Yangmingshan National Park in Taiwan

COVID, A Compost Bin, & My Approach to Math 

Date: 7/6/2020

Recently I was building my own compost bin for a garden, one of my many pandemic projects, and in this process I reached a point where I needed to determine how much paint would be required to cover a cylindrical 55 gallon plastic barrel drum, in other words a fun math problem. I researched the type of paint needed for exterior plastic, settled on the color “Golden Sunset”, and upon reading the label discovered one can of paint could cover 12 square feet. The stage was set, I had a fun and practical math problem.

My main task was in determining the surface area of this cylindrical object. Hmm, that is an interesting question I thought. Now of course, I could have used the surface area formula for cylinders, A = 2π *r*h, or try to Google my way to an answer, but I question whether or not that would have satisfied me or been all that rewarding. I much preferred to look at this afresh, to experiment, and most importantly, to think for myself and rely on my own curiosity and creativity. That seemed much more fulfilling and valuable, there was a certain freedom and excitement to think for myself, and I was confident that whatever I happened to learn along the way would be that much more likely to stick afterwards.

So, with a playful attitude, I started to ponder different ways of determining the surface area of this barrel. Initially I thought, if this were a rectangular sheet of plastic, this would be a straightforward problem. I could measure the length, then the width, multiply the two, and voila, I would have the area. But this barrel was cylindrical, not rectangular. However, I thought it is simple enough to measure the length of the barrel, and I sensed having that information would be helpful, so with measuring tape in hand I determined the length to be approximately 3 feet. Halfway there I thought! But I was still looking at a cylinder, not a rectangle. Thinking, thinking, thinking. Then, quite organically, I started to imagine taking a rectangular sheet of paper and rolling one end of it to the other, in effect creating a cylinder. Then if I released my fingers, that paper would return to its rectangular form. Then it dawned on me, the area of the paper has not changed! Whether I rolled it up from one end to the other creating a cylinder, or laid it out flat as a rectangle, it was the same area. Furthermore, and crucially, I realized the distance around the top of the paper cylinder was the exact same distance of the width of the paper when laid out flat (try it for yourself!). 

With confidence, and excitement, I grabbed some string, wrapped it around the barrel, then laid the string out flat and measured it to be roughly 5 ½ feet. I now had, in a sense, the width of the barrel (if it were to be rolled out flat like the paper). I grabbed a calculator, multiplied this width by the barrel’s length, and with a sense of satisfaction determined the surface area to be 16 square feet, no Google necessary. Feeling that healthy sense of accomplishment that comes through preserving and discovering something through one’s own efforts, I finally knew how much paint I would need for my compost bin.

Now the reason I went through the trouble to describe that experience in such detail is that it quite accurately captures my spirit when it comes to math, and also the type of learning experience I aspire for students to have for themselves. Math, above all, is a medium. A medium for students to be curious, creative, ask good questions, and persevere. The more I see a student engaged in and growing in any of these areas, the more I know I am doing a good job. In fact, the most memorable experiences I have had as an educator are the ones where I am working with a student, typically low in confidence, and am able to guide and witness them persevere through their doubts, tap into their own curiosity and creativity, and ultimately reach the understanding and answer they hunger for. And most importantly, they did it themselves. I was merely a guide providing encouragement and support. Personally, it is these types of experiences I find most rewarding for both student and teacher. 

My interest in teaching math in a more enriching way began in graduate school. I was fortunate enough to take a year-long sequence in Math Education with some great professors and researchers, including the well-known math education expert Dr. Pat Thompson. Through many long hours of discussion, countless readings of a diverse body of math education research papers, and my own experimentation with teaching as a Teaching Assistant, a new door was beginning to open for me as far as what I saw possible with teaching math. Gradually, I began to see math as much more than simply reaching a final answer. It was becoming an opportunity for students, every type of student, to really think,explore, get creative, and ultimately come to realize they too can genuinely understand concepts and abstract ideas (it was not limited to just the math teachers). Math was beginning to become more alive for me and I found myself motivated to bring it to life for others.

Sharing this newfound appreciation for math has evolved over many years. I have had extensive opportunity and hands-on experience teaching math to a diverse body of students and throughout this ever-evolving process, I have learned a lot, failed a lot, tried and tried again, and ever-so gradually have fine-tuned my craft to create, as best I can, the most meaningful experience possible for students. Over time, learning to work with each student’s unique way of thinking and striving to steer it in positive directions, rather than rigidly imposing my own thinking or a textbook’s onto them, which may simply not be a natural fit depending on the student. It is a skill that has matured over countless hours of hard committed work, and it is something I am personally quite proud of. 

Finally, back to the compost bin. My whole inspiration for teaching math again was born from sharing this compost bin math experience with a former 3rd grade teacher, who is self-proclaimed “bad at math”, and watching her reach the same insights that I had, and doing so with confidence. There and then I thought my uniquely developed skill set, coupled with my joy for working with struggling students, may be of value to others and serve a genuine need...

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