The slide on the third floor of the City Museum. A co-ordinate system is overlayed, and points showing the curve of the slide are selected.Elegant curves.
I asked my students to take pictures of the curves they found while on our field trip to the scrap metal playground that is the City Museum. The plan is to see if we can determine what functions best fit the curves. To do so, we need to transfer the curves from the images to a co-ordinate system. Since I’m primarily interested in what type of functions might best fit the data, the scale of the co-ordinates does not matter that much.
Feet, inches, meters, centimeters, pixels, or any other units can be used. In fact, I use a purely arbitrary set of coordinates in the image above. All I require is that the grid be evenly spaced (although the vertical and horizontal spacing don’t have to be the same, it’s more straightforward if they are).
Now we take a set of points that lie on our shape and try to match them to some sort of curve using a spreadsheet, and, if we’re able, least squares regression.
There were lots of shapes to choose from.
There were lots of shapes to choose from, including the nice sinusoid in the background.
Our middle and high school students tried their hands at geocaching on our visit to the Audubon Center at the confluence of the Mississippi and Missouri Rivers.
They got their GPS units and instructions on how to use them: basically just choose the right waypoint and follow the arrow. They were told that they wouldn’t need to walk through the prairie.
But the arrow pointed toward the prairie.
Following the GPS.(These guys were actually on a trail). The Mississippi River is in the background.
The results were scratched legs and quite a number of boarders.
Seedpod boarders.
Afterwards, our guide pointed out that they could have found all the caches by using the paths.
Looking into the narrow passageway that our guides called the "Birth Canal".
They took us into a sculpted, limestone cavern they called “Twins Cave”. The entrance was large, but, for those with the predilection, there were narrower passageways that required crawling, wiggling, and a definite lack of claustrophobia.
Apart from the wonderful speleotherms, the cave was home to some charismatic fauna.
An owl sits amid the stalactite formations near the roof of the cave.A salamander wanders the floor, picking its way through the limestone debris.
Though I did not capture any pictures of bats, they flew around us, and we found evidence of their presence just under the cloying red mud that covered most of the cave floor.
Much of the cave was floored with a sticky, red, residual clay, which, in places, covered deposits of bat guano.
The limestone precipitated cave formations were quite beautiful: fluted, cathedral-organ-like stalactites;
Fluted stalactites reminiscent of Gaudi.
thin, precise straws hanging from the ceiling:
Looking up at the crystal encrusted straws hanging from the ceiling.
The juxtaposition of the beauty above us and the mess beneath our feet brought into focus the idea that happiness is not an absolute thing, but rather comes from the difference between misery and joy.
Observing my students figuring out how to canoe on the river this last outdoor education trip has reinforced my belief in the effectiveness of authentic team-building experiences over simulations and co-operative games.
Each morning, I assigned different pairs of students to each canoe. One of the main objectives of the outdoor ed trip is to help integrate the 7th and 8th graders, and the new 8th graders into a cohesive group. Good relationships among the students are necessary to achieve the benefits of the multi-age classroom.
Figuring out which way is upstream and which way is downstream.
It took them a while (sometimes up to an hour on the water), but they eventually figured out how to work together.
And when one of the canoes tipped over — more from overconfidence than from anything else — everyone pitched in to help recover the canoe.
Recovering the tipped canoe.
Then, when the storms came, they pulled together and all the practice paid off.
Paddling through the storm.
No simulation could have matched the experience.
Forging a team out of cold water, thunder, and lightening.
Out along the Current River, we found evidence of large, vegetarian animals (see above). When we described the feces to our guide, he suspected that they might be from one of the small herds of wild horses that roam the area.
The story goes, that when the government acquired the lands for the Current River Conservation Area and changed the rules about what could be done in the area, horses were released in protest by the local farmers.
Students take a break for journaling during our canoe trip on the Current River.
It was not all dark and stormy on our Outdoor Education canoe trip. The first afternoon was warm and bright; the first splashes of fall color spicing up the deep, textured greens of the lush, natural vegetation. It was so nice that, in the middle of the afternoon, we took a short break, just shy of half an hour, to reflect and journal.
A time an a place for reflection.
Our guides chose to park our boats at a beautiful bend in the river. Most of my students chose to sit in the canoes or on the sandy point-bar on the inside of the meander, but a few to be ferried across the river to a limestone cliff on the cut-bank of the curve. An enormous, flat-topped boulder had fallen into the water to make a wonderfully picturesque site for quiet reflection for two students. A third student chose to sit in a round alcove sculpted by the solution weathering of the carbonate rock itself.
A shady place to stop and think.
The cut-bank of a river’s meander tends to be deeper than the inside of the curve, because the water is forced to flow faster on the outside of the bend where it has more distance to travel. This proved to be quite convenient for my students, because it meant that the stream-bed around their boulder was deep enough that they could jump into the water after the hot work of writing while sitting in the sun. And they did.
Rain falls.
Some runs off,
Some seeps into the ground.
Water drips from the tips of limestone straws on the roof of Twins Cave.
It trickles through soil.
Leaching acids, organic,
Out of the leaf litter,
But even without these,
It’s already, every so slightly, corrosive, From just the carbon dioxide in the air.
Gravity driven,
The seeping water seeks the bedrock,
Where it might find,
In the Ozark Mountains,
Limestone.
Planktonic shell (from Coon Creek which is 30 million years old, compared to the limestone rocks in the Ozarks which are 300 million years old.)
Limestone:
Microscopic shells, of plankton,
Raining down, over millenia,
Compacting into rocks,
In a closing ocean,
As North America and Africa collide,
From the Devonian to the Carboniferous.
Orogenic uplift,
Ocean-floor rocks,
Become mountains,
Appalachians, Ouachitas,
The Ozark Plateau.
The collision of North America and Africa uplifted the limestone rocks from the closing ocean (the Rheic Ocean) to create the Ouachita Mountains and Ozark Plateau. (Figure adapted from iimage by Dr. Ron Blakey - http://jan.ucc.nau.edu/~rcb7).
Limestone dissolves,
In acid water.
Shaping holes; caves in bedrock,
Where we go,
Exploring.
The middle school has been studying The Tempest over the last quarter. In order to give students a deeper connection with this Shakespearean play, we arranged for students to experience the titular meteorological phenomenon on our outdoor education trip last week. Since we’re located in the mid-continent, replicating the precise maritime conditions and acquiring the appropriate vessel would have been cost prohibitive. Instead, taking advantage of the local geography and socio-cultural predilections, we improvised by arranging for a series of thunderstorms during a canoe trip in the Ozarks.
In truth, the main purpose of our outdoor education trip was to integrate the upcoming 7th graders and new students into the middle school class. The key advantage of the multi-aged classroom is the opportunity for older students to mentor the younger students, and propagate the appropriate classroom culture and expectations from year to year. But for this to work well requires students to develop strong working relationships and communication skills. The isolation of the trip (no technology) and the coordination required for the tasks we perform (such as paddling a 2-person canoe) greatly facilitate this process.
Despite being drenched, chilled, and a little scared, the group’s performance was remarkable. They endured the worst of the storms, looking out for each other with encouraging words and heartening smiles. They found the strength within themselves as individuals and as a group to keep morale high while on the river. And, when we pulled over, were able to bask in the giddy relief that a good group feels after stressful situations. By the end, they had developed a genuine camaraderie forged by a shared, intense challenge.
P.S. We also did some rock climbing, caving, spent a night on a sandbar, journaled, and learned a bit about geology, hydrogeology, fish surveys, the rock cycle, and some vocabulary (“hubris” was a term, new to many, that was ably demonstrated by the pair who flipped their canoe).
Rock climbing.Spelunking.
P.P.S. Our excellent, invaluable guides on the trip were from Discovery Ministries, which is a religious organization, but they do non-religious programs for groups like ours.
