Middle and High School … from a Montessori Point of View
An elegant, non-poisonous, eastern garter snake has been hanging around my container garden. On these last few days with the scent of winter in the air, it’s been sunning itself on the warm gravel on the southern side of our building.
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.
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.
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.
(From our Eminence Immersion)
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.
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.
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.
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).
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 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.
You can plot these data to show the relationship.
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.
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?
My middle school class has been looking at organ systems and we’ve started doing a few dissections. We compared chicken and pig hearts last week.
Pig hearts are large and four-chambered like ours, so they should have matched up very well with the diagrams from the textbook. However, real life tends to be messy, which is one of the first lessons of dissection. It was tricky finding all the chambers, and identifying the valves, even when you knew what you’re supposed to be looking for. It is especially difficult, as one of my students noted, because everything isn’t color coded.
Chicken hearts are a bit trickier, because they’re a lot smaller. They also have four chambers, but the main chamber (the left ventricle) is so dominant that it’s easy to assume that there’s only the two (or even just one) chambers.
One student’s interesting observation was that the pig heart was a lot more pliable than the chicken heart. My best guess was that the chicken heart is made of a tougher muscle — it’s denser and more elastic (in that it rebounds to its original shape faster) — because has more work to do: chicken heart rates can get up to 400 beats per minute (Swinn-Hanlon, 1998) compared to 70 beats per minute for the pig.
To get a better feel for the texture, and to engage our other senses in our observations on the hearts, at the end of the dissection, which was conducted in the dining room using kitchen utensils, I fried up some of the chicken hearts with onions for lunch.
There are a number of nice labs for heart dissections online:
The hearts were purchased at the Chinese supermarket, Seafood City. There seems to be a greater organ selection on the weekends.
William Sieghart does a wonderful question and answer in his Poetry Pharmacy in the Guardian, where he recommends poetry to salve his questioners existential (and not so existential) needs.
For example:
Hi William,
Do you have any poems that clear up a hangover or diarrhoea (preferably both)?
Sounds like you have been living life to the full! Why not congratulate yourself on the good times you enjoyed yesterday rather than being miserable about your today’s predicament? Dryden’s Happy the Man is a good bet:
Not Heaven itself upon the past has power,
But what has been, has been, and I have had my hour.
Another:
It’s a restriction insisted upon by my tenancy – I’m not allowed to keep a dog. I need a poem to help fill the gap left by the absence of a faithful hirsute canine companion. Dr Sieghart, what do you suggest?
Dr Sieghart’s remedy:
I prescribe some of the most famous words in English – ‘You’ll Never Walk Alone’ by Oscar Hammerstein II. The great consoling line of the title comes after the pain of isolation:Walk on, through the wind
Walk on, through the rain
Though your dreams be tossed and blownWalk on, walk on, with hope in your heart
And you’ll never walk alone
You’ll never walk alone.
Elements can be identified from the color of light they give off when they’re ionized: their emission spectra. Ms. Wilson’s chemistry class today set fire to some metal salts to watch them burn.
She placed the salt crystals into petri dishes, submerged them in a shallow layer of alcohol, and ignited the alcohol. As traces of the salts were incorporated into the flames, the metal atoms became “excited” as they absorbed some of the energy from the flame by bumping up their electrons into higher electron shells. Since atoms don’t “like” to be excited, their excited electrons quickly dropped back to their stable, ground state, but, in doing so, released the excess energy as light of the characteristic wavelength.
Table 1: Emission colors of different metals.
| Metal | Flame |
|---|---|
| Copper |  |
| Strontium |  |
Sodium |  |
Lithium |  |