Monday, June 4, 2012

Mathematics and Marathons

Achievement in higher level mathematics and completing a marathon are very similar. Both are done by few people. Most think that they are too hard or that you need to have natural ability to complete them. If you are successful at either (or both), naysayers will say it’s because you are born with that ability or that you are CRAZY! The fact is, both are essentially easy. They only take hard work, dedication, commitment, a belief that you can do anything you set your mind to.  There is a tremendous sense of satisfaction in completing or being successful at them. (I cannot decide which I am personally more proud of-getting an A in university level calculus or completing my first half marathon). Ultimately they are both solitary endeavors to which you alone accomplish albeit with a lot of support and encouragement from like minded individuals. You need not compete against others; the satisfaction comes from simply doing what others feel is too hard to do. Training for a marathon is a lot like learning the skills necessary to be successful in mathematics. Let’s look at the seven process expectations for mathematics as is found in the Ontario Curriculum documents.
Connecting-In math, students are expected to make connections among mathematical concepts, procedures and relate ideas to situations or phenomena drawn from other contexts.  Long distance runners are always making connections: I ate something different before my run today and now have a terrible cramp in my stomach only 5kms into the run; the bottom of my feet are sore, I’m in need of new shoes. Runners and mathematicians alike make connections between different things every day.
Selecting Tools-students select and use a variety of concrete, visual and electronic learning tools and appropriate computational strategies to investigate mathematical ideas and to solve problems. Runners select many types of tools for their running, from running shoes to athletic wear to what I consider to be the best gadget out there for runners, the GPS running watch. This electronic tool does countless computations for you, everything from how far you have run, to how fast you ran, the change in your pace in relation to the change in elevation,  how many miles you ran this week, this month, this year. Like a calculator in math, the newest running watches do all the mind numbing computations for you.
Reflecting-students will be able to demonstrate that they are reflecting on and monitoring their thinking to help clarify their understanding as they complete an investigation or solve a problem. Runners routinely reflect on their runs and training. Runners reflect on and monitor everything they do and how it affects their running. There is a constant drive for improvement and how to achieve that. Reflection is the only way to do that.
Communicating-students communicate mathematical thinking orally, visually and in writing, using mathematical vocabulary and a variety of appropriate representations, and observing mathematical conventions. Runners use their own vocabulary (to communicate what they are doing and how they are training to others). Runners even use programs like to communicate these things visually to other runners. Runners have their own vocabulary. For example, if a runner were to say “I just ran a half”, other runners would know exactly the distance they are referring to, non runners may ask “half of what?”

Representing-students create a variety of representations of mathematical ideas, connect and compare them, and select and apply the appropriate representations to solve problems. Runners represent themselves, rather than their ideas. Runners represent themselves with numbers, usually in the form of their bib numbers or with items signifying how far they can run. The only bumper sticker I have ever had (and possibly will ever have) on my car is a 13.1 sticker. I do not share my political beliefs or my religious beliefs with very many people, but my running, I shout out to the world “See me; this is what I can do!” This, along with a photo of my bib posted as my profile picture on facebook for weeks, are how I represent myself to the world. I am a private person, but this is what  I allow anyone and everyone to know about me.

Problem Solving-Problem solving is as important for runners as it is for mathematicians. Runners must sometimes figure out what is causing the aches and pains they are feeling when they run.  Is it bad form, shoes that are tied to tight, shoes that are too old etc? Runners must also sometimes experiment with different strategies/methods to determine what works best for them (just as mathematicians must sometimes try different strategies to solve problems to see if a solution is easier). I personally also find running to be the ultimate place to solve problems. When running for hours alone, one must distract oneself from focusing on the time or distance and must think of something else. I have found this time to be my best for solving the problems of my life. Your head is clear and focused on something completely different. Perspective changes and things that previously seemed difficult are suddenly simple and clear. I think in solving math problems, this is sometimes necessary too. You must walk away from the problem, clear your head and focus on something else in order for the solution to become clearer in your mind.
Reasoning and Proving-students develop and apply reasoning skills to make mathematical conjectures, assess conjectures and justify conclusion, and plan and construct organized mathematical arguments. At the beginning of training for the first time, runners make the conjecture that they will be able to do something that they have no experience doing. That is they have no proof that they will be able to do it. They simply have the idea in their head that they can. Runners assess their goal and then plan and construct the training plan that they will believe will help them prove they are correct and can reach their goal. Their final proof comes only on race day, when they run what others thought impossible. They have justified all the long hours and hard work by reaching the elusive goal.
I hope you have been able to see how math and marathons are alike. My wish is that this has encouraged all those mathematicians who think they cannot run, and all the runners who think that they cannot do math, to go out and try something new. You never know, it might have more in common with what you already know than you think.

1 comment:

  1. I love this post. As a runner and a person who loves math I completely relate to the analogy. Your examples from the curriculum are strong and make a clear connection. It got me thinking that a math class could take on the project of running a race (maybe not a marathon) and find all the mathematical connections they can during the process. just a thought.

    Thank you for sharing.