The Challenges of Trip Planning; or, How Do We Make This Decision?

A little over a month ago, Patrick Honner, a math teach I follow on Twitter (@MrHonner), wrote a blog post about his Saturday morning trip to the grocery store. He took a simple question, what’s the best way to maximize the one-time 20% discount he’d earned from his local grocery store, and explored it as a constrained optimization problem. (If you want to read more about it, his post is here.)

I was reminded of this post the other day as my wife and I were talking about a part of our upcoming trip that had been challenging to plan. We wanted to go to Yellowstone and Grand Teton National Parks during our trip, but we were having trouble making the timing and logistics work. After talking for a while and getting completely frustrated that we couldn’t resolve the issues, my math brain finally kicked in and I remember to ask the question I always tell my students to ask: what if?

Original Trip

Twenty minutes later, we had decided to ditch these widely-recognized national parks in favor of a different route, one that would allow us to see more, do more, and avoid the conflicts that had been plaguing us earlier. Yes, we were giving up the chance to see two the country’s most famous parks, but what we were getting in return made the sacrifice worth it.

Revised Trip
So what does this have to do with Mr. Honner’s groceries? Like his grocery shopping, our trip planning dilemma fits quite nicely into a useful area of mathematics. Unlike his problem, though, which dealt with mathematics covered in multivariable calculus, our problem’s solution can be found in a far less taught topic: multiple-criteria decision making (MCDM).

MCDM is a sub-discipline of operations research that focuses on making decisions when there are several criteria involved, and is especially valuable when the criteria are in conflict with each other. When we were trying to make a decision about our trip, we were weighing one criteria (our desire to see these parks) against two others (time and flexibility). While I didn’t sit down to quantify these factors, I know that time and flexibility were our biggest priorities, and once we’d identified this it was easy to make the change.

The same ideas can be applied to a variety of decisions that our students have to make. From big questions like the colleges they should apply to, to smaller questions like what they should do with their free time, these decisions can be broken down, quantified, and analyzed. So that’s my big what if question for the day: what if the mathematics of decision making was a part of our new integrated mathematics curriculum?

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Getting Ready to Hit the Road

We are tantalizingly close to road_trip_by_public_domain_pics-d5tisqitwo of my favorite words: summer vacation. Two weeks from today, my family and I will head out on a six-week road trip. We’re heading acoss the northern United States to the Pacific Northwest, hitting National Parks and science museums. We’ll visit friends in Portland, OR and then circle to the south to see the redwoods, travel across northern Nevada and Utah, and after some stops to see family and friends in Colorado we’ll head towards home.

We have some things we want to see, like Hanford Reach National Monument, the Seattle Childrens’ Museum, and the Great Salt Lake. Mostly, though, our agenda is open, and intentionally so. The goal of the trip, really, is to explore, to be surprised, and to go where our interests lead us. In other words, our goal is to spend the summer doing school the way I hope to someday do it for the other nine months of the year.

Along the way, I hope to see some things that inspire me, some things that make me wonder, and some things that I can bring back to my classroom and my school. Over the next couple of years, I will be taking the lead in writing a new, integrated mathematics curriculum for The Hill School. This trip is about resting and recovering from a long school year, but it’s also about laying the foundation for next year and beyond. I hope to blog on a daily basis during our trip, documenting the things we’ve seen, the things I’ve been thinking about, and the questions I want to explore further when I return. If nothing else, I’ll have a great diary of our travels. Hopefully, though, some people will decide to join me virtually and extend my trip far beyond the summer.