Newsletter September 15, 2012

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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at: moby@moebiusnoodles.com

Moby Snoodles

Book news

There are just a few chapters left to illustrate. This should be all done by the beginning of October, when we start rounds of final reviews. If you would like to participate in reviews, drop me a note!

One of the main ways we make mathematics accessible to babies and toddlers is… symbols.

“Wait, what?” – you may ask. Isn’t symbolic mathematics harder than hands-on work?

It depends on what types of symbols we use. Here are a few examples.

“Baby signs” are hand gestures parents and kids establish for everyday needs of the baby, such as “Bring me that thing” or “More food” or “Pick me up.” Yes, a hand gesture is a type of a symbol.

Have you ever met a toddler who is crazy about horses, or in love with trucks? Anything referring to the beloved topic, such as a saddle or a wheel, will be dear to that child’s heart. Marketers know this and decorate pajamas, pens or backpacks with horseshoes or hot trucks. A saddle is not just a saddle – it’s a symbol of riding, caring for horses, and a whole world of interesting horse-related things!

Kids around the age of four of five often fall in love with particular colors. A child may only want to wear yellow shirts, or to build with yellow blocks and to draw with yellow markers. More often than not, colors have deep symbolic meaning to children. One mainstream example is “pink” symbolizing “ballet” for kids who love to dance. Sometimes these color symbols come from the media. For example, most cartoon characters have their colors, such as Batman and black. Of course, color combinations are symbols for a lot of things too – like green+red for winter holidays, or colors of its flag for a nation.

Here are two examples from the Moebius Noodles book. In the chapter on mirrors, we switched from formal symbols (numbers and multiplication signs) to visual diagrams that are more accessible:

Mirror Multiplication Tables

And here are symbols for function machines in this incredible triple composition! Can you guess what the functions do? Three-year-old kids with whom we work can!

Three function machines

 

Our blogs

“The favorite number of Count von Count from Sesame Street was 34969. Why? And what is YOUR favorite number?” – was our question on Facebook.

Paul Solomon’s answer:

My favorite is 27. 3 is lovely, but this is 3^3. Also, I was born on May 27, lived at 27 Midpark, and other such connections. 27 is for me. :)

Read more on his blog post “Exponents and the scale of the Universe” where this picture can be found. Talk about visual symbols!

Talk to you again on September 30th!

Moby Snoodles, aka Dr. Maria Droujkova

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Posted in Newsletter

Newsletter August 30, 2012

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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com

Moby Snoodles

Moby’s mail

As Sue VanHattum guessed, my native language is Whalish. And now Ever discovers my favorite color is 33 80 DE. Translated from Whalish (hexadecimal, base 16) into human, these are three numbers:

51 128 222

coding red-green-blue parts of a color. You can see there is not much red (51), but a whole lot of blue (222), mixed with about half as much of lovely green (128). The color of endless oceans and evening skies!

The topic of different number bases was made somewhat accessible to young children in the sixties and seventies of the twentieth century. There are already many games and stories about it. The main thing parents need to know is that young kids love small bases. Base 16, which digital artists use, is no good for toddlers, and neither is, sadly, base 10 that most humans use. Little kids need tiny bases – binary (2), ternary (3) or at most base 5. But this is a not a tiny topic – we will explore it on the blog!

– I thought Moby needed some color, hahaha… I hope you like :) – Ever Salazar

– Thank you, Ever. Not just “some” color, but my favorite color! I like! – Moby

Book news

Mathematics is deeply playful. How deeply? It’s fractally playful! It’s playful at every conceivable scale of resolution! Zooming in on any part of any mathematical endeavor finds parts every bit as playful as the whole.

Why is mathematics playful?

How can people who are not mathematicians experience math play?

Both questions have the same answer, which is, in turn, a question: WHAT IF?

If I weren’t a whale and could climb, I would shout “What if?” from the roofs of the tallest buildings, because the world needs more of it. Mathematics is playful because it constantly asks this silly, hilarious, game-like question, “What if?” You can experience math play if you ask this question, a lot. What if you make parallel lines intersect? (Non-Euclidean geometries.) What if you took square roots of negative numbers? (Complex numbers.) What if you divided by zero? (Infinity, which young kids love.)

The chapter we worked on this week is about composition of functions. It uses a lot of animal examples. What if dogs had 8 legs? What if you could reverse time and turn hens into baby chickens? What if you used a spinner instead of a die in your favorite game? Play on!

Dog with 8 feet

Our blogs and lapware

Mobius strips

Yelena describes storytelling play involving mobius strips, inspired by the lovely Vi Hart video “Wind and Mr.Ug.” We highly recommend the story and the video to you and your kids!

http://www.youtube.com/watch?v=4mdEsouIXGM

Velocity Raptor

http://www.testtubegames.com/velocityraptor.html

From our Facebook write-up: “Lapware: A game about relativity theory, accessible to young kids. Play past level 4 for cool effects that blow your mind! I am sitting here laughing out loud as the dinosaur makes the room around him stretch in bizarre ways as he runs at near-light speeds. Thank you for the link, Chris Hazard!”

Velocity Raptor

 

Talk to you again on September 15th!

Moby Snoodles, aka Dr. Maria Droujkova

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Math Stories – Moebius Ants

httpv://www.youtube.com/watch?v=4mdEsouIXGM


This is a story inspired by Vi Hart’s “Wind and Mr Ug” video. I so wanted to tell it to my son myself, but my drawing skills fall way short. So instead we talked about ants. Once upon a time two ants lived on a strip of paper. A strip of paper has… how many sides? how many edges? [I drew two ants on a strip of paper] Each ant lived on his own side of the strip. They never saw each other, but since ants have an excellent sense of smell, they smelled each other. And they really, really wanted to have a playdate or maybe a tea party one of these days. They tried visiting one another, but each time they reached an edge of their little flat worlds and would get scared. Then one day something happened. There was much shaking and twisting and the ants got scared and closed their eyes and covered their heads and tucked their antennas. When the twisting and shaking stopped, they opened their eyes and saw something strange. Their flat world was no longer flat. Instead, it became cylindrical [At this point I glued the edges of the strip together to create a cylinder] Hooray! said the ants. Maybe now we can visit each other! One of the ants, who was a bit braver and more adventurous than the other, immediately set out on a round-the-world trip in hopes of meeting his friend. He crawled and crawled along, leaving tiny prints behind him [I’m drawing ant’s path with a marker]. Will he ever see his friend? Soon the ant came to a set of tiny footprints. At first he got excited. Was that the marks left by his never-before-seen friend? Is he getting closer? But soon the ant realized that those were his own prints and he’s been crawling round and round his little world. But what about the other ant? He too sat out on a journey, crawling along. Will he have better luck? [I’m drawing second ant’s path with a different colored marker]. Nope, he too finds no one, just his own footprints. Their world had… how many sides? how many edges? Poor tired ants needed a rest. But just as they were going to take a nap, their cylindrical world shook and twisted again. Again they got scared and closed their eyes and covered their heads and tucked in their antennas. [Here I cut the cylinder to turn it back into a strip; then I twist the strip and glue to form a Moebius strip]. When the twisting and the shaking stopped, they opened their eyes and looked at their strange new world. Maybe now that it changed they will be able to meet each other. The first ant, the braver one, set out on his round-the-world trip once again. He walked up the hill and down the hill and across the valley [I’m tracing the ant’s path with a marker] until… he saw the other ant! Hooray, the two cried and hugged each other. And then they walked back to the first ant’s home [a child is tracing the ants’ path with a different color marker]. Their world was no longer flat. Was it a cylinder? Nope, it became something called a Moebius strip. How many edges does it have? How many sides? And that was the story. But then we experimented some more. We made another cylinder and another Moebius strip, each with its own pair of ants. This time my son traced ants’ paths all by himself. Then I brought out the scissors and both worlds underwent another cataclysm, this time it was a continental drift (thanks, Ice Age 3, for the idea) as I cut the cylinder and the strip in half. Want to know what happened to the ants? Try it for yourself. It’s really very fun!

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Posted in Grow

Newsletter August 15, 2012

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Welcome to adventurous math for the playground crowd! I am Moby Snoodles, and I love to hear from you at moby@moebiusnoodles.com

Moby Snoodles composes the newsletter

 

Moby’s mail

I adored the responses to our last newsletter. It feels good when your work is supported and appreciated. Take a look at these examples…

I love the 3D function machine drawing. It makes me think of a train going up and/or down a large mountain, and every time the train passes through a tunnel the number of cars increases (or decreases). Thanks for sharing. – Ryan M. Combs, M.S., HRD, Instructional Design, eLearning Development, First-Rate Human Being

  • How interesting, Ryan! We actually have a picture of a train doing just that later in the chapter. What an interesting coincidence – or maybe the chapter’s front picture evoked the same image both in you and in Ever, our illustrator? Wow… – Moby S.

Function Iterations Train

These newsletters are so beautiful, and so full of goodness, I’m delighted each time I read one. I see, though, that Moby must be struggling a bit with English grammar. (Is Moby’s first language whalish?) I’d be happy to be your final copyeditor/proofreader, to catch those just before it goes out. Warmly, Sue VanHattum, Math Mama Writes

  • Thanks, Sue! I would love this! The newsletters go out twice a month. I can send you the text a few days before the letter goes out. – Moby S.

“Welcome to adventurous math for the playground crowd!” Love that. Is it alright if I use “adventurous math” and “playground crowd” in the future? I won’t make it a tagline, but those are brilliant turns of phrase. – Paul Salomon, Math Munch

  • Thank you for your kind words!  Yelena, the lead writer of “Moebius Noodles”, came up with this one. One of my favorite aspects of Yelena’s intrepid style is the bold, clear, but also metaphoric way she names entities such as math concepts, games, and in this case the main idea of the project. The whole project is Creative Commons, so you can share the motto too. I think it would be good if the idea of advanced math for the young kids – the playground crowd – spread as a meme! – Moby S.

Book news

One of the big challenges in making the “Moebius Noodles” book is the balance between three key types of the content.

  1. Mathematics. We need to introduce topic-specific math actions. Our topics are way beyond “counting and shapes.” Many of the readers, even adults, have never seen this math or never thought that its deep roots can be made accessible for young kids.
  2. Pedagogy. There are very few people in the world who work on making advanced math accessible to young kids. The lore on how to do it is far from being common knowledge. Last year at a conference in London, I met one of my pedagogy heroes, Richard Noss, who said it well: “Are you on the quest, too?”
  3. Well-being. We are inviting people, who often suffer from math anxieties, into adventures in uncharted territories.  To help overcome fear and ease the anxiety, we provide some techniques for supporting cheerful disposition, mindful state of consciousness, and relaxed stance of the body.
Last week, we worked on games with grids. The mathematics of grids has to do with covariation between two aspects, organized along rows and columns of the grid. But young kids don’t see it this way. Pedagogical observation: young kids see each cell in the grid as a separate entity! 

 

You can conduct an experiment to see this. Several parents told me this experiment is an eye-opener because it shows how different, and bizarre, the young mind really is. Offer a young child a printed or drawn grid and ask them to draw a copy. More often than not, children will draw each cell separately, often forgetting about row/column structure altogether.

Several of the “Moebius Noodles” games help kids see a row or a column as a whole, rather than as a collection of separate disjointed cells. This more advanced reasoning is a cornerstone of many concepts, such as multiplication. In grid games, it has to do with how you draw. Explaining a totally new concept of drawing, in words, to a very young kid, is a sure road to much frustration!
Our favorite well-being technique here is a mixture of kinesthetic guidance, caressing touch, and a tango where the child leads almost all the time. It looks like a parent drawing with the child’s hand. What you actually do is support the child’s own movements most of the time, but convey mild changes by slight hand pressure, so the child can follow your guiding hand as needed.
In the illustration, we tried to show all three aspects of the grid activity: the math, the pedagogy and the well-being technique. Here is a sketch, where you can see the typical kiddie “nongrids” in the background.
Hand-holding Technique Sketch

Our blogs

From the “math stories” department comes a story of cutting and folding.

The story I told my son was about three friends. He immediately made it about him and his two best buddies and how they were ninjas. Each friend was represented by a square of origami paper. We then folded each square, trying to predict what would happen to them after each fold…

We have been nominated for a top site award at the Circle of Moms. We entered the voting late (just a day before closing), though. If you know of a good lists of resources we should be trying to join, please let us know!

Talk to you again on August 30th!

Moby Snoodles, aka Dr. Maria Droujkova

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