Rebecca Zook - Math Tutoring Online

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?

Related Posts:
I cried myself to sleep over my algebra homework
Algebra Tears
“I Think I See A Mathematician!”

In line with Carol Dweck’s recent findings that excessive praise can actually undermine student motivation and achievement, I’ve been working on praising my students less in general.

I’m realizing that a lot of what was coming out of my mouth was praise. So now that I’m praising less, I’m also talking less overall. This has created some interesting new situations in my tutoring sessions.

Example: I was walking through an algebra word problem with a rising 9th grader, when she announced, “I think I know how to do this,” took the paper out of my hand (politely), and proceeded to confidently approach the problem in a way I’d never seen before.

I let her run with it and sat back and waited to see what would happen. When she started to get off-track, I jumped in and explained what had gone awry, and then we finished solving the problem together her way with my corrections/explanation.

After we finished solving the problem the way she had invented, I demonstrated the “math class” way of solving it. I told her that “her way” was totally valid, but I wanted her to know both ways in case her teachers only wanted to see the “math class way.” I asked her which way made more sense to her, and she said, the one she had made up herself.

I thought about this a lot after we had finished. Isn’t the whole point of learning math to become a confident problem-solver? As a Kaplan teacher, I was trained to model a fast, effective way of solving the problem, and then encourage students to recognize similar problems and solve them the exact same way.

I think that’s a great way to approach timed standardized tests, when you don’t have the luxury of experimenting. Yet without realizing it, I think I’ve unquestioningly incorporated that philosophy into my own tutoring style.

I’ve always thought that my “strength” as a tutor was my factual proficiency. But there have been times when, faced with an unfamiliar problem, I honestly wasn’t totally sure of exactly what to do. So I’d say, “Hm, let’s try this… let’s work backwards… does this match the way they did it in the example? How can we test our hypothesis?… That didn’t work, how about this other approach?…”

I only felt comfortable doing this in front of students with whom I had a mutual trust and camaraderie, and at the time, I would have preferred to have understood everything in advance. But what if that kind of tutoring, the let’s-try-this-and-see-if-it-works kind, was the most beneficial of all?

There is definitely a time and a place for jumping in and showing a student exactly what to do. I mean, what a relief, right? Algebra tears no more! But what about all those times, facing a homework assignment or even a confusing test problem, when it’s something no one has modeled for you yet? I’m starting to think that part of what I need to model is a willingness to experiment in the face of the unknown.

(Extra thanks to Maria Droujkova of the Natural Math blog for inspiring me to reflect on this topic.)

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

I Cried Myself to Sleep Over My Math Homework
Tips on Effective Praise from Ashley Merryman

After my last post about how I used to cry myself to sleep over my math homework in middle school, one of my friends wanted to know, when did math start to make sense to me again?

Two words: Nancy Oliver.

My amazing ninth grade geometry teacher.

Nancy taught in a classroom where a former student had painted a colorful mural of the trig mnemonic “SOH CAH TOA” as a tribute to her on the back wall. In her room, I felt relaxed, focused, and safe. I had just spent three years of middle school algebra feeling panicked, utterly frustrated and incompetent in the math department. But with her instruction, I finally felt like math was something I was completely capable of doing.

How did she do it? Like any good teacher, she showed us what to do, and then gave us a chance to do it. At the beginning of each class, she’d demonstrate a new type of problem. Then, after answering our questions, she’d assign practice problems so we could practice what she’d just shown us. With her, even challenging proofs seemed like enjoyable puzzles to figure out. My brother and I still talk about what an amazing math teacher she was, over ten years after we took her class.

But when I reflected on my friend’s question, I realized something I’d never thought of before. Nancy Oliver, the only math teacher I had from 6th to 12th grade who was a woman, was also the only math teacher I had from 6th to 12th grade who really made sense to me. Coincidence?

Obviously there are some great male math teachers out there. I’ve worked with some of their students (Byron Parrish’s, at the Winsor School), I read their books and watched documentaries about them (Rafe Esquith), and I follow their blogs (Sam J. Shah). I was just never lucky enough to actually have one of them as a teacher myself! (Disclaimer: I also know from experience there are bad female math teachers out there.)

Maybe my personality and teaching/learning style was just more compatible with Nancy than with any of my other teachers. But it’s also possible that the fact that Nancy was a woman was a big part of why math finally started to make sense to me, a girl, when she was my teacher.

Maybe the secret ingredients were:

I felt completely comfortable asking her for help—more comfortable than I did with any other math teacher. I never, ever felt stupid or ashamed, no matter how confused I was. (In comparison, I often felt embarrassed asking my male teachers for help, even though I knew most of them wanted to be patient and kind with me.)

I understood her explanations. Nancy consistently explained things to me in a way that made sense to me. (I often felt discouraged even approaching my male math teachers for help. Not only did that mean I couldn’t figure it out by myself, but also, their explanations didn’t clear up my confusion as consistently as hers did.) It’s possible that Nancy approached math in a particular way as a woman that made it easier for me as a girl to understand her. Or, maybe she just had a larger repertoire of explanations than my male math teachers did.

She was a role model to me. Maybe I thought—even subconsciously—“if this awesome lady can do geometry, maybe I can too.”

Now that I’m a math tutor, I feel a special bond with many of my students who are girls. (I bond with my male students too, just over different things, like biking through Boston in the snow.) At first I thought that girly bonding—over the release of Mean Girls, or Betsey Johnson handbags shaped like strawberries, or mutual admiration for each other’s style—was just part of establishing rapport and helping my students feel comfortable. But now I wonder if maybe some girls just feel more comfortable with me as a role model because I’m female.

So, thank you, Nancy Oliver, for being my female math role model, and helping me turn everything around. I hope I can carry your torch!

Related Posts:
I cried myself to sleep over my math homework
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Case study: regaining love of math
Case study: confused by math instruction in a foreign language

Each ADHD student I’ve worked with has been totally unique from any other, so I always adjust my approach accordingly for each individual. But since this is a case study, here are some things that really helped this particular student.

This student first came to me the summer before ninth grade. The previous year she had struggled with focus, especially in math, and at the end of eighth grade, her math teacher had encouraged her to use the summer to review. So we started tutoring over the summer, which was perfect: tons of time, without the pressure of classroom tests or other school-year commitments.

Find the missing gaps and fill them in. Math is so cumulative that missing a single class or even spacing out for a few minutes can make a student feel totally lost! So a big part of our initial work together was retracing my student’s steps and seeing what skills were missing. Once those prerequisite skills were identified, she could master them and move forward.

Focus on conceptual understanding. A lot of students prefer to learn how to do something before learning why it works that way. However, this student craved conceptual understanding. Frequently, once the big picture became clear to her, her face would light up, and she’d exclaim excitedly. Off and running, she’d dive right into the problem, knowing exactly what to do even if I hadn’t told her first. Because this student thrived on big-picture teaching, we focused on that first in each session.

Adjust the curriculum. A easy but helpful psychological “trick”: when we started working together during the summer, we used the textbook for the upcoming year instead of using her old textbook. The material at the end of 8th grade and the beginning of 9th grade is usually the same. But she could start the year confidently, knowing that she’d already mastered the exact material that would be covered in the first few weeks of school. Also, after the school year began, when appropriate, we’d consult an alternative textbook for explanations better suited to her learning style.

In addition to our summer meetings, we continued to meet periodically during the year. After barely four months working together, I was thrilled to learn that my student earned a grade of 108 on her algebra test: 100 plus the 8 point extra credit problem. The highest grade in the class!

Related Posts:
Case Study: Confused by Math Instruction in a Foreign Language
Case Study: Regaining Love of Math
Case Study: Learning Geometry with a Spatial Disability

I don’t think I’ll ever forget the time one of my students broke down and cried during a tutoring session. I was working with a ninth grader who was struggling in her Algebra II class. She had a great teacher, but she’d gone to a “progressive” elementary school where she’d never learned to do long division—apparently the school’s philosophy was that students would just “figure it out.”

We were seated at an enormous wooden table in the beautiful Boston Public Library. Her math book was opened in front of us, and her enormous backpack rested on a nearby chair. I think we were working on completing the square, which challenges many students. We’d been working on it for several sessions, and my student became extremely frustrated.

Basically, she told me she didn’t want to go on, and didn’t want to do any more work. And then she started to cry. I started to panic. What was I supposed to do? How was I supposed to “act professional”? Should we take a break? Weren’t her parents paying me a lot of money to have her do math? I couldn’t just sit here and let her NOT do math!

In my panic, I started to ask her a series of idiotic questions, and the conversation went something like this:
“What will happen if you don’t finish this homework assignment?”
“I won’t understand the material.”
“And then when you take the test, what will happen?”
“I won’t do well.”
“And then what kind of grade will you get?”
“I’ll probably fail.”
“And then what will happen?”
“I’ll probably have to take the class again.”
Wow, talk about encouraging my student to visualize failure! Then I said something even more totally idiotic like, “If you don’t want to repeat Algebra 2, then we need to work on completing the square right now.”

Things continued in this vein until it was time to walk down to the lobby of the library where her parents picked her up.

Afterwards, I was so confused about what had happened. I was afraid that I had totally blown it and that this student would probably never want to talk to me again. And obviously I wasn’t a good tutor for her if she cried on me during tutoring.

I pre-emptively called her Mom and explained that the session hadn’t gone so well and that the student had cried. The Mom actually told me that that was a good sign—that her daughter would only cry in front of someone who she really trusted!

In my next meeting with the student, I apologized and told her I was sorry that I had stressed her out. Paradoxically, from that session onward, my student’s attitude toward math totally changed.

It was almost like the breakdown set the stage for a breakthrough. After weeks of struggling with the completing the square, she found an awesome new way to approaching it using a drawing of a square (more on that later). Even though none of my previous explanations had clicked, this approach made immediate intuitive sense to her. And we spent another great year and a half working on math together.

Looking back on how I handled her crying in tutoring, I feel like it was one of my lowest points as a tutor. Obviously it wouldn’t have been the end of the world if we took a break, or even if my student ended up repeating the class.

If I could live that moment again, I would have handled it totally differently—asked my student if she wanted a hug, packed up, and taken her to Starbucks. I’m amazed that our relationship wasn’t ruined by my insensitive response to her algebra tears. And I’m grateful to my student, for forgiving me for my ineptness, having the guts to keep going after that session, and teaching me a huge lesson about how to handle breakdowns.

A student came to me this past spring with an unusual proposition. She wanted tutoring because she felt that she’d lost her love of math and she wanted to regain it. (Also, she was already earning Bs in school, but she wanted to learn math without so much stress.) What a really cool reason to seek tutoring! Plus, I was excited to work with a student who was already intrinsically motivated.

Since every student is different, I wasn’t sure until we started working together what would help her regain her love of math. She was already very organized and would come to each session with a plan for what she wanted to discuss.

It quickly became apparent that she really just needed some time one-on-one to go over the things she had questions about. The way that her classroom teacher explained things wasn’t always the way that made the most intuitive sense to her. (This isn’t unusual, considering that every single human has a unique way of approaching their own learning).

Another thing that worked was introducing alternative ways of thinking about particular math concepts. This student was great at evaluating what options worked best for her. She’d explain which approaches made total sense and which ones really didn’t help her. She’d also use her synaesthesia to create her own mnemonic devices.

This student would tackle tough problems with gusto. Once, after she cracked a particularly challenging problem, I drew a star with shining rays next to her final answer to show how proud I was. We jokingly named it “The Star of Vanquishment”—vanquishing seemingly impossible problems! This became a running joke. We’d draw it when we felt like we needed inspiration to get through something unfamiliar, or to celebrate when we solved a tough problem.

My student’s school year ended later than any other schools in the area. I was concerned because before I’d committed to working with her, I’d made plans to be out of town for a music festival during her final exams. So she was one of the first students to test-drive my online tutoring technology with me.

During our final session online, she told me that her past three quiz grades had been an 100, an 103, and a 93—“but the 93 was the highest grade in the class on that quiz.” I was so proud of her!

Most importantly, it seemed from her confident and enthusiastic attitude that she had regained her love of math, or at least was well on her way. Overall, I think the “secret ingredient” here was just supporting her and personalizing her instruction in a relaxed and encouraging environment.

Related Posts: Case Study: Learning Geometry with a Spatial Disability
Case Study: Confused by Math Instruction In a Foreign Language

One of my favorite success stories was a star hockey player who was failing geometry because he had a spatial disability. For many people, geometry is very intuitive because of the diagrams, but for this student, reading diagrams was extra difficult.

One of the first things I tried with this student was using erasable colored pencils to label different parts of the diagram in different colors. I hoped the different colors would help him distinguish different parts of the diagram, un-jumble them, and process the information better. But he didn’t seem to be into the colored pencils, so we stopped using them after a while.

However, I knew he must have excellent kinesthetic-spatial intelligence in order to be such an awesome hockey player. I mean, he specialized in creating and responding to vectors on ice, right? So I tried to talk with him about visualizing things in motion. I would tear up pieces of notebook paper and create animated versions of the diagrams by moving the pieces of paper around.

In the end, I think the teaching strategy that helped him the most was just really breaking down the geometry diagrams. I realized that he was missing a lot of crucial information about how to interpret diagrams that most teachers probably never explain, most likely because it seems so “obvious.”

For example, someone without a spatial disability would look at a diagram of a triangle and just infer that if a number is tucked inside an angle, then it is the measure of that angle. Similarly, it would be easy for them to intuit that if a number is next to a line, then it’s the measure of that line.

But because of his disability, these things weren’t obvious to my student, and no one had ever explained them to him before. So we filled in the missing pieces. We broke down the different parts of those diagrams so he’d know exactly what to look for and which numbers affected which part.

The awesome part is that after a couple months, he went from failing to getting As and Bs!

Related Posts: Case Study: Regaining Love of Math
Case Study: Confused by Math Instruction in a Foreign Language