best. And when I’m learning that way, it might not even feel like I’m working hard—it might actually feel effortless! From the outside, it might look like I’m a “hard worker,” but actually, I just don’t want to stop, because I’m in the zone.

As an educator, I feel like my own role is to help students learn how they learn best—so they can choose to learn what they want to learn, how they want to learn it, and do what they want to do, how they want to do it. Not just in school, but for the rest of their lives.

There’s always going to be some sort of gap between the way people teach us and the way we best learn. Our task is to find out how to create our own optimal conditions, no matter what we’re given.

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Over on their Newsweek NurtureShock blog, Po Bronson and Ashley Merryman recently posted an awesome article about the downside of always telling kids to work harder.

The article explores a conundrum. In the US, recent research on praise indicates that we should praise students for their process, not for any perceived “innate qualities.” “Process praise” (such as, “I love the colors you used in your painting, can you tell me how you picked them?”) is constructive, because you can control your process and effort. But praising someone’s innate qualities (“You’re such a great artist!”) is not helpful because you can’t control your innate qualities. And kids will do anything to hold on to a positive label—including no longer taking risks that might show the label to be untrue. (For example, only making paintings they think others will approve of, or that would support the “great artist” label.)

Here’s the kicker. In the US, we believe that the amount of effort we put in is something we can control. But in China, where the emphasis is already on effort (a variable that we in the US believe we can control), many Chinese students believe that their ability to try hard is a fixed trait beyond their control.

I thought that the crux of the article was that teachers in China don’t teach strategies. They just tell students to try harder, but they do not tell students how to apply effort more skillfully.

However, I don’t think that this problem is limited to the Chinese educational system—American educators do it too. (The Chinese schoolteacher’s instructions to “try harder” reminds me of Rafe Esquith’s observations that math teachers in the US frequently tell struggling students to “read it again” or “use their head,” even though he’s never seen any teacher get results with these instructions. Which is understandable—they’re not strategic instructions. So Chinese educators are not alone in having this problem.)

To take a step back, let’s consider the research that forms the background for this article’s discussion of education in China: the work of psychologist Carol Dweck. Her groundbreaking research into the effects of praise on children’s motivation is frequently summarized this way: you should praise students for effort because it’s something students can control.

But Carol Dweck isn’t just saying that we should praise kids for their effort—she’s saying that we should praise their process, and also help them explore their process.

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When Persistence Isn’t Enough

I’ve been so impressed and intrigued with Malcolm Gladwell’s observations on the relationship between persistence and success in math. So, at an appropriate moment, I eagerly told one of my students about the woman Gladwell describes in Outliers, who kept trying to understand the slope of a vertical line until she finally got it after quite some time.

“How long do you think she kept working on that problem?” I asked my student.

“I don’t know,” my student said. “Maybe three hours?”

Then it hit me. I want all of my students to cultivate persistence, and some of my students definitely need to work harder. But maybe the woman I was telling my student about wasn’t exceptional because she kept trying. Maybe she’s exceptional because she kept trying and she finally got it.

What if students are already persistent and diligent and still not able to understand the material? Is telling them to persist and try harder really the answer?

When I was in middle school, I was an extremely diligent Latin student. I would dutifully copy out the text we were translating, look up every single word in the dictionary and in declension and conjugation charts, and list my English translation under the Latin word. Then I would randomly try to string the words together into a complete sentence.

For whatever reason, my Latin teacher adored me and repeatedly praised my thorough preparation in front of the class. But wasn’t it completely obvious that I had absolutely no idea what was going on?

Even though she was a world-reknowned Latin scholar who cracked jokes in fluent Latin with her friends at the Vatican, she didn’t seem to notice (or care) that I had no idea how the Latin words worked together to create meaning.

Maybe I wasn’t paying attention. Maybe I didn’t understand her explanations. Or maybe she never actually explained it. Even though I was totally clueless, I got straight As in Latin for three years. But my effort was not enough. I never understood Latin.

It happened to me in other classes too. When I was an Algebra 2 student, I’d work on a math problem until I got totally stuck, and I’d approach the teacher’s desk for help. “You need to try harder to figure it out for yourself,” he’d tell me dismissively, and then send me back to my desk.

Now, some of my students confide in me that when they ask their teacher a question, the teacher responds, “If you had been paying attention when I explained it, you wouldn’t need to ask that question. So shut up and pay attention!” But the student was paying attention, and still didn’t understand!

It’s clear that “trying harder” and “paying more attention” aren’t going to fix anything if the effort is misguided, or if what you’re paying attention to doesn’t make sense in the first place. So why are students chastised to work harder and pay more attention as if those are the only variables in the equation that can be changed? I’ve found that frequently the missing link isn’t more effort or focus, but a better explanation or an alternative version of the procedure.

Students (and teachers) can actually change many variables in the equation. They can get a book that works better for them, ask someone else for help in hopes of getting a better explanation, watch an instructional video, or even switch to a different instructor entirely.

Maybe teachers hesitate to encouage students to explore these alternatives because it might undermine their authority. But it’s to the detriment of many hard-working and attentive students who struggle in silence, mistakenly believing that if they just try harder or pay more attention they’ll finally get it—or fearing that if they don’t, they must be incapable.