Rebecca Zook - Math Tutoring Online

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 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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I was so excited to discover that in Malcolm Gladwell, his recent book, Outliers, presents a bunch of new research on learning math!

There’s so much good stuff in there that I can’t even begin to tell you all about it. But one thing that struck me in particular was Gladwell’s discussion of the cultural differences between Asian and Western attitudes towards learning math. (You can read an excerpt from the chapter here.)

To start, language differences give Asians a linguistic advantage. In Asian languages, numbers are more transparent. For example, when an English speaker has to do mental math, they need to translate words into numbers first. Before we add “forty-three” to something else, we have to break it down into “four tens and a three.” By comparison, in Chinese the word for “forty-three” is already broken down: “four-tens-three.”

Similarly, we say “three-fifths” to describe a fraction in English. But the Chinese for the same number literally translates as, “out of five parts, take three”: the definition of how a fraction works is built in. These linguistic differences make calculation easier in Asian languages. And because it’s easier to figure out what things mean just from the words, there’s an attitude that it’s normal to be able to figure math out.

This creates what Gladwell calls a “virtuous circle”: because the names for numbers are a little bit easier to understand, arithmetic is a little bit easier to do, which means that maybe students like math a little bit more, which means that maybe they take more math classes and ultimately achieve more in math. In contrast, Western children, by third and fourth grade, start to feel that “math doesn’t seem to make sense; it’s linguistic structure is clumsy; and its basic rules seem arbitrary and complicated.” And the trouble begins…

When I mentioned this to my friend, the Future Doctor Jones, she said, “We’re stuck with this language! What are we supposed to do with it?” Her question is valid—if I tell my tutoring students to say “two-tens-seven” for 27, will they just get beat up on the playground for talking crazy numbers?

So recently I was working with a fifth grader on fractions, and I casually mentioned that in Chinese, they say fractions like, “out of four parts, take one,” instead of “one-fourth.”

I was totally surprised when later in the lesson, this same student spontaneously started saying fractions “the Chinese way.” “Out of seven parts, take four!” “Out of two parts, take one!” When I slipped up and said, “Out of two parts take five,” she corrected me immediately, which meant she completely understood the concept.

Most importantly, she didn’t want to stop doing fractions. She was begging for more!

I’m grateful to my student for spontaneously showing me how we, as English-speakers, can adopt a “Chinese” way of thinking about numbers.

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This summer, one of my students got to go to Video Game Making Camp. My student explained to me that he wanted to make a video game where you killed vampires by throwing garlic at them. But there was no “garlic” graphic available to build into the game. So he took a graphic of a giant melon and made it so tiny that it looked like a head of garlic!

Part of what I want to teach all my students is how to customize their education when I’m not around. So later in the session, I seized the teachable moment. This particular student has dysgraphia, ADHD, and a really unique brain. I told him that everyone, whether or not they have dysgraphia or ADHD or whatever, has learning situations where they’re not getting what they need. And we all have to learn how to invent our own ways to work around it.

“It’s just like the tiny garlic melons,” I concluded. “Sometimes you don’t get what you want and you have to turn it into what you need.”

So when life gives you melons, make….tiny garlic melons!!!!

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Ana Reynales earns her BA at age 82