Collaborative Investigation and the Flipped Classroom

Introduction
My first year of teaching was in 1995 at an innovative, elite private high school in San Francisco named Lick-Wilmerding. The math department at Lick-Wilmerding employed a method of teaching which was unfamiliar to me and to most teachers at the time. Students worked in small groups of 3 or 4, exploring geometric relationships on a shared laptop and reporting their findings in documents written as if they were lab reports. Studying algebra, students used graphing calculators to explore functions dynamically and again, report their findings in written form accompanied by detailed examples and analysis. Students would receive direct instruction when necessary, but for the most part questions were explored and answered by members of the groups themselves. I adapted hesitantly to this new structure, as I myself had been taught by teachers and professors using lecture combined with repetitive homework. Over my subsequent years of teaching in the states I explored a range of methods tailored to the various cultures of the schools at which I taught. This included straight lecture and homework, a mixture of lecture and independent class work, and collaborative group work supported by a traditional textbook. Finally, now at the American School of Valencia, I’ve developed a suite of collaborative investigations which allow my ninth and tenth grade math students to explore mathematical concepts much as they explore scientific concepts in laboratories. This is supported by online resources which include videos and extra practice problems.

When are we ever going to use trigonometry?

In the summer of 1994 I worked at an outdoor education center in Montana. We lived in crumbling Forest Service barracks on the north fork of the Flathead River. The Douglas Fir forest swarmed with deer, at night we heard mountain lions. Every week a bus would ramble up the dirt road and empty a rabble of fifth graders versed enough to recognize a bull trout but still thrilled to see otters riffling the river, and recoiling in nervous delight from binoculars when they spotted a grizzly on the adjacent huckleberry mountain. Teaching kids about the outdoors in a place so wild was like teaching art history in Le Louvre.

The Memory Stream

Long ago. Throwing a baseball in North Carolina summer listening to a boom box. Sleeping curled next to a fire amid the pregnant lush of Nantahala. Thimbleberries. Napping under pines in Idyllwild, waking to boulder until sunset. The stillness of Potomac herons and the gleaming floors of Congressional offices. The crunch of bicycle tires on gravel, grinding towards cornfield horizons in summer Iowa. Writing love songs as the marine layer burns away in Santa Barbara. The tang of redwood sorrel, the story of the field mice and the Douglas Fir. The golden plumes of sunset dust at the base of the toothed cliffs of Smith Rock. My Geo Metro in LA with a longboard on the way to Baja. The rough texture of baguette and saucisson while hiking in the Pyrenees. The blue curtain of thunderstorm rain while climbing limestone towers over the Andaman Sea. The way a motorcycle smoothes the rutted dirt roads of Crete. Storming the castle walls in Sintra. The wind and rattlesnakes of Wild Iris. Feeling the waves move me and my spear with the fish at Punta Perfecta. Kids debating parabolas on the last day of school in La Jolla. Seeing my niece and nephews play wave tag at Emerald Isle. Today.

About Rock Climbing

Some Guidelines

1) The less you care about numbers, the more fun you will have and the better you'll climb.

2) Try hard to climb like it's easy. Climb safely and gracefully.

3) Learn and practice using gear at grades below your limit.

4) Learn and practice self-rescue techniques.

5) If you are impatient, progress stops. Be patient and you will improve quickly.

6) We all over-reach sometimes. Back off early if you're in over your head.

7) Really spot people when bouldering, and wear a helmet when doing routes.

8) Treat auto-locking devices like ATC's, with break hand always on.

9) Enjoy the gym but go outside as much as you can.

10) The goal of climbing is not to get to the top, but to have fun outside with your friends. 

Note: The following destinations are not the places to first learn the skills needed to climb there. First learn the technical skills to climb safely. To do this, climb locally and often, with people who really know what they are doing. Do not be reluctant to take classes or ask someone to teach you. Anchor building, leading and self-rescue courses are great. Practice incessantly in safe environments, and ask yourself questions like: "What do I do if I drop my ATC?" and "What do I do if the rope gets stuck?" If you aren't totally sure you know what you are doing and what you'll do if things go wrong, don't climb.