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.)

Linkfest for Saturday, April 26

Partly I'm compiling these links for my own benefit, but some of this week's posts were pretty exciting. I hope you're out there enjoying them. Please let me know. Thanks.

• Varied, interleaved learning feels less effective, but is shown to be significantly more effective.
• Visualizing solutions to n-th degree algebraic equations using right-angle geometric paths. (I want to try to read this when I have more time and mental energy.)
• Mr. K describes how substitute teaching has made him a better teacher.
• Yakov Sinai models motion on a square pool table with a round cushion in the middle. He's proved that the ball will eventually hit every point on the table. This helps physicists understand gasses.
• Fawn's shopping contest - a way to practice percents (for discounts and tax) in a more challenging context.
• Nix the Tricks is a free ebook created by Tina Cardone with the help of dozens of math teachers online. Which 'tricks' are you attached to? Which make you cringe when your students mention them?
• A number of bloggers are answering some questions Grant Wiggins posed. Number one, why is division by zero undefined?
• Cathy O'Neill interviewed Fawn Nguyen on the math Common Core standards. Fawn is an optimist. I fear that the goodness she describes in the standards may be overpowered by the harm done with the endless testing, money for testing (instead of for teaching and learning), evaluations of schools and teachers determined by testing, etc.
• A game. Make a graph with the given number of edges at each node.
• Geoff's series of posts (especially number three on summer school with Jo Boaler, and number four on Chirstopher Danielson's hexagons) about the workshops he attended at the NCTM conference in New Orleans made me wish I could have been there.
• What do proofs with 5-year-olds look like? Rodi tells them, “I hear with my eyes and see with my ears.” And they work very hard to prove her wrong.
• I am dedicating Playing With Math: Stories from Math Circles, Homeschoolers, and Passionate Teachers to Seymour Papert.  You can get some nuggets of his by following The Daily Papert. From Wednesday: “You learn in the deepest way when something happens that makes you fall in love with a particular piece of knowledge. “ 
• When students make their own definitions...
• Mr, Honner, Solving Pallet Equations.
• I have not managed to solve the Robot Maze Puzzle. Can you?
• Leading into calculus, estimating areas.
• Parametric projectile motion simulated in Desmos.
• Are you required to have the standard you are teaching on the board? Mr. K describes why that sucks. Spoilers, anyone? And then Brooke Powers describes how helpful it is to share your bigger goals at the beginning of a unit. (I don't think my way of doing that would satisfy the folks hovering over high school teachers. Thank goodness I teach college.)

This one's not math, but it's too good not to mention: Researchers are analyzing similarities between the behavoir of ants and neurons.

Linkfest for Sunday, April 20 (a small one)

• Nat Banting on making practice more conceptual - ask students to do the last step in posing the problem. Nice!
• Andrew Knauft descrbies why he thinks Geogebra > Desmos.
• A site for finding, building, and storing formulas online, Formula Sheet. (hat tip to Glenn Waddell, whose diigo account may have inspired me to get one - which I don't use. Maybe I should ask him to teach me how to make it useful. I love his real posts, but his Diigo Links (Weekly) are often full of useful ideas too.)
• Malke wonders whether lack of recess (and the movement it encourages) is taking away children's ability to make sense with their bodies.

Linkfest for Friday, April 18

• Jen Orr's first graders tell number stories and make a video of it.
• David Cox's post, Fostering the Hypothesis Wrecking Mindset, includes a list of a dozen good problems.
• Dan Finkel has been enjoying how much thinking goes on when people play his Horseshoes game, a variation on a classic number game. (Winner is the one who gets closest to the target number, using 4 given numbers.)
• Got some interesting data in a pdf file, and want to put it into a spreadsheet? Flowing Data points to a nice program to help with that.
• The 109th Carnival of Mathematics points to a game the author seems to like as well as 2048. I'll try it - Lunar Lockout.
• Toomai made a video - All Parabolas are the Same Shape.
• Mimi's Parametric Equations Animation Project
• Mr. K is introducing exponent properties with geometric series. I think I'm going to try to involve series in as many pre-calc topics as possible next semester.
• Jonathan Claydon wrote A Year with Desmos.

Linkfest for Saturday, April 5

• This video shows multiplying by using a parabola. Completely impractical, but I was curious why it worked. I figured it out and then wondered if my pre-calculus students could figure it out too. I wanted a demo instead of a video, so I built something in Desmos. (Hide the equations, and click on the three dots. The middle dot will always multiply the absolute values of the other two.) It's not perfect, but it might be good enough to impress my students.
• I've seen this cute list of functions, with the person's arms illustrating the graph, on a number of blogs lately. I see two that are wrong. Henri sees one wrong, and has quibbles with four of them. What do you see?
• Common Core for math... I keep hearing that the math standards are pretty good. But if the tests ignore the most important standards (the process standards, which describe mathematical thinking), then they're being used badly. This post by Jonathan Katz goes into some detail.
• Nice exercise. One person looks at the board, and describes the graph drawn there. Their partner must draw it from the verbal description.
• Quintic polynomials. There is no formula for the roots. But there is this. I want to learn more!
• Fawn's lesson for proportional thinking.
• Papert on "hard fun."
• I like this diagonal problem, but when I tried it in class my students were not persistent enough to succeed with it. David Cox's post on how he used it with his students makes me want to try it again.
• In whatif?, xkcd's creator, Randall Munroe, takes a silly question and analyzes it with math and physics to come up with an answer. In this episode, he figure how how big a splash you'd get from a tree as big as all trees on earth falling into an ocean with the water of all the ocean's on earth.
• In this post from her calculus for kids series, I like Maria's thoughts on how we help kids learn problem-solving.