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When you were a kid, do you remember folding a paper cup or paper football for lunchtime finger-flicking fun, or perhaps a little game that tells you your fortune? Well, you were essentially doing origami. I have been curious about this ancient art form, and this summer I purchased a basic text in order to try it out and explore its academic value.
Last year, I worked on a subcommittee focused on literacy. Our objective was to look at past results of the High School Graduation Qualifying Exam and the ninth-grade Terra Nova test to identify specific skills needing more direct instruction and practice. From the results of our research, two problem areas stood out to me that I thought I could work on: following multi-step directions and understanding and using vocabulary effectively.
Geometry, albeit mathematics in general, is a foreign language to many students. Terms like adjacent, collinear, consecutive and corresponding are not frequently used in the new Juneau-Douglas High School commons. Likewise, many of my students lose credit because they do not read the directions or they fail to stick to a problem long enough to explore it fully. Sometimes approach is half the battle. Part of problem solving is struggling. Research says that struggling to a point is good for your brain. I believe pushing students to expand their level of tolerable struggle is good for them. Origami is all about being patient, being precise, understanding vocabulary, reading, following directions and, for many students, trying and trying again.
I started my year by teaching my students some basic origami folds and giving them the directions for one construction each Friday to be due on Monday. Paper folding takes more time than I am willing to devote class time to, but the weekend assignment gives students a set of written instructions to follow and a visual aid to assist them. If they are not successful on their own, they are invited to join me for lunch on Monday to walk through the steps with them and they can still get full credit.
As we wrap up the first quarter of the school year, I reflect on the value of our origami work with respect to time and the content of my course. Not all good ideas should be taught in school. Here are a few things I have observed so far. My students have been asked to produce a dozen constructions thus far; most have completed them all. Most of my students are eager to see what we are going to construct next; one called it addictive. Students who come to me for help have often not read the written instructions, but rather they have depended heavily on the sometimes poorly photocopied visuals. I make them read the directions with me and I help with the translation of ideas. I like it when students who come to me for help start out by saying, "I'm stuck on step seven - what does this mean?" They are reading it - good. On any given Monday in my classroom, one can observe a proud display of completed work by many students. Complex terms are flying around the classroom. Several students scramble to get help from their peers to complete a fold before I check them off. Some pull out a crumpled mess, look glum and let me know their frustrations. I'm generally flexible. Sometimes I need to take a minute to get the whole class over the hump of a difficult instruction and give them another day. I thought I would take the first semester to introduce methods and vocabulary, establish a routine of weekend folding and expose them to a variety of ways to manipulate a simple square. My classroom is a sea of origami - it is almost distracting.
Will my students gain needed skills and perform better on the HSGQE through their origami work? I think it is too early to tell. Now that they know the basics, we can explore more direct connections with their daily work. There are great ways to teach concepts like transformations, congruency and proportions through paper folding, so we still have much to explore. Half the fun of teaching is learning and trying new things. On any given night you may find me at home folding paper and looking for good connections. I like to have some fun while I learn. My students do, too.
Mary-Lou Gervais is a math teacher at Juneau-Douglas High School.