Year: 2012

Caving

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.

(Eminence Immersion)

Authentic Teambuilding

Figuring out how to work a canoe.

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.

From our Eminence Immersion.

Evidence of Wild Horses

From horses?

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.

(From our Eminence Immersion)

Journaling on the River

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.

Cool water after sitting in the sun.

(From our Eminence Immersion)

OpenStreetMap


View Larger Map

I’ve been using Google Maps on this blog and for a lot of my applications (e.g. Mariner A.O.), but I’ve just come across OpenStreetMap, which I should be able to use instead. It has an API, nicely embedable maps (including significant topographic coverage), but most importantly, is free and open-source.

Now I just have to see if I can get it to work reliably.

↬ Carl Franzen on TPM ↬ Reddit

Shrimp

Drawing an external diagram of a jumbo shrimp.

Our middle-school dissections have moved on from hearts to whole organisms. This week: jumbo shrimp.

I particularly like these decapods because the external anatomy is simple but interesting, including: eyes on stalks; a segmented body; 5 pairs of swimming legs; 5 pairs of walking legs. The simple, clear layout make them a good subject for students to work on improving the accuracy of their full-scale drawings.

External anatomy of a shrimp.

The internal anatomy is a bit harder to distinguish, however, since the organs are relatively small. Most of my students found it difficult to remove the carapace without smushing everything inside the thorax, which includes the stomach, heart, and digestive gland.

Dissecting the shrimp.

The abdominal segments were easy to slice through, on the other hand, and we were able to identify the hindgut (intestine), which runs the length of the back side, and the blueish-colored, nerve cord that is nearer the front (ventral) side.

Under the microscope, you could see little mineral grains in the contents of the gut. Although I did not manage to, I wanted to also mount the thin membrane beneath the carapace on a slide. If I had, we might have been able to see the chromatophores, “star- or amoeba-shaped pigment-containing organs capable of changing the color of the integument” (Fox, 2001).

References

Richard Fox (2001) has a good reference diagram and description of brown shrimp anatomy.

M. Tavares, has compiled some very detailed shrimp diagrams (pdf) (originally from Ptrez Farfante and Kensley, 1997)

Inverse Relationships

Inverse relationships pop-up everywhere. They’re pretty common in physics (see Boyle’s Law for example: P ∝ 1/V), but there you sort-of expect them. You don’t quite expect to see them in the number of views of my blog posts, as are shown in the Popular Posts section of the column to the right.

Table 1: Views of the posts on the Montessori Muddle in the previous month as of October 16th, 2012.

Post Post Rank Views
Plate Tectonics and the Earthquake in Japan 1 3634
Global Atmospheric Circulation and Biomes 2 1247
Equations of a Parabola: Standard to Vertex Form and Back Again 3 744
Cells, cells, cells 4 721
Salt and Sugar Under the Microscope 5 686
Google Maps: Zooming in to the 5 themes of geography 6 500
Market vs. Socialist Economy: A simulation game 7 247
Human Evolution: A Family Tree 8 263
Osmosis under the microscope 9 219
Geography of data 10 171

You can plot these data to show the relationship.

Views of the top 10 blog posts on the Montessori Muddle in the last month (as of 10/16/2012).

And if you think about it, part of it sort of makes sense that this relationship should be inverse. After all, as you get to lower ranked (less visited) posts, the number of views should asymptotically approach zero.

Questions

So, given this data, can my pre-Calculus students find the equation for the best-fit inverse function? That way I could estimate how many hits my 20th or 100th ranked post gets per month.

Can my Calculus students use the function they come up with to estimate the total number of hits on all of my posts over the last month? Or even the top 20 most popular posts?