I recently had students do a project where they apply the distance formula to finding the shortest path for a traveling salesperson to travel between 8 cities. The basic idea is, the students use the longitude and latitude coordinates as substitutes for the x and y coordinates of the city, then they can use the distance formula to find a pseudo-distance between the cities. Of course, on any kind of largish scale, this makes no sense, but on a small enough geographic scale the error in the distances is small, and I made sure the kids were aware of this deliberate error. This project was intended to be a chance for the students to get lots of practice using the distance formula.
If all of our students work was so neatly arranged and so carefully done, I think very soon we'd soon have much different jobs. Instead of 'instructing our students' we would be learning from them as equal partners. This what I strive for in my teaching.
David is a Formative Assessment Specialist for Mathematics at New Visions for Public Schools in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his Masters degree in Educational Technology from UBC, and is the co-author of a mathematics textbook. He has been published in ISTE's Leading and Learning, Educational Technology Solutions, The Software Developers Journal, The Bangkok Post and Edutopia. He blogs with the Cooperative Catalyst, and is the Assessment group facilitator for Edutopia. He has also helped organize the first Edcamp in Canada, and TEDxKIDS@BC.