Rebecca Zook - Math Tutoring Online

A while back, I wrote about how limiting the amount of material you’re responsible for can be a very effective way to reduce math overwhelm.

But this technique doesn’t just work with math. It works for just about anything. For example, Kenny Werner discusses how he overcame his overwhelm in his amazing book, Effortless Mastery.

For months, if not years, Kenny Werner woke up every morning telling himself he needed to practice for five to ten hours that day. Paralyzed by this expectation, he’d frequently go to bed without practicing a single note, feeling like a total failure.

Until he met an insightful piano teacher who gave him a totally new kind of assignment. A simple exercise he only needed to practice for five minutes a day. That was his only duty. Any practice beyond that was just a bonus.

But his new teacher’s five-minutes-only assignment seemed so feasable that Kenny actually did it. And once he sat down at the piano with the intention of practicing for five minutes, sometimes he would practice for much longer. Gradually he learned to practice effortlessly for hours and hours a day—not because he was obligated or he needed to compensate for something, but out of sheer joy. That simple five-minutes-a-day assignment dissolved a huge complex of self-loathing he’d had his whole life.

Before I read Kenny’s book, I believed I was the only person in the world struggled with my own practice expectations. When I paged through Kenny’s book and realized I wasn’t alone, I wept with relief.

Yet while I was still in graduate school, I struggled to put his advice into practice. I was responsible for more material than I could ever thoroughly prepare: orchestra music, chamber music, sonatas, concertos, solo pieces, scales, arpeggios, technique books, exercises, etudes. And no matter how hard I worked, I would go from rehearsal to rehearsal, day after day, never mastering anything. This didn’t help my playing at all.

But everything changed once I got out of school. I started working on a very small amount of material at a time, and this allowed me to go deeper than I’d ever gone before.

What happened is that I decided to take an audition where most of the material had to be memorized. But I was only responsible for preparing a very small amount of material: maybe three and a half pages of Bach, two pages of de Falla, three and a half pages of Saint-Saens.

I had always struggled with memorization. So I tried an experiment. Every day I tried to memorize a tiny little new chunk of material, something I knew I could digest. Every night, laying in bed without my cello, I’d review the new material in my mind before I fell asleep, looking for gaps in my memory. Every morning, I’d wake up and go over the material from memory to reinforce it, before adding on a new little chunk.

Instead of waking up in the morning, looking at my stack of music, and having no idea where to begin or when I’d be finished, I knew exactly what to do every day. Even though I only had a month to prepare for my audition, I felt like I was learning more than I did in all those years of graduate school.

This process completely transformed my playing. And in the end, I performed that audition with a freedom and conviction that I’d only dreamed I possessed.

I wished that I’d learned to overcome overwhelm by limiting my material earlier. But I am so grateful that I found this process.

Related posts:
Dealing with (math) overwhelm (1)
I used to cry myself to sleep over my algebra homework
When learning feels like a forced march
What a Balinese dancing queen taught me about praise and encouragement

I’ve been thinking a lot about the math learning discussed by Malcolm Gladwell in Outliers. In one part, a student takes twenty-two minutes to solve a single math problem. In another, a KIPP student takes twenty minutes to solve a math problem on the board with the help of his classmates .

Obviously, one way to master material is to have more time: at KIPP, ninety minutes of math class per day. Or in my own tutoring, a luxurious hour or more to discuss whatever the student wants to go over without any pressure or grades.

Slowing down and diving deep is awesome if you have time. But what do you do when you don’t have time?

When I was in eighth grade and routinely cried myself to sleep over my math homework, if someone had suggested to me that I spend twenty minutes on a single problem until I got it, I probably would have just cried harder. I, like many other students before and after me, had way too many problems to finish.

More time is not always an option.

However, as a student, I would have been a lot more open to the idea of slowing down and exploring if I only had to do it for a few problems. If I, or my teacher, had given myself permission and said, “Why don’t you just try to solve one of these problems, and take as much time as you need,” I would have been more willing to try diving deep.

I’m not talking about dumbing things down or making students less responsible. My philosophy has two parts. If you give a student a page of twenty math problems they don’t think they can do, they’ll feel pressured to do them all so at least they can show you they tried, but they probably only have time to attempt to do them poorly.

But if you give a student one to three difficult math problems instead of twenty, there’s a much better chance that the student will actually solve the problems. Doing it correctly, once, is more effective than doing it incorrectly or incompletely twenty times. And once they’ve untangled the process correctly, they’ll be in a better position to replicate that process later.

Also, reducing the amount of material can be used as a temporary measure to get a particular student through a rough patch and help them overcome a block.

Related Posts:
Algebra Tears
Break things down so you don’t have a breakdown
When persistence isn’t enough
Failure is not the enemy

Given the counterintuitive new research that has found that certain kinds of praise can undermine student motivation and achievement, I’ve been working over the past year to refine how I praise my students.

Here’s some very specific advice from NurtureShock co-author Ashley Merryman’s blog archive (to read the original, keep scrolling, scrolling, scrolling until you get to the post titled “How not to talk to your kids – Part 4″):

A common praise technique that people use (I know I did it with my tutoring kids… up til a few weeks ago, that is….) is to use a present success to control future performance. For example, if a typically-sloppy child writes an essay that’s atypically legible, a parent or teacher may say, “That’s very neat: you should write all of your papers like this.”

The better thing to have said was, “This is really neat,” and left it at that.

I have been waiting for a year for a chance to try this out with one of my own students. I finally had a chance to implement this a few days ago while tutoring a rising fifth grader online.

He did a particularly neat job of writing out a problem on the online whiteboard, so I told him, “You did a good job of writing that out neatly and lining up the decimal points and the columns.” That’s it. I didn’t say anything about how he should write future math problems.

When he wrote out the next problem much less neatly than the last, I didn’t say anything.

Without me saying anything at all, he scratched out the messy version. And then he started over and wrote out a new, neat version, all my himself.

As a tutor, I am so excited that this style of feedback encouraged him to manage this on his own, without any cajoling or controlling from me — just an objective assessment of what he did well.

And I love having this clear guidance from Ashley Merryman’s archive on how to praise my students without worrying that I’m doing it the wrong way.

Related Posts:
Tips on Effective Praise from Ashley Merryman

What a Balinese dancing queen taught me about praise and encouragement
Praise and Intrinsic Motivation: An Answer?

It dawned on me in 2005. I was in Bali working with a renowned dance teacher every day for two hours to learn an intricate, difficult dance. I realized that if she told me that what I was doing was great, I would do the dance again and again and again for her out of sheer enthusiasm. And in doing it again and again, it would get even better.

After our lesson, I reflected on my response to my teacher’s praise and how I’d responded to criticism in the past. In a flash of self-understanding, I realized: If I’m doing something I love and you tell me I’m doing great work, I will work sooooooo hard! However, if you tell me that I’m doing terrible, I want to stop working and die.

Ever since, I’ve held this realization close to my heart. But now that I’m learning about all this new research about praise, I’m wondering: Is something wrong with me? Am I a praise junkie? Why am I so sensitive to what my teachers tell me?

When teachers have told me that I was doing bad work, or even worse, that “I didn’t have what it takes,” I would spend hours and hours of mental energy processing those statements. If I am so bad at X, how was I accepted into program Y? Am I so bad that I deserve to be placed with other students who really don’t seem to care? If I am incapable of achieving XYZ, how is it that I was able to achieve ABC? And on and on.

But now I’m realizing that those hours of processing negative messages never helped me learn a single note or dance move or improve in any way. In fact, some of those teachers’ discouraging statements led me to spend months or even years avoiding my true heart’s desire—or pursuing my true heart’s desire in utter solitude—out of fear that I was essentially inadequate.

In contrast, when I eagerly danced over and over for my Balinese teacher, I honestly don’t think I was seeking the reward of praise or avoiding the punishment of a scathing critique. I believe that her encouraging praise really fed my own intrinsic motivation. Maybe her praise couldn’t “hurt” me because I was intrinsically motivated. (Sort of like how the Book It Pizza Hut pizzas could never dim my love of reading.)

On the other hand, I notice a pattern when I look at the withering “feedback” that distracted me and discouraged me:
“You’ll never achieve…”
“You will never be able to …”
“You aren’t going to attend school for ….”
“I really don’t see you as [having the career you desire] but [in a completely unrelated career]”
“You think you know how to do X but what you’re doing is not X at all…”

These statements didn’t give me any clear direction on what to do differently to improve! What could I do to achieve my dreams? What did I need to learn to prepare for school? If I really didn’t know a technique or skill, how could I acquire it?

Those statements did not answer those questions. They were just judgment. They did not provide guidance, except perhaps “guidance” to abandon my dreams. (Needless to say, I never speak to my students this way.)

Then I remember my teacher in Bali. She did not come from a culture of excessive praise and self-esteem boosting. I believe in my heart that she really believed that I was doing well. She wasn’t just trying to make me feel good.

But now I realize that when she told me I was doing well, she wasn’t just praising me. She was engaging with me. She was going to continue to help me to grow and improve. But the other teachers’ statements were statements of disengagement. They were no longer interested (or able?) to help me grow and improve.

So maybe what really matters is engagement.

Dancing with my awesome Balinese dance teacher, IGA Raka

Related Posts:
The Power of Praise (#1)
Tips on Effective Praise from Ashley Merryman
Toning Down the Praise: Experiment #1
Toning Down the Praise: Experiment #2 (I am going through praise withdrawal)

In his book Outliers, Malcolm Gladwell spends a whole wonderful chapter discussing cultural attitudes towards learning math, and he wraps up by profiling the Bronx Knowledge is Power Program Academy (also known as “KIPP”).

With high expectations and extra-long school hours (among other things), KIPP takes students from poorest of neighborhoods and gives them a chance to pull themselves out of poverty. Founder David Levin observes that when students leave KIPP, “they rock in math.”

So how do they do it? For one, all students do ninety minutes of math every day. Eighth grade math teacher Frank Corcoran explains:

I find that the problem with math education is the sink-or-swim approach. Everything is rapid fire, and the kids who get it first are the ones who are rewarded. … It seems counterintuitive but we do things at a slower pace and as a result we get through a lot more. There’s a lot more retention, better understanding of the material.

Wow! I totally agree! Corcoran’s astute observations that math classes today have a sink-or-swim approach really resonated with me. I don’t think this approach is acceptable, because it leaves so many students behind. I used to be one of them.

When I revisted this quote, I loved hearing how having more time to go over the material helped both the students and the teacher relax, and how going over it more slowly actually helped them cover more material. That has totally been my experience in my tutoring sessions with students.

A sink-or-swim approach also perpetuates the myth that one is either a “math person” or “not a math person,” because it doesn’t give students a chance to fill in the missing pieces in their prerequisite knowledge, really internalize the material, or explore how they learn best.

Moving slower also helps students who otherwise would think of themselves as “not math people” to grow their math abilities through persistent effort, and creates a world richer for having more mathematicians in it!

Related Posts:
Malcolm Gladwell on Math and Persistence
Doing Fractions “In Chinese” ?!
I think I see a mathematician!

I recently posted about how external rewards can destroy children’s intrinsic motivation, and noted that my participation in Pizza Hut’s read-a-book-get-a-pizza program, “Book It,” did not interfere with my extremely strong intrinsic motivation to read.

However, what actually did come close to killing my intrinsic motivation to read was the crushing required reading lists I had during my first three semesters of college. This experience turned reading from something I loved doing to something to just be endured.

For example, in my first semester of college, I took a required course on the Epic in Western Literature. My amazing teacher taught with great passion, drawing on her experience both as a poet and a scholar fluent in multiple languages.

She was the only professor I had in my undergraduate career who incorporated the arts into an academic class. In addition to our analytical essays, everyone also completed an art project of their own design inspired by what we’d read. My art project, a cello piece based on text from the Aeneid, actually ended up growing into a much larger piece after the class was over.

Despite my teacher’s exceptional amazingness, this class almost caused me to lose my love of reading. I experienced the course as a forced march through the great works of Western literature. In one semester we plowed right through the Iliad, the Odyssey, the Aeneid, Paradise Lost, and Dante’s Inferno. I read it all, but I rarely enjoyed it, and I almost lost my love of reading.

At the end of the year, I actually told one of my friends that I “didn’t like books” anymore. This is coming from a kid who inhaled literature out of sheer pleasure my entire life until I got to college.

What happened? When I had been inhaling books before, they were all books I chose freely. And I moved at my own pace. But I definitely couldn’t choose what I was reading in this course. The course itself was required. And moreover, I felt there was no time to understand anything or connect to anything.

In retrospect, it reminds me of the trips I made to the National Gallery of Art when I was in fourth grade. My teacher tried to cram as much as possible into each trip—upon entering a new room, she’d instruct us to stand by our favorite painting before purposefully marching on into the next room. At the end of the trip, she would proudly exclaim, “We saw so much art!”

I’m sure her intention was to cultivate a love of the arts in her students, but even though I loved art before and after those trips, I don’t remember anything about the art I saw on those fourth grade trips.

I feel like a work of art can be like meeting a person. There’s so much to be revealed. But what is the point of speed-dating artworks? What do you really learn from speedwalking through galleries or speed-reading through epics?

I believe the point is not exposure, but connection. If we read something but don’t connect to it and don’t remember it, does it even matter? The one bit of the Aeneid that I do remember is the piece of text I used in my art project. I spent so much time setting it to music that now it’s part of who I am.

Once, while visiting a small art museum in DC, I stumbled across a Miró painting I never dreamed I’d see in person, and I was so happy that I actually laughed out loud. The museum guard glared at me—I guess for breaking the silence of the deserted gallery. In my heart, I thought Miró would have been glad I was excited to see him.

I think the whole point is that a piece of art will pierce your heart and help you feel less alone, and move you to laughter and tears.

I wish we were encouraged to digest things more, and had enough time with what we’re learning to get to know it and let it affect us.

Related Posts:
Praise and Intrinsic Motivation–an answer?
On Stickers
“Simple, but not easy.”

Yay!!! After reading Bronson & Merryman’s thought-provoking article on praise, I really wanted to know about the connection between praise and motivation. So I was excited to find a partial answer in a fascinating post on Bronson and Merryman’s blog (to find the post, scroll down and look for the title “How Not to Talk To Your Kids – Part 2″):

… University of Rochester’s Edward Deci and Richard Ryan…have argued that motivation can be divided into two types – intrinsic and extrinsic.

Intrinsic motivation is when you do something just because you love it – for the sheer joy and satisfaction of the experience. Extrinsic motivation is when you do something for a reward that comes from someone or something else than yourself.

For children, there seems to be some consensus that tangible rewards are destructive for children’s intrinsic motivation. (All those read-a-book, get-a-pizza-party programs may be killing a generation’s love of reading for pleasure.) But the effects of praise on intrinsic motivation seem less clear.

So it seems that the key to make sure that praise doesn’t damage intrinsic motivation is to use it only infrequently and sincerely.

A personal reflection … I was the queen of Pizza Hut’s book-it reading program and it definitely didn’t kill my intrinsic motivation to read. Maybe the dopa/reward I got from reading was so much deeper and stronger than the dopa/reward I got from eating my personal pan pizza hut pizza (with sausage) that my dopa circuits remained strong and intact. ???? Or maybe I am just a weirdo.

Related Posts:
When Learning Feels Like a Forced March
The Power of Praise (1)
The Power of Praise (2)
The Power of Praise (3)
On Stickers

A couple years ago, a friend of mine, who’s a violin teacher, had a huge realization while working with a younger student. He gave his student a dog sticker to congratulate his student for learning something hard. The student got sooooo excited. Reflecting on this, he realized that the sticker gave his student a sense of completion.

No one ever gives us stickers as adults. But how deeply satisfying would it be to get one—to have someone return an assignment to us with a little colorful sticker on the top. To have the feeling that we had really finished something.

After my friend’s sticker realization, I started giving my math students stickers all the time. I believe I did this because I wanted to give my students a sense of completion. And I wanted them to feel that math, like stickers, could be sparkly, colorful, bite-sized, and fun. A source of delight, excitement, pride, and surprise. I didn’t think I was using stickers as a reward—more as a way to celebrate their work.

Now, after reading all this recent research about how using any reward can undercut students’ intrinsic motivation, I am asking myself, are stickers wrong? Am I actually creating a situation where I’m training my students to expect and be dependent on immediate gratification? I wonder if I am preventing them from learning to persist through struggle and confusion without me sitting there ready to cheer them on and give them a sticker at the first opportunity.

I’m not sure I can wean myself off of stickers completely. But maybe I’ll try to give them to my students the same way I’m trying to learn to give praise: intermittently, and only for things that the student actually had to work hard to learn.

But that doesn’t mean I’m going to stop carrying my secret sticker stash around with me everywhere I go.

Related Posts:
Power of Praise (1)
Power of Praise (2)

And one last awesome bitlet from Po Bronson’s praise article. Persistence is not only an act of will, but also “an unconscious response, governed by a circuit in the brain.” Dr. Robert Cloninger at Washington University in St. Louis actually found this brain circuit.

…[This circuit] monitors the reward center of the brain, and like a switch, it intervenes when there’s a lack of immediate reward. When it switches on, it’s telling the rest of the brain, “Don’t stop trying. There’s dopa [the brain’s chemical reward for success] on the horizon.”

… “The key is intermittent reinforcement,” says Cloninger. The brain has to learn that frustrating spells can be worked through. “A person who grows up getting too frequent rewards will not have persistence, because they’ll quit when the rewards disappear.”

First, I wonder how these findings relates to researchers such as Edward Deci (author of Why We Do What We Do)’s work on intrinsic motivation and autonomy support. Despite the fact that dangling a “carrot” in front of someone is supposed to increase their motivation, Deci found that many, if not most, reward systems weaken intrinsic motivation instead of strengthening it. How does the “reward” of praise relate to his findings? If we reward students with praise less frequently, does that strengthen intrinsic motivation?

Related posts: Power of Praise (1)
Power of Praise (2)

I’ve been reflecting for a while why we need to be told that things are easy. I stumbled across Rafe Esquith’s discussion of the same conundrum in his book There Are No Shortcuts. I recommend the whole passage in its entirety (it’s in Chapter 2), but I wanted to share some of the highlights here:

…We have books entitled Algebra Made Easy. Well, algebra isn’t easy. Success at algebra takes hundreds of hours of hard work and disciplined study. I began to identify the problem the first year I decided to teach my sixth-graders algebra. They had mastered all of their arithmetic skills. They had a terrible time conquering algebra.

… When class began fifty-odd hours later, I laid out a better plan. There was a banner stretched across the front of the room proclaiming THERE ARE NO SHORTCUTS. …from that day on, the dream [of life beyond the disadvantaged neighborhoods of Los Angeles] became closer, because that motto changed the way my students attacked their work. It brought a new approach to learning. …We decided to lengthen our school day. … [The students] spoke of sacrifice. … They not only rejected the culture [of everything being easy], they created one of their own.

I haven’t yet seen anyone else write so honestly about how challenging it can be to motivate students to persist when faced with difficult material. And I’m inspired by how Esquith succeeded in challening his students to do something that really isn’t easy. (I also think that this is the only stories I’ve ever read that connects the two things I do almost every day—teaching algebra and playing the cello!)

Thank you, Rafe Esquith, for all the work you do to inspire students to master what is not easy, and for sharing your experience with others.

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