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The Carletonian

The Carletonian

The Carletonian

Look But Please Touch: A Weekly Musing By Alissa Pajer: The art of effective communication through mathematics

<m happily a math major, so I spend many enjoyable hours thinking about math. And this term I am also happily enrolled in two English classes, so during the past few weeks I’ve spent many enjoyable hours reading and writing. Upon reflection I’ve found that the way I’ve learned to think in my math classes helps me to express my ideas effectively in my English classes. Almost every mathematical idea can be reduced to a set of symbols, and I consider these symbols to be the alphabet of mathematics. When a mathematician writes out a proof, he or she arranges these symbols in a specific order and by doing so creates mathematical “sentences.” The order of these mathematical symbols in the “sentence” matters immensely; therefore a mathematician must put great thought into the order of the symbols so that the proof will read exactly as it should. Rigorous mathematical proofs use precise language to make their claims, and I believe that great authors are great because they use the English language just as precisely as mathematicians use the language of mathematics. I see each English word as a symbol that conveys some meaning in the same way that each symbol in math conveys a meaning. And if I am not able to coherently and precisely put my ideas into words in English class, then my ideas would be useless because I’d have no way to share them with anyone else. Thus, through my math classes, I’ve learned the importance of the precision with which I choose my words in my English writing.

It is especially important for kids to learn how to express their ideas coherently and precisely so that they won’t become frustrated and lose interest in their classes. And it’s my hope that my comps will help kids acquire this skill. For my comps I teach fifth graders advanced math once a week in Northfield, and I will continue to teach them in the winter and spring terms as well. I have complete control over the curriculum, and for one hour every Thursday morning, my six kids and I sit in their school library and have fun with math. We solve problems together, and I try to lead them to the solution rather than tell them the answer outright so that they can feel the joy of figuring out the problem on their own. It’s my goal to give each of the kids in my group the opportunity to practice expressing their ideas in words, and to do this I ask them to explain to each other the answers to the problems. I hope that by the end of the school year each student will have enjoyed learning math and will also have learned how to effectively express his or her mathematical ideas. I figure that if they can explain math problems to each other, then they will also be more able to coherently explain their ideas in their other classes as well.

By teaching kids I’ve learned how important it is that I am able to express my ideas; it’s impossible for me to teach a concept if I can’t express that concept coherently. And, since I learned how to speak and write clearly through my math classes, I’d like to use math to teach kids the skills of effective communication. At its core, math isn’t about theorems or axioms or definitions; it’s about how mathematicians use these mathematical facts to make a claim, to argue a point, and ultimately to express an idea that otherwise would only reside as a vague feeling in some mathematician’s mind rather than live forever as a proved and trusted result.

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