Origami Connects More Than Pieces of Paper

The first homeschooler I ever met was an avid origami enthusiast. I've no idea how many kids learned the art of paper folding from Mileva, but I imagine there must have been hundreds. She taught her own kids who, when they were old enough, ventured into the public schools and shared their craft with others. My kids and I learned how to fold simple origami boxes under her tutelage, and we in turn taught our friends. Even though the results weren't always worth saving, we enjoyed losing ourselves in the meditative practice, focusing intently on sharp creases and perfectly aligned edges.

Mileva introduced us to Origami USA, a national society devoted to origami. Although I originally contacted them to get bulk rates on origami paper—necessary when your kids are going through stacks of the stuff—I also appreciated the informational resources and sense of community they fostered. Discovering fellow enthusiasts was part of the fun. While we were studying the diagrams and feeling mystified by the instructions (often written in Japanese), we thought about our relatives in Japan and the Japanese friends we had made through the Labo International Exchange Program.

I have fond memories of a wonderful, sunny afternoon spent in the company of an elderly woman at an event hosted by the Japanese American Citizens League (JACL). The unassuming woman sat at a table and quietly demonstrated fold-after-fold to a steady stream of visitors. Young and old learned how to create beautiful stellated octahedrons (12 pieces of paper; pictured right) and icosahedrons (30 pieces of paper). These projects, which seemed impossible to us at first, quickly grew into a habit-forming routine—all thanks to this lovely demonstrator. We filled our house with polyhedrons.

I'm sure Mileva, a brilliant woman with an aptitude for mathematics, used various origami lessons to teach her children about geometry. Rectangles, triangles, parallel lines, right angles—it was all there, somewhere, in the art of paper folding. While her explanations of math through origami might not have impressed someone like Robert Lang (TED Talk: "The Math and Magic of Origami;" website: Origami Mathematics), her creativity and enthusiasm inspired many fans. My kids and I were among them.

Unlike Mileva, I didn't use origami explicitly for math instruction. However, I suspect origami nurtured my kids' natural interest in patterns and connections: if they could take a two-dimensional sheet of paper and turn it into a three-dimensional object, what else might be possible? Origami fostered their ability to visualize a shift from 2D to 3D, which in turn seemed to ease their later studies of molecular structures, fractals, and chaotic systems. Skills such as tenacity and attention to detail—essential for success at origami—also happened to be quite useful for math—and life.

Origami is a good metaphor for the way we learn as homeschoolers. It's something we can do alone or with others. It appeals to us artistically, intellectually, and practically. We respond to the challenge with a desire for mastery and understanding, and we devote ourselves to the task. When our first attempt is unsuccessful, we try again or from a different angle. If we get stuck, we consult books or experts or online tutorials. And, sometimes, we just have to feel our way around and hope for the best as we nudge pieces gently into place.

There are many things worth doing, but we can't always see the value in advance. Sometimes, we have to trust what feels right, give in to our creative impulses, and avoid worrying excessively about outcomes or assessments.

Origami Resources
Interested in learning origami? Check out Origami Spirit (includes YouTube tutorials) by Leyla Torres. She recently posted "Twelve Lists of Top-Notch Origami Video Tutorials." Her videos range from simple to complex, and her enthusiasm for origami is contagious.

For anyone who would like to learn how to fold a simple, modular origami "ball," I found these helpful instructions by TheZocar on YouTube:

Can a Class Be Too Small?

In his book, David and Goliath: Underdogs, Misfits, and the Art of Battling Giants, Malcolm Gladwell opens a can of worms when he asks the question, "Can a class be too small?" When it comes to the number of students in a classroom, most of us assume smaller is better. I know I do. The low student-to-teacher ratio makes sense to me intuitively: the fewer students a teacher has in his or her class, the more individualized attention each student would receive.

And yet, Gladwell argues that "The small class is potentially as difficult for a teacher to manage as the very large class size." To test his theory, Gladwell polled a large number of teachers in the United States and Canada. In David and Goliath, he quotes some of those teachers as they offer plausible explanations for why small class sizes are problematic:

• Interactions are too intense. While there are, presumably, fewer interactions in a small class for a teacher to manage, the interactions that do occur are more difficult to handle. "There is simply no way for the cantankerous kids to get away from one another." There's no place for students to hide. According to one teacher, "the students start acting 'like siblings in the backseat of a car.'" 
• Insufficient "critical mass" for discussions and group activities. As a middle school teacher explains, "students are awkward and self-conscious and anxious about seeming too smart. Getting them to engage . . . can be 'like pulling teeth.'" Also, as one teacher states, "It's difficult to play games . . . the  momentum just isn't there." 
• Lack of peers at a similar academic level within a class.  In a really small class, it is harder to find others who are just like you. There are no subgroups. Complains one teacher, "The chances that children are surrounded by a critical mass of other people like them start to get really low." As one teacher explains: "What you need [as a student] is to have people around you asking the same questions, wrestling with the same issues, and worrying about the same things as you are, so that you feel a little less isolated and a little more normal." 
• Lack of diversity in discussions. Fewer students means fewer (if any!) participants in a discussion. If the group is too small, "it's like they have a muzzle on." 

The magic number for class size, according to the teachers Gladwell polled, seems to be between 18 and 30 students. Since I have trouble understanding why a teacher would actually prefer to work with so many students at one time, I would like to contrast my experiences as a homeschooler with the experiences of the teachers Gladwell interviewed. The main question I'm attempting to answer is this:

Exactly what is it about certain settings—in particular, the various discussion-based classes that are taught by homeschooling parents like myself—that makes small class sizes desirable?  

(Although my response is necessarily based on my experiences as a home educator, I imagine there are many other situations where small class sizes are preferable, too.)