Rebecca Zook - Math Tutoring Online

When this student first came to me just before the summer between her freshman and sophomore years, her mom told me that the tutor they’d just worked with had told the family that to this student, math was like a foreign language where she only spoke five words.

Somehow she’d made it to the end of 9th grade with Bs in math, but none of it actually made any sense to her. It was like she just knew enough to “get around” – like how to ask where the bathroom was and order a hamburger – but not enough to really understand what was going on around her, or communicate herself.

Once we started working together the summer before she headed into pre-calculus, this student’s mastery, confidence, and grades began to steadily improve. By mid-sophomore year, my student’s teacher mentioned to her that he had to be careful to call on other students because my student always gave the correct answer!

The “piece de resistance” was when my student had to take an oral final for her math class at the end of her 10th grade year. Her teacher gave them five very sophisticated problems that synthesized everything they’d ever learned in new ways they hadn’t seen before. They had unlimited time to prepare, and then each student was asked to explain one of the five problems, picked at random on the spot, in front of the entire class. My student did such a good job that she got an A, and she told me later that she walked out of that class feeling like, “I can do anything!”

When it came time for this student to decide what math class to take after pre-calculus, instead of taking the statistics class that many students take as a way to avoid math, my student opted to enroll in AP AB Calculus. Because math had become beautiful, fascinated, and intrinsically rewarding to her, she wanted to keep exploring and growing.

Here’s how this student and I worked together to completely transform her experience of math from a source of unbelievable stress and anxiety into a source of joy and strength:

1. We worked in an atmosphere of total camaraderie and trust. Our tutoring sessions were totally a lighthearted, safe zone where there was absolutely no judgement. This student was free to ask as many questions as she wanted, go over as many examples as she desired, or go over the same example as many times as she required, without any fear of being embarrassed.

2. We focused on filling in the gaps, while also addressing whatever she needed to learn that week or that day. When we would go over her current material and encounter a gap, we’d keep excavating backwards through the layers of prerequisite knowledge until we found the original misunderstanding. Then we’d fill that in, then the idea on top of that, then the idea on top of that, until we’d build back up through the layers to what she was responsible for learning today. This way she was able to repair gaps in her foundational knowledge, while also staying on top of her weekly curriculum and being prepared for tests and quizzes.

3. We really focused on approaching the material in a way that worked for HER. This particular student craves conceptual understanding, so we would approach the material from different angles until she understood WHY it worked that way. She also loves learning math visually, so we would frequently approach concepts and procedures in a visual way – like FOILing using a box instead of just parentheses – that made the concepts more intuitive for her, and easier to internalize.

During moments like this, she would share observations like, “I don’t know how I lived through math without completely understanding this, because it’s so much easier than I thought it was. My whole childhood with math has been completely relearned.”

As my student’s mastery naturally led to greater confidence and grades, her enthusiasm for math grew more and more. She recently shared with me, “This is actually so cool – when actually I understand it, it’s so much fun!”

Would you like your daughter or son to go from feeling like math is a foreign language to experiencing math as genuinely enjoyable, meaningful, and fascinating?

Just click here to get started with your special application for my one-on-one math tutoring programs.

Once your application is received, we’ll set up a special complimentary phone call to get clear if it would be a fit for me to support your child with math. I can’t wait to connect!

Related posts:
Case study: a 5th grader goes from believing “math doesn’t like me” to singing and dancing about math while wearing a purple tutu
Case study: a rising 8th grader masters her summer math packet
How to multiply binomials using a box (alternative to FOILing)
An easy way to remember how logarithmic notation works

A lock growing out of a tree?

That’s what I found on the trunk of a holly tree in my neighborhood!!

Who did this and what does it mean? It is completely intriguing to me – a door lock that looks like it’s been grafted onto (or growing out of) this beautiful tree!

A lot of times, kids can feel that talking about math is like a door they just can’t open all the way.

Maybe they know some of the words, but really expressing what they understand or asking about what they don’t understand – that might feel like just a tiny sliver, like they can only open that door a crack.

I want to share a powerful question I use all the time to get kids to open up about talking about math.

This is especially helpful when you want your kid to explain something back to you to really check that they understand.

After spending some time working through problems together, I will ask, “How would you explain this to your best friend?”

A lot of the time that is all it takes to get them talking. Instead of worrying about not using the right “math words” or making a mistake, they’re able to connect to the feeling of just helping their best friend.

Occasionally, a student will be totally tongue-tied even with this question – and that’s OK. That usually just means they need to spend more time doing the concept together before trying to explain it to someone else.

Also, kids can even use this technique if they are completely by themselves. This can actually be a bridge towards encouraging students to talk themselves through problems more, like we talked about in my recent post about talking math out when you’re in doubt!

Do you want your kid to experience math as an intriguing, fun puzzle, instead of a monster in the closet?

Is the pain of your kid’s math challenges actually causing you pain as their parent?

Are you ready for high-level one-on-one support?

Just click here to get started with your special application for my one-on-one math tutoring programs. Once your application is received, we’ll set up a special phone call to get clear if my approach would be a good fit for your child.

Sending you love,
REBECCA

Checking out this mysterious holly tree that the lock “grew” out of

Related posts:
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What an awesome way to remember what some of the essential functions look like!

Next time one of my students needs to remember what a function looks like, I’m gonna say, “Let’s DANCE!!”

*Via coeurdewhale at tumblr (I believe this is who created the image, but I’m not sure) and dong6241 at piccsy, a lovely site that showcases user-submitted images and has a great visual image search (blogger’s delight)!

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Gallon Man to the Rescue!
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Self-made heroes: the dancers of Planet B-Boy

No classroom experience can meet every individual student’s needs at all times. Though teachers use a variety of approaches to reach different students and give them multiple chances to “get” the material, sometimes a student’s needs are so particular that a teacher just can’t address them in a crowded classroom.

Recommending a student work with a tutor can allow you to leverage your own expertise. You tell the tutor what you’ve noticed the kid needs to spend more time on. The tutor works with your student to help them internalize material and prepare for tests.

During the process, the tutor will share their observations about your student—information which may help you in your classroom interactions. And this kind of open and specific communication between you and the tutor will make a huge difference for your student.

Good tutors work with you as a team to accelerate and amplify what you’re already doing in your classroom. And while some teachers fear that a tutor will do their student’s work for them, a good tutor will encourage your student to take ownership of their work using specific, explicit strategies.

Here are some suggestions on when a teacher should recommend that a student get a tutor.

The student has major gaps in knowledge.

Maybe a student missed a couple years of math because they went to a bilingual school and were supposed to learn fractions in French. Maybe a student shows up in your Algebra 2 class having never learned long division because they went to a school where they were supposed to “figure it out themselves.”

When a student struggles with major gaps in material from previous grade levels that other students have down cold, a tutor can give a student the opportunity to really learn the foundational material.

Moreover, a student who might never admit to their official teacher how much they don’t know might feel comfortable sharing their problems with their tutor. The tutor can discreetly pass that information on to you, and you can use it to make the most of your classroom interactions with your student.

The student needs more one-on-one time.

If a student doesn’t have a lot of gaps in their prerequisite knowledge but they’re still struggling to keep up with the pace of the class, working with a tutor can be beneficial.

Tutoring can be a safe space for a student to ask more questions than they might want to admit they have in front of their peers. Also, one-on-one tutoring can allow your student time to drill or explore something as much as they need, instead of feeling like they have to “get it” right away.

More one-on-one time has another benefit. Often, when a student gets customized instruction from a tutor, they start to understand how they learn best and become more active learners both in and out of the classroom.

A student needs more differentiated instruction than can be provided in the classroom.

Maybe you already have a strong sense of your student’s learning style, but it’s hard to meet their needs in the classroom. Perhaps you’ve got a student with a diagnosed learning issue or disability, or a student who just marches to a completely different drummer. Maybe they need to experience the concepts in a way that wouldn’t make sense to anyone else in the class.

A good tutor can provide a completely differentiated learning experience, customizing their instruction to the individual student.

For example, a kid who feels pressured by flashcards might do a great job learning his multiplication facts by building squares and rectangles out of Legos. An ADHD kid who struggles to sit through a whole class period might thrive with a tutor who takes frequent breaks to shoot hoops. A dyslexic kid who’s overwhelmed by FOILing binomials might master the technique using a more visual box method.

When a tutor is successfully customizing your student’s learning experience, that student will be able to more effectively participate, contribute, and succeed in your classroom.

Tutoring boomerangs back to your classroom

An example: recently, I started working with a new tutoring student who, at the outset, was disinterested in learning math. But after a few weeks together, she started engaging more in her own learning. She spontaneously made up new lyrics to the tune of Michael Jackson’s “Beat It” to help herself remember that numbers that end in zero are even. A few weeks later, I heard that she was so engaged in trying to answer questions in math class that her teacher remarked, “I think I see a mathematician!”—referring to this same previously disengaged student!

The best kind of tutoring—the kind where you, your student, and the tutor are all communicating openly—can help kids transform. These students become more active self-advocates for their own learning. They participate more, engage more, and ask more questions in the classroom.

When a frustrated or overwhelmed student renews their love of math in part because of the tutoring experience you’ve helped them co-create, they’ll probably bring that new enthusiasm and confidence right back to your classroom.

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On Optimal Challenge

When this student first came to me, her dad was concerned that she had lost interest in learning math. During the school year, it also emerged that the student was in danger of not passing fifth grade.

Here’s what worked for this student:

Supporting the student’s own efforts to be proactive
During one of our first math tutoring sessions, I pointed out to this student that numbers that end in zero are even. Somehow she hadn’t learned that before. To help herself remember this new fact, she spontaneously made up new lyrics to the tune of Michael Jackson’s “Beat It.” They went like this: “Even! Even! Numbers with a zero are even!”

The next time we met, I added to her original lyrics: “Even! Even! Numbers that end in zero are even! So are the numbers 2, 4, 6, 8. They are all even, and they’re all great! They’re even!”

She would sing the zero song whenever this topic came up. Not only did my student create a great way to remember this fact (and inspire me too), but singing also allowed her express her enthusiasm for math and let off a little steam.

Another time, she suggested we create a “Mistakes Log Blog” to help her analyze what mistakes she had made on a test that we were reviewing. I ran with this idea. When she wrote down where she’d made mistakes, the patterns became much clearer to her. In later sessions, she’d refer back to the “Mistakes Log Blog” when analyzing errors.

“Field trips”
In order to make concepts more concrete, we’d take field trips—to my living room, where we’d practice perimeter and area by measuring my rug, or to the kitchen, where we’d measure a round plate to show where the number pi comes from.

At my kitchen sink, we poured water between different containers to show the relationships between units of measurement. And we acted out word problems using food from my refrigerator. Field trips were way more engaging to her than sitting with a worksheet, so I tried to maximize this.

Multi-sensory learning
From taking all those field trips during math tutoring, I noticed my student benefited from hands-on learning. So we also used fraction overlays and math blocks from Math U See to build fractions and do “fraction of a number” problems. Using the manipulatives made abstract concepts concrete for my student, and really helped her “get” the material. Plus it was fun!

When I realized my student didn’t know her 9s times table yet, I taught her the Rockin’ the Standards song for the 9s, to the tune of the hokey pokey, so she would remember them forever. I also taught her the Place Value Rap to remember key facts about place value. Not only were these songs a great chance to stand up and play air guitar, but they were also an excellent way to internalize crucial material and build on the success of the Zero Song.

Managing focus
During the year, we met twice a week for either 60 or 90 minutes. If I noticed my student was losing focus, we’d take a break to jump up and down to rejuvenate ourselves. After a while, my student would ask to jump when she was having trouble concentrating. It might sound silly, but I was proud that my student was starting to pay attention to whether or not she was paying attention and that she knew how to refocus herself. (Thanks to Gretchen Rubin for inspiring me to try this!)

Brainology
When I realized my student was in danger of not passing fifth grade, I decided to use Carol Dweck’s Brainology curriculum, one of the most powerful motivational tools I know of to address one of the underlying cause of low achievement: low motivation. For several weeks, we would spend part of each tutoring session doing Brainology, which uses basic neuroscience to teach students that their brains are plastic and they can grow their intelligence.

My student enthusiastically embraced the Brainology program. She talked about the characters like they were her personal friends, and she responded to questions like “what is happening in your brain when you think?” with answers like, “Neurons are sending messages within a trillion connections.” She also used Brainology concepts like getting enough sleep and eating “brain food” while she was taking her end-of-year standardized tests (the CRCT).

The results
Three or four weeks after we began working together, her teachers reported a positive change in this student’s attitude. She started sitting in front, participating, and speaking up when she didn’t understand.

After about sixth or seven months of meeting twice a week, this student mastered the material, pulled up her grades, and successfully passed fifth grade. Her final math test score was so high that she was only either 10 points or 10 questions away from placing into the advanced math class in sixth grade. I am so proud of her!

Related Posts:
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Do you need a way to remember unit conversion effortlessly and forever? Or just a way to calculate how many cups there are in a gallon?

Here’s how to figure it out. Draw a gallon man!

First, draw a really big capital G. (This is the gallon.)

Inside the G, draw four big Qs. (These are the quarts.)

Inside each Q, draw two Ps. (These are the pints.)

Inside each P, draw two cs. (These are the cups.)

For the final flourish, draw an arrow to one of the cs and write “8 ounces.” (There are eight ounces in every cup.)

When one of my students, a fifth grader, taught me about Gallon Man, I thought, I wish I had learned about this in fifth grade! My entire life, I’ve had to look up each of the conversions and never really internalized how they all fit together.

Since I’ve been introduced to Gallon Man, I’ve gleefully shared him with a fourth grade tutoring student (online), a friend who is a professional organic farmer (in person), innocent bystanders (at a restaurant), and most recently, my Mom (over the phone…”first, draw a really big G…”)!

They’ve all found Gallon Man helpful. Responses have included: “Can I take that drawing home with me?”, “Oh…I get it!”, and “I’m going to hold onto this.”

Gallon Man is totally visual and works for many learning styles. You can SEE how many quarts are INSIDE a gallon. Gallon Man is intuitive for all grade levels (unlike dimensional analysis, you don’t have to worry about the numerators or denominators). Gallon Man is practical. You can use it in your kitchen or in the grocery store. Gallon Man is easy to remember. And Gallon Man is fun to draw!

Gallon Man has recently gotten some airtime from other math bloggers, including Sam J Shah, who pointed out that it really helped him to see someone drawing Gallon Man. Here’s Sam’s post and video.

Yay for mnemonic devices!

*Are you looking for an online math tutor who uses multisensory methods? I’d love to help! Give me a call at 617-888-0160 to discuss your situation.

*Visiting from the Math Teachers at Play Carnival (Adventure Edition)? Welcome, I’m glad to see you here! Below are a few other posts you might enjoy!

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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
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I stumbled across this curriculum while looking at a website of suggested resources for Visual-Spatial Learners. Math U See is designed to be a homeschool curriculum, but I’m wondering why more people don’t know about it and use it. I really wish I had learned about it a lot earlier—like when I was in middle school.

Some core principles set this curriculum apart. Students use blocks (aka “manipulatives”) to build all the numbers first. So for every problem they “build it, say it, AND write it”—thus appealing to many different learning styles—tactile, visual, verbal, etc. An integral goal of the curriculum is that students not only know how to do math operations, but also that they know when to do each one.

Also, teaching Math U See style involves four steps: preparing the lesson by watching a DVD of Math U See founder Steve Demme teaching the curriculum; presenting the lesson to the student; practicing in the workbook; and proceeding when the student can demonstrate mastery by teaching the material back to you.

I love the autonomy support aspect of this curriculum. Steve Demme explains that many people ask how long they should spend on a lesson, and he believes you should really take as much time as you need. I think it’s so cool that the student really sets the pace for when it’s time to move to the next new idea.