In a course I am leading for future teachers, one of the discussions was about comparing math, sciences and the humanities. I always encourage my students to read (and to write) Wikipedia. Lisa R. quoted the definition of the humanities from there, namely: “The humanities are academic disciplines that study the human condition, using methods that are primarily analytical, critical, or speculative” – and then she talked about humanizing numbers. What a neat idea!
The “analytical” part is common between math and the humanities. I realized that one of well-loved activities I do with young kids is all about adding critical and speculative elements to numbers.
I ask kids to draw numbers as characters, and to tell their stories. What color is each number? Do numbers have tails or wings? What clothes do they wear? Which ones are kind and which ones are mean? What are some numbers you personally like? What note would you play for each number on the piano?
Have you ever done activities like this with kids? Do you have favorite books or movies that do it? One of my favorite childhood stories, “The Magister of Absent-Minded Sciences,” in addition to humans, had several characters who happened to be numbers! Zero was young, proud and prone to be spectacularly wrong about the world. One was more meticulous – she would always rescue him and help him save face, too. Here’s how Zero looked:
Of course, you can do the same activity about any other object, like functions or equations.
Many mathematicians claim they hear melodies of equations, or see equations in color. The name for this effect is synesthesia.
The more I learn about the exquisite connections between shape, number and nature, the more convinced I am that combining numbers and shapes is a win-win situation for building number sense in young children. For example, consider the benefits of exploring the basic, but charming, triangle. This mesmerizing video provides some exquisite, thought provoking examples of three-ness:
What three-ness did you notice? I noticed three colors, triangles with three sides and three corners, many different types of triangles and, best of all, a lovely waltz rhythm (1-2-3, 1-2-3)! The video is also a demonstration of the power of doubling – double 3 is 6 (a hexagon or a snowflake) and double 6 is 12 (a dodecagon). My seven-year-old watched the video all the way to the end the second time (the first time she was waltzing along to the music) and said: “T. [a friend] and I saw a big snowflake once – it looked like that!”
Back in November I read a Moebius Noodles post that mentioned ‘iconic numbers’ – numbers that are so ubiquitous in our daily lives that we don’t really notice them but are perfect for building number sense. One iconic number object is the clover.
I, for one, had never given its ‘three-ness’ much thought until the day my daughter brought me one with a clear triangle scribed on its leaves. As soon as I saw it I knew exactly what to do with it.
We picked more clovers, flattened and dried them in a sketchbook, and finally found some time (and a glue stick) to paste them down. Although my daughter sometimes eschews direct participation in the projects I think up, she is generally always around as I’m making something. In this particular case, I chatted with her about what I was doing while I glued and pasted, and she made a lot of observations, which is good enough for me.
Isn’t it cool?!? It’s a Sierpinski triangle fractal made out of clovers, a true monument to three-ness!
It is fun to find math wherever we go and it’s even more fun to make math out of the things we find. What other three-ness will you find today? Here are a few ideas to get you started: tricycles; three little kittens who lost their mittens; morning, noon and night; a triple junction created when three bubbles come together and, as a final adieu…
…perhaps my favorite example of three-ness so far: This one I made out of a little circular piece of cookie divider paper. Presenting the teeny, tiny, translucent tetrahedron!
Some time ago Maria and I had a chance to present the Moebius Noodles project at an Open Source/Creative Commons event hosted by Red Hat. As we tried to distill our big ideas into a 3-minute presentation, we had to choose the most important points to cover. They are
- In many ways, young kids already are mathematicians.
- Beautiful mathematical adventures are all around us.
- Math is not a worksheet.
- Freeing ideas and experiences (i.e. through Creative Commons licensing) is critical for success.
Want details? Check out a video of our presentation.
If you are developing, teaching, or playing rich early math games, we want to hear from you!
P.S. Can you tell this was my first public presentation?
Yelena recently reviewed the book “1+1=5″ and shared the game of “I spy” she plays with her son.
The book inspires kids (and adults) to see everyday objects as sets, or collections of other objects. For example, a triangle can be viewed as a set of 3 sides while a rectangle is a set of 4 sides. An octopus is an example of a set of 8 (arms) while a starfish hides a set of 5 (arms) in plain sight. If one set has 8 elements and another set has 5 elements, then when added, the two sets have 13 elements total. Hooray!
I thought it could be fun to invite readers of this blog to play a round of the game. Here is the big question I am contemplating: “How can we make our descriptions of games we design so interactive that they become, literally, playable games?”
Add your own example! Of course, this is the ocean, for our Moby Snoodles.
This is what people added so far! It takes about five minutes for your answer to appear here. Wait and then reload the page to see!
Days are flying by and everyone is busy preparing for the holidays. While you might not know what gift(s) you will be getting this year or whether the kids will catch the sniffles right before the party, one thing you can count on is tangled lights. Seriously, no matter how carefully we pack them, when we open the boxes next year, here they are, all knotted up. Turns out, it’s all about math and physics as opposed to our carelessness. Check out this NPR article for details. Here’s the best part – next time you have knotted up strings of lights, give them to your little one to undo and proudly tell your friends he was busy solving a knot theory problem.
In addition to tangled lights, another thing you can count on is a broken ornament or two or three. If your tree looks a bit bare, don’t rush to the store. Instead, consider some really cool last-minute DIY ornaments. Bonus is they are all about math. The easiest ones are paper chain garlands. This year, add a twist, (ok, half a twist) and turn them into Moebius chain garlands. Or bend pipe cleaners into shapes and grow Borax crystals on them. What shapes you choose is totally up to you. Inspired by Vi Hart’s Borromean Onion Rings video, we made this Borromean Rings ornament.
Finally, we’d like to share a holiday printable we found thanks to the link from one of the readers, Elena T. She printed it for her daughter to color days ago, but we just got around to it. This Christmas tree might seem like just a giant cute coloring page, but don’t let it fool you. It’s got lots of things going on, including some great math. Can you find examples of gradients, tessellations, pattern, rotational symmetry, radial symmetry, iconic quantities and a lovely Sierpinski triangle?
Share your holiday math with us on the blog and on our Facebook page.
There is so much math goodness on the web this week, that we are bursting at the seams and need to share our finds with the world!
First up, a math dictionary for kids (and adults). Now, we did mention in one of our newsletters that we were working on creating a math dictionary for the Moebius Noodles book. Our goal was to avoid formulas and connect rigorous and concise mathematical definitions to everyday experiences and objects. It was both difficult and fun.
This week we saw a post and a video on MathFour blog about an online math dictionary for kids. We checked it out and yes, it’s terrific! Instead of just reading, you get to take each definition for a spin, sometimes quite literally (as with “rotation” and “rotational symmetry”). It seems to be designed with older kids in mind, but pre-readers can explore it with your help. Ability to print out the results of your experiments is an added bonus.
If you have an iPad or an iPhone you are likely on the lookout for new math apps. Check out the freshly released and free MIT-P app. Designed by the Embodied Design Research Laboratory (EDRL) at UC Berkeley’s Graduate School of Education and built by Terasoft, the Mathematical Imagery Trainer for Proportion (MIT-P) is “designed to support discovery-based instruction of multiplicative concepts, primarily proportion.”
I’ll do a separate review of our experience with the MIT-P app next week. Even though this app is designed primarily with elementary- and middle-schoolers in mind, let your younger child try anyway. After all, babies are smarter than we think.
According to the 2009 NYT article by Alison Gopnik, “in some ways, [babies and very young children] are smarter than adults”. It’s a great article to keep in mind whenever we feel inclined to teach our young kids anything, including math. It explains why certain techniques that work with older kids will not and physically cannot work with younger ones. It also talks about the most effective way of teaching young kids and it is surprisingly simple.
Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at firstname.lastname@example.org
Bon “Math is not a four letter word” Crowder of, you guessed it, MathFour.com asks:
Can I post this picture on my site? The ant one? And to where should I link and attribute it if so?
Glad you asked! It reminded me I need to put a licence on the newsletters (see below) and the website. Yes, I am happy for you to use this or any other picture, with attribution to MoebiusNoodles.com
Dor Abrahamson of UC-Berkeley shares a lovely story about his family. Gabi is Dor’s wife and Neomi is their daughter. This story goes with our chapter on intrinsic multiplication! Do you have a Moebius Noodles story? Write me!
We were eating home-made Mexican food with my parents, who’re visiting here.
My dad asked why the brown paste is called ‘re-fried‘ beans.
Gabi said she’s not sure, but she guesses it’s cooked twice.
I said, “What if they cooked it yet again — they’d have to call it ‘re-re-fried‘ beans!”
Neomi said, “No, ‘re-re-fried beans’ would mean they cooked it four times.”
I asked, “How come?”
And Neomi said, “Because the ‘re’ at the beginning means you have to do the ‘re-fried’ over again, so that’s two times twice, so that’s four.”
I stammered something about sequences vs. nested structures, but that was where Neomi lost me and dug into the avocado.
The ant picture Bon liked is an example of a nested structure, too.
We’ve finished the first draft of illustrations and layouts for all chapters. In the coming weeks, we will put it all together as the finished book. It is a rather surprising amount of work, considering the writing and the illustrations are done! We need to figure out pages, introductions, covers and so on. At the same time, we will be discussing chapters with volunteer reviewers.
The cover is in the early stages of design. We know the elements we want on it, but not how they will come together – or their particulars! We want a big picture of kids, playing with complex math objects, and then some recognizable graphic elements that can be reused for other books in the Moebius Noodles series. Your ideas are very welcome. Here is an early draft.
You are welcome to share the contents of this newsletter online or in print. You can also remix and tweak anything here as you wish, as long as you share your creations on the same terms. Please credit MoebiusNoodles.com
More formally, we distribute all Moebius Noodles content under the Creative Commons Attribution-NonCommercial-ShareAlike license: CC BY-NC-SA
Talk to you again on October 30th!
Moby Snoodles, aka Dr. Maria Droujkova