Secretive Mathematics

Curiosity should always be welcomed. Not a single person in the world knows everything which is why we should be able to ask, "Why?," or "What if?" During my free time I enjoy watching TED talks that incorporate a multitude of ideas. Recently, I ran across one that stood out to me. Randall Munroe is a web cartoonist that answers people's questions "What if.." using mathematics, physics, general knowledge, and logic. The talk starts out by Munroe answering a question about what would happen if a pitcher threw a ball at 90% of the speed of light? Basically, the surrounding city would explode from the ball without anyone seeing anything.

As the talk progresses, Munroe receives an interesting question. The question regards the estimate of punch cards that Google goes though. Google is a company that releases limited information except what is expected from them. With research, Munroe comes up with a staggering number of punch cards. The estimated amount would cover the region of New England that would rise 3 times higher than the glaciers height during the last Ice Age. I'm not sure how others reacted to these findings, but I know my mind was blown. Interesting enough, Google ended up hearing about these findings and sent Munroe punch cards in which a code was needed to define what the punch cards held as a message. Instead of ruining the talk for my audience, check out the video for yourself included here.

After watching the talk, I started to think about this concept of punch cards. To those that are not within the Computer or Mathematics world, it would come as a surprise to some that mathematics plays an important role in encryption. I, for one, have never done much work with coding or encryption but the idea is rather enticing. My mind started to wander on how great this would be for students to get intrigued by math. There have been many articles and research done for the idea of starting class with an interesting concept to bring students into the math world. For starters, it might be interesting to see if codes could be used at the beginning of class to introduce concepts or topics that will be covered that day or that week. Or there could be an elongated code that goes across multiple days in which the students gain knowledge about specific hints that they would find useful for the topic that has been chosen for that week or however long the lesson is planning to take. 

As I progress through my education, I either learn or find ways in which math becomes "easier" in a way. Or I find a way to connect my earlier teachings of mathematics to my teachings now or the way that I plan to teach a concept or topic to my students. A goal that I have always had was getting the people around me to enjoy mathematics instead of being scared of it. This might be one of those ways. By presenting mathematics as a secretive concept, there is a chance that it will involve some of those who have distanced themselves away from it. The best part about this is that the equations that can be involved in developing and solving these secretive codings are unlimited. They could stretch across all different age groups or concepts and involve all types of students no matter their learning styles.

But...don't you want the right answer?

Coming from a family of teachers has many advantages. Recently, I had the opportunity to visit my mother's 5-8 grade classroom. Her students know that I am obtaining my degree in mathematics with an emphasis in education. The students insisted on impressing me with their math skills so I put some challenging problems in front of them and told them that I wasn't looking for a correct answer but wanted to focus on their process. I loved their skeptical looks. Was I testing them? Was I really looking for the right answer but wanted to make it seem as if it was okay if they didn't get the right answer the first time? The amount of effort that they put into the work brightened my day.

Some of the students were working with decimals, some working with word problems, some wanted to be given some questions regarding my research Set, and some just wanted to be challenged with some of the work that I have been doing in college (of course I had to improvise and make it so that they could understand the gist of what I was talking about). As they attempted the problems, I went about the room peeking over the shoulders of some of the students. When the students got frustrated and wanted hints or the path to the answer, all I would say is try your best. I cared more about their process than the answer anyway. Even when they had the right answer and asked if it was correct, I would shrug my shoulders and say, "Can you find a different way to get an answer?" And if they thought that they could, then I would say, "See if you get the same answer in that case." The students may not be satisfied at first, but once they find another way, they answer their own questions. When compared to the previous answer, if they are the same, then the student feels satisfied that they were able to find it in two distinct ways. They can then go on to see the similarities and differences between the two ways that they approached the problem. Now, if they didn't get the same answer, they checked their own work and found their mistakes. What better way for students to learn from their mistakes?! They are defining where they are, how to change them, and how to avoid them next time.

From time to time the students would ask me, "If you don't want the right answer from me, then why am I doing this?" I had to sit and think about this one for a second. We, as people, do things on a daily basis in which we do not know the correct answer to. If we knew the correct answer all of the time how would we better ourselves? We wouldn't be able to because we would be too scared to try anything that we didn't know the answer to. Mathematics is the same way to me. How would we ever better our understanding and comprehension without taking the plunge into the unknown world? I know that we live in an education world where the right answer counts on tests. We obtain money from these tests to further our education and there is no alternative for that quite yet. However, our students can't be afraid of the math that lies before them. My phrase for the day with the students was, "take the leap," and that's just what they did for me.

My decision of becoming a teacher is defined more and more with each passing moment that I share with students. The students have been working with my mom for more than a year now in which they know that she does not look for right answers from them, but cares about their processes and how they believe to go about a problem. It shocks them that I didn't care about the right answer though. Maybe they thought that my mom was a rare teacher that doesn't expect the one correct answer, but it needs to be voiced more to students. Instead of being scared about what lies before them, they take that leap and better their understanding and comprehension without something holding them back. And that right there is what we want from our students.