Rebecca Zook - Math Tutoring Online

If you’re an educator (math or otherwise) & you’re lucky enough to be in the San Francisco Bay Area next week, my wonderful colleague, Linda Akiyama, is offering some workshops in physicalizing math using body music. I had the pleasure of meeting Linda and experiencing her work in person last year, and her work is a delightful, fun, and deep multisensory way of helping kids learn math and understand it in every cell of their being. (Using rhythms to find least common multiples, anyone?)

If it’s geographically possible for you, go, go, go! And take your friends! Details follow.

Crosspulse & THE 4th INTERNATIONAL BODY MUSIC FESTIVAL present

ALL NEW TEACHER TRAINING WORKSHOPS

Integrating Arts & Academics: Physicalizing Math using Body Music

• Learn Rhythm Blocks, an easy yet effective rhythmic approach for teaching essential math concepts & skills

• Create instructional activities that motivate and inspire your students through arts integration

• Discover how to use Body Music to fully engage your students in math learning and beyond

• Basic Rhythm/Basic Sanity – learn to cultivate calm in the classroom

Tuesday, November 1
San Francisco School
300 Gaven St., SF
4pm-6pm, $25
Terry, Akiyama, Goodkin

Thursday, November 3
First Unitarian Church
685 14th St @ Castro, Oakland
4pm-6pm, $25
Terry, Akiyama, Santi Owen

Instructors:

Keith Terry is the Artistic Director of the IBMF, and has developed a Body Music methodology well-used by classroom and music teachers for a host of applications throughout curricula. Keith has two instructional DVDs on Crosspulse Media, with the third DVD and accompanying book due out in 2012.

Linda Akiyama has 25 years of experience teaching in public elementary schools and has taught science education courses through the SEP program at UCSF. She uses rhythms, chants, and rhymes extensively to support the teaching of academic subjects.

Doug Goodkin teaches music based on Orff Schulwerk to children 3 yrs – 8th grade at The San Francisco School. A director of the prestigious San Francisco Orff Course and author of many books on music education, Doug travels extensively internationally giving courses on Orff Schulwerk.

Jim Santi-Owen has taught for nearly 20 years in public and private schools as a music specialist. Trained by some of the top percussionists in the world, and a certified Orff instructor, Jim is currently the Music Director for the San Francisco World Music Festival where he also directs the Festival’s International Youth Orchestra.

To reserve a space, purchase advance tickets at www.brownpapertickets.com. Tickets also available at the door.

For more information on IBMF concerts and workshops, including a Family Matinee Sunday Nov 6, visit www.internationalbodymusicfestival.com

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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This goes out to all the kids who are working on summer math packets without having a textbook to refer to. If you need a good online math reference, I highly recommend Purplemath (one of my personal favorite math websites).

This site has a GREAT lessons index so you can quickly find the exact topic you need. The lessons (written-out explanations) are very thorough and easy to follow. They’re not written like a math book, but like having someone really smart and kind explain things to you in a conversation. The lessons do an excellent job of going over concepts AND steps, integrating the “what do I do?” with the “why it works!”

The site also features community forums sorted by level—starting with arithmetic and going all the way up to trigonometry. So if you have a math question, you can post it in the appropriate forum and get help from other community members. Elizabeth Stapel, the founder of purplemath, frequently responds to students’ posts in the forum herself!

Thank you, Elizabeth Stapel, for this totally user-friendly and expert site!

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Here’s a fun way to remember the formula for surface area of a cylinder—singing these lyrics set to the tune of Camptown Races (in the style of Foghorn Leghorn):

2 times pi times r times h; that’s the middle.
2 times pi times r times r; top and bottom, too.
Surface area!
Of a cylinder! It’s
2 times pi times r times h plus two times pi times r times r.

If you’re not sure about how to fit the lyrics with the Camptown Races melody, just listen to the intro of this sweet rendition on YouTube:

With this handy mneumonic device stuck in my head, I feel the urge to belt “Surface areAAAA! Of a cylinDERRRR!” while walking around my neighborhood and puttering around my kitchen!

Many thanks to Becky Brickell for sharing this great idea on the Texas Instruments Classroom Activities website!

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Growing up, I remember learning to remember the difference between the greater than and less than signs by imagining a hungry alligator with an open mouth getting ready to “eat” the bigger number.

I recently got to work on this concept in an online tutoring session with a student of mine who’s a fifth grader.

First we had a regular < sign and we talked about the "alligator" idea.

He drew in some pointy alligator teeth:

Then he spontaneously drew a whole alligator:

As we worked on different inequality problems, he took it further. He drew a picture of a bird and explained that the bird’s closed little beak is shaped like an inequality sign. The bird would go for the smaller meal, while the alligator would go for the bigger meal.

And he topped it off – with sound effects.

The smaller number, which the bird would eat, has a “peck peck” sound. The larger number, which the alligator would eat, has a “chomp chomp” sound. Oh my gosh, I love it!

I’d never seen the alligator metaphor pushed this far before, and I wanted to share my student’s creative ideas!

What’s your favorite way to remember (or teach) the difference between the two signs?

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Pizzas. They’re the best way to represent fractions, right? Everyone has seen a pizza. Everyone knows you can slice a pizza different ways. When you need to visually represent fractions, pizzas are the go-to metaphor, right?

Well, that’s what I thought until I tried using pizzas to teach equivalent fractions. Sure, it’s easy to use a pizza to represent quarters, sixths, eighths. Thirds aren’t even too bad.

But just try dividing a circle into five equal pieces. Or seven. Or ten. Even though I’m a grown-up and a professional math educator, it’s really hard for me to consistently do this.

And as for showing visually how two fifths equals four tenths? Unless I do an impossibly immaculate job of dividing those pizzas into pieces, forget about it.

Are they really the same?

Fortunately, I’ve found a much better way to represent fractions visually: the Math-U-See fraction overlays. If we’re going to use a food metaphor, they’re flat and square, like brownies from a square pan.

And like brownies, they are much easier to slice evenly than pizzas. In fact, because they’re reusable transparent overlays, you don’t even have to draw (or slice) anything. You just arrange them on top of each other.

Check it:

Awwww, yeah! Those fractions are DEFINITELY equivalent!

You can use the overlays to represent basic fractions with divisors from two through seven, or combine multiple overlays to build other denominators.

Not only do they make it really easy to see how equivalent fractions work, but using them is way easier than drawing pizzas and hoping the slices come out even.

The fraction overlays make the concepts extremely clear, and because they’re tactile, visual, and kinesthetic, they make fractions feel like a game instead of work. Whenever I’ve used them with my students, either in person or during online tutoring sessions with a webcam, they’ve react the same way: “This is fun!”

Now that’s how I want my students to feel about fractions!

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I’m totally psyched! I have a new guest post up on mashable about five of my favorite fun technologies to help kids learn math over the summer — technologies which involve incorporate hip-hop, wailing rock guitar solos, talking calculators, brain science, and pirates.

So if you’ve ever dreamed of helping your kids learn their times tables by rapping, or just want to find some fun new ways to help your kids learn math this summer, click on over and check it out!

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Be yourself, do what you want, wear what you love (Ada Lovelace/Coder Barbie Follow-Up)

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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To celebrate 3.14 – PI DAY – here is a beautiful music video of an awesome song about PI !!

It’s a delightful way to learn or remember some important facts about this lovely number, 3.14159….

Here are the lyrics. I would love to know who wrote the song (couldn’t figure it out on google) and who made the gorgeous video (the info was all in Russian).

(Thanks to Sue Van Hattum for posting this on *her* blog today, and to Maria D for sharing it on her Natural Math google group!!)

In my seven years as math tutor, I’ve probably worked with twenty algebra books. Hands down, no contest, this is the absolute best I have used: Algebra: Structure and Method, Book 1. (Brown, Richard G. et al. McDougal Littell, Evanston, Illinois: 2000.)

This book doesn’t have a ton of frills—there are barely any pictures or “extras.” But
what makes this book exceptional is its GREAT sequencing. It does an excellent job of breaking the math down without dumbing it down. The problems get harder very incrementally. There are so many practice problems to choose from that you can really practice until each procedure becomes second nature. And the book only introduces new concepts once you’ve already mastered the prerequisite skills.

For example, when this book introduces factoring trinomials, it introduces each pattern that you might encounter one at a time. You practice that pattern extensively before facing a new pattern. Once you’ve practiced all the different patterns separately, THEN it mixes all the different patterns together in one problem set. But by now you know how to recognize the different patterns and what to do differently for each pattern. So when faced with a page full of different types of factoring patterns, you can just think, “OH—difference of squares!” or “OH—perfect squares!” instead of having to do trial and error until you erase a hole in your paper!!

The students I’ve used this book with acquire very, very strong algebra skills without getting bored or frustrated. And I think it’s because the sequencing forces students to learn how to “chunk,” a concept I learned from Daniel T. Willingham’s book, Why Don’t Students Like School?

For example, take two algebra students. One is still a little shaky on the distributive property, the other knows it cold. When the first student is trying to solve a problem and sees a(b + c), he’s unsure whether that’s the same as ab + c, or b + ac, or ab + ac. So he stops working on the problem and substitutes small numbers into a(b + c) to be sure he’s got it right. The second student recognizes a(b + c) as a chunk and doesn’t need to stop and occupy working memory with this subcomponent of the problem. Clearly the second student is more likely to complete the problem successfully. (p 31)

Thank you, thank you to those who wrote this book so chunk-fully: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, and William L. Cole!