This has been a very interesting past five weeks for me: two 1-week workshops, a week of backpacking, and the lost of one of my two dear, loving 11-year old cats. It's good to be back on schedule - at least for now - and to have time to write my mathematical musings again!
I truly believe math is everywhere – even (especially) on a backpacking trip in Wyoming! Steve and I just got back from another adventure in the Bridger National Forest near Pinedale, WY on which mathematical examples were as prevalent as the many gorgeous vistas!
We packed from the Big Sandy Trailhead to our camp site at Dads Lake. Unlike previous trips, instead of moving to a new camp each day, we stayed at Dads Lake and made day-hikes the next two days.
On one adventure, the trail crossed a rock field and the worn path was no longer visible. We had three ways to solve the problem of finding our way that correspond to problem solving processes used in mathematics: Map, visual clues (blazes, cairns, landmarks), and GPS.
Map: Using the wilderness map for that region use identified landmarks such as visible mountain peaks. When the teacher gives critical information needed to solve a problem and gives the process, then the students have a map.
Visual Clues: Forest rangers or other hikers blaze a mark on trees (picture at right) to indicate the direction where a confusing set of alternate routes may be present. 
Another way they indicate a trail is to build cairns (picture at left) by stacking smaller rocks often on a large rock or boulder: formations which are obviously not created naturally. Not all problems in everyday life come with a map showing critical information to be used in an indicated process, but critical information is there if students know what to look for.
GPS: A Global Positioning System device shows the user’s location at a given moment in time and can track the trail taken over time. System maps may show critical information of the area but paths are not indicated. Just like on our day-hike, sometimes the path to solving a problem is not obvious and the critical information is obscured. This is when we need to see where we are in the moment so we can search for other critical facts of the problem.
No surprise to anyone who knows me, I was intrigued by and thrilled with the mathematics I encountered on the hikes. I will be meeting my fall semester classes at Drake University in about a month. One of my goals for my students will be to observe where they encounter mathematics (such as calculus) in their everyday life. A simple way for me to help them meet this goal is to share my everyday mathematical experiences. In problem solving it is important for students to know there are multiple ways to approach problem solving just as it was important for us to be able to use more than one way to navigate in backpacking!
Tags: Bridger National Forest, Mathematics Education, Math Education, GPS, Orienteering
In loving memory of Lomy, named for Shalom at a time when I needed peace!
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