Caption Contest - Sometimes Learning Math Is Like Reaching Into a Hurricane

The book I've been putting together for the past 5 1/2 years, Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers, is almost done. We have chapters from over 30 authors, each chapter followed by a game, puzzle, or activity. It's looking great.

We are finishing up the illustrations now, and I need your help with one illustration. It illustrates the idea which informs the title of a chapter - At the Eye of the Hurricane, by Melanie Hayes. The illustration has two panels, sort of like a comic strip. And it reminds me of those collections of photos, with captions saying what different groups think you do. (Like this homeschooling one: http://www.lisaoutloud.net/Websites/lisaoutloud/images/homeschool.jpg)


Here's the text it illustrates:

We usually think of mathematics as a series of steps, starting with the foundational building blocks and eventually building a stairway to higher mathematics. We don’t move students up the stairway until they have mastered each previous step. We feel compelled to make sure they thoroughly understand algebra before we allow them to try trigonometry or calculus. For mathematically-gifted children, this lock-step method can kill their creativity and their desire to fit the pieces of the overall mathematical puzzle together.

The learning style of some mathematically-gifted children* is more akin to a hurricane; they stand at the eye and watch all the information swirling around them. Their curiosity urges them to reach into the hurricane and pull out bits and pieces of mathematical data. They ponder and experiment until they fit those bits and pieces into their prior knowledge and come up with the whole picture. To the casual observer or bewildered teacher it often seems disjointed and messy, but wonderful things are happening within the eye of the hurricane. These children are making deep connections, internalizing knowledge, and building concepts that will allow them to experiment and try out their own theories. Teaching mathematically-gifted children requires an open mind and a willingness to throw out most accepted notions of how to teach math.

And here's what we have so far...  (Thank you, Linda Palter!)

 

It needs a title and two captions. I think the title is just 'learning math', but maybe you have a better idea. The top panel could be 'what people think' and the bottom one, 'reality'. But that doesn't quite work. What do you think?


Prize: A signed copy of the book.



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* Although the author identifies this as a trait of gifted children, I think it is likely to be a good description for anyone who loves math. (The captions do not have to refer to gifted kids.)