If I Had a Hammer

Peter, Paul & Mary

I just read a great blog post by Tracy Zager. Her blog is called Becoming the Math Teacher You Wish You’d Had.

It is about getting students out of the normal (sometimes boring) routines they’ve become accustomed to in math class.

Tracy describes being in a workshop with Brian Hopkins and doing a bunch of math problems in groups. Her group solved a problem and then there was discussion and learning about the mathematics that best fit that problem. When Brian posed a seemingly similar problem, Tracy assumed they would be applying that same mathematical construct to the new problem. That was not the case, which surprised Tracy.

“...Brian disrupted the predictable, pitter-pat routine of math class...

What I see in schools is we cue kids to know what tool to use. If we’re two weeks into a unit on fractions and we give them a story problem, the kids figure fractions are involved. If the name of the chapter is “Multiplying Two-Digit Numbers” and it’s written on the bottom of the worksheet, the kids are going to assume they should multiply some 2-digit numbers. If we’ve written an objective about linear equations on the board, kids figure the answer is going to involve linear equations. If my new tool is the hammer that divides fractions, I’m going to use that hammer until my teacher tells me it’s time to switch hammers.”

As educators, we are often frustrated by our students’ lack of ability to make sense of and solve problems (the first Common Core math practice standard). Yet, are we giving students experiences in math class that help or hinder their ability to solve problems?

Wind Map

Wind Map during Hurricane Sandy, October 30, 2012

My friend, Michael Lye, just showed me a live wind map you can access online at http://hint.fm/wind/

The above picture is a saved image of the wind map during Hurricane Sandy.

School is starting soon. This would be something to put up on the screen as students enter the room. Ask them questions like...

What do you notice?
What do you wonder?
What information are you being given?
How do you interact with the map?
How was this map created? What do you think the creators needed to know and be able to do?
When would you most like to look at this map?
If you had created the wind map, how would you have done it differently?
What other data might lend itself to being displayed in a similar way? 

Geodesic Dome Building, Part II

The dome actually worked! All three fourth grade classes rolled, measured, cut, marked, counted, and assembled two geodesic domes at the Integrated Arts Academy. A quality assurance team was established in order to ensure the newspaper rolls were strong and tight. Partner work was important, so students had one person tape while another person held newspaper rolls in place. Math was happening all around. The domes initially worked great, but then started to droop and fall after a few days. Students fixed them up and brainstormed ways to make them stronger.

This project was shared during an all-school assembly. Three of the fourth graders presented the work with a slideshow created by their class. More fourth graders sat inside one of the domes (to everyone’s delight!) in order to hold it up if it started to droop during the presentation. It didn’t need any support but it was really fun to have them sitting in there. The presentation touched on the math, art, and engineering in this project. Students also explained Buckminster Fuller's humanitarian vision for the geodesic dome.

I loved collaborating with Ada Leaphart, Judy Klima, and the fourth graders at IAA. I hope to do it again soon. There are so many wonderful opportunities to connect math and art in meaningful ways.

How much time do you have?

Teachers: Do you ever find yourself with a little time on your hands and nothing planned? There are zillions of videos out there these days - many are awful and many are wonderful. If you have a short space in the day, you can treat your students to something fun and thought-provoking. Here are some videos I like, with running times, to keep up your sleeve for just the right moment.

Eratosthenes (2:16)
This guy figured out the size of the earth a very long time ago in an elegant way using his knowledge of geometry.

Richard Tapia (2:21)
The kid loved race cars and became a mathematician.

Frostie Dancing to Shake a Tail Feather (2:43)
What can I say? It’s a surefire mood improver.

OK Go, This Too Shall Pass (3:54)
A band makes a music video ala Rube Goldberg. A TV smashes, people are shot with paint.

Doodling in Math Class: Infinity Elephants (4:36)
Makes you want to grab a pencil and start drawing fractals.

Artist of the Floating World (4:47)
An artist creates a giant pair of floating dice and sets them adrift in the ocean.

Brooklyn’s Rube Goldberg (5:34)
A real page turner.

Music for the Eyes

Joe Garofalo, C.P. Smith music teacher and captain in the Lyric Theater’s recent production of Titanic, kindly shares his room with me. Often, before the students arrive in the morning, we find ourselves discussing the math-music connection and how we might help bring this to life for students. Last week, Joe showed me some animated music he’d discovered. I had a hard time tearing myself away. See for yourself. Here is Johann Sebastian Bach’s Toccata and Fugue in D Minor  by a company called Musanim. Musanim says it will send a free DVD of these videos to public libraries and schools. We’ve got ours on order.

Scale of the Universe

 

What do Gomez’s Hamburger, Palm Jebel Ali and Mimivirus have in common? They are all found in Scale of the Universe 2 at 2.5 x 1015 meters, 8 x 103 meters, and 4 x 10-7meters, respectively. Scale of the Universe 2 is a cool, interactive website which goes nicely with my earlier blog post about the Powers of Ten lesson and video. Visitors can zoom all the way down to teeny Quantum Foam and then all the way out to the observable universe and the Hubble Deep Field.

Each object has a brief description, so you will not be left wondering what Palm Jebel Ali is (the largest human-made island) and you’ll know Gomez’s Hamburger is a heavenly body, not a menu item. There are commonplace entries like a Boeing 747 and a sunflower, too.

Students can use this site to explore relative magnitude even if they are not yet ready to learn about exponents in math. Author Istvan Banyai has written a wonderful book called Zoom, which does something similar in low-tech. Students might try to create their own book in this format.

John J. Flynn library super-star Corey Wallace brought Scale of the Universe to my attention. This is just another example of how my own universe is constantly expanding with the help of my talented and enthusiastic colleagues.

 

Making Math More

Woman sewing quilt : New York World's Fair, 1939-1940. NYPL

Did you know there is a new museum in New York City called the Museum of Mathematics (or MoMath for short)? They say the grand opening will be in 2012 at 11 East 26th Street in Manhattan. I am hoping to visit it over April vacation.

For now, we've got MoMath guru George Hart's Math Monday column in MAKE Magazine. Here's a nice piece on quilting and geometry. Check it out. You and your students could try building octiamonds with pattern blocks if you aren't a big quilter.

Math and Image

Lately, I’ve been thinking about the role of images in mathematics. When it was time to create fliers for upcoming elementary school Math Nights, I decided to forgo the usual clip art. I used some mathematical images, including Sierpinski’s Triangle and a fractal tree like the one shown here. I’m happy with the way the fliers turned out.

Professor Tim Whiteford blogged about these fliers and more in a post entitled “Sierpinski and the Joys of Learning Math”. Says Tim, “...communicating the aesthetic component of math, [is] a critically important element if we are ever going to help students enjoy math for what it is, the science of pattern. Imagine learning to read and write without poetry, fiction, literature and creative writing? Imagine if the only thing we learned in language arts was the ability to read directions and write formal descriptions? Imagine if reading and writing were reduced to a purely utilitarian function?”

Teachers often use more than words and numerals to teach mathematics. They incorporate image and structure by encouraging students to work with manipulatives, make towers, draw tesselations, and create patterns. In light of this good work, should we continue to explore creative ways of teaching math? I think so.

Matthew Peterson discusses how language can get in the way of math in his TED talk called “Teaching Math Without Words”. In this 8 minute video we get a glimpse of a software program designed to show math with pictures. I found the software visuals intriguing, as are other apps and interactive math websites (i.e. a Tetris-like game called Factor-tris). As I watched the video, I found myself wanting to defend the role of language and dialogue in mathematics education but Matthew beat me to it. He shared a poignant story about a student with autism finding richer language as a result of his work with the math program.

A great companion to Matthew Peterson is Temple Grandin’s “The World Needs All Kinds of Minds”. If you haven’t read her book, Thinking in Pictures, you can get the gist in this 16 minute TED Talk. Temple mentions math, saying “You see, the autistic mind tends to be a specialist mind. Good at one thing, bad at something else. And where I was bad was algebra. And I was never allowed to take geometry or trig. Gigantic mistake. I'm finding a lot of kids who need to skip algebra, go right to geometry and trig.” Temple is one of my heroes. I love what she has to say about her visual thinking and I love the embroidery on her quirky western shirts.