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 mapmyrun.com 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?”