Radishes ready for harvest.

The radishes did well this year. Planted in containers on March 29th (in St. Louis, USA), they were harvested one month later. The short, early season means that they’re a workable crop for school. Students can plant, harvest, and consume them all within a semester.

The CDC’s Fruit and Vegetable of the Month website has a little history, some information about the varieties, nutritional information, recipes, and more information about radishes. The University of Illinois Extension also has information about planting and growing.

NutritionData.self.com has some very nice graphical representations of the nutritional value of the food (although their serving size is 1 cup of slices, which seems a bit much).

These sites, however, focus on the radish bulbs, and not on the fact that the leaves are edible. Radish Leaf Pesto is quite good.

Harvested radishes. Both the red bulbs and the green leaves are edible. You'll note that radishes also spot a long tap-root.

Citing this post: Urbano, L., 2012. Radishes, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: biology, cooking, radishes, school garden

I told my two (elementary aged) kids that if they didn’t behave Santa would fill their stockings with coal. They were so excited. Since the coals we use on the grill can’t melt metal, they were hoping some real coal would burn hotter. They want to make rings.

Citing this post: Urbano, L., 2011. Coal in Their Stockings, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: curious

Energy cannot be either created or destroyed, just changed from one form to another. That is one of the fundamental insights into the way the universe works. In physics it’s referred to as the Law of Conservation of Energy, and is the basic starting point for solving a lot of physical problems. One great example is calculating the average temperature of the Earth, based on the balance between the amount of energy it receives from the Sun, versus the amount of energy it radiates into space.

The Temperature of Radiation

Anything with a temperature that’s not at absolute zero is giving off energy. You right now are radiating heat. Since temperature is a way of measuring the amount of energy in an object (it’s part of its internal energy), when you give off heat energy it lowers your body temperature. The equation that links the amount of radiation to the temperature is called the Stefan-Boltzman Law:

Now if we know the surface area of the Earth (and assume the entire area is radiating energy), we can calculate how much energy is given off if we know the average global temperature (the radius of the Earth = 6371 km ). But the temperature is what we’re trying to find, so instead we’re going to have to figure out the amount of energy the Earth radiates. And for this, fortunately, we have the conservation of energy law.

Energy Balance for the Earth

Simply put, the amount of energy the Earth radiates has to be equal to the amount of energy gets from the Sun. If the Earth got more energy than it radiated the temperature would go up, if it got less the temperature would go down. Seen from space, the average temperature of the Earth from year to year stays about the same; global warming is actually a different issue.

So the energy radiated (E_R) must be equal to the energy absorbed (E_A) by the Earth.

Now we just have to figure out the amount of solar energy that’s absorbed.

Incoming Solar Radiation

The Sun delivers 1367 Watts of energy for every square meter it hits directly on the Earth (1367 W/m^-2). Not all of it is absorbed though, but since the energy in solar radiation can’t just disappear, we can account for it simply:

• Some if the light energy just bounces off back into space. On average, the Earth reflects about 30% of the light. The term for the fraction reflected is albedo.
• What’s not reflected is absorbed.

So now, if we know how many square meters of sunlight hit the Earth, we can calculate the total energy absorbed by the Earth.

The solar energy absorbed (incoming minus reflected) equals the outgoing radiation.

With this information, some algebra, a little geometry (area of a circle and surface area of a sphere) and the ability to convert units (km to m and celcius to kelvin), a student in high-school physics should be able to calculate the Earth’s average temperature. Students who grow up in non-metric societies might want to convert their final answer into Fahrenheit so they and their peers can get a better feel for the numbers.

What they should find is that their result is much lower than that actual average surface temperature of the globe of 15 deg. Celcius. That’s because of how the atmosphere traps heat near the surface because of the greenhouse effect. However, if you look at the average global temperature at the top of the atmosphere, it should be very close to your result.

They also should be able to point out a lot of the flaws in the model above, but these all (hopefully) come from the assumptions we make to simplify the problem to make it tractable. Simplifications are what scientists do. This energy balance model is very basic, but it’s the place to start. In fact, these basic principles are at the core of energy balance models of the Earth’s climate system (Budyko, 1969 is an early example). The evolution of today’s more complex models come from the systematic refinement of each of our simplifications.

Advanced Work

If students do all the algebra for this project first, and then plug in the numbers they should end up with an equation relating temperature to a number of things. This is essentially a model of the temperature of the Earth and what scientists would do with a model like this is change the parameters a bit to see what would happen in different scenarios.

Feedback

Global climate change might result in less snow in the polar latitudes, which would decrease the albedo of the earth by a few percent. How would that change the average global temperature?

Alternatively, there could be more snow due to increased evaporation from the oceans, which would mean an increase in albedo …

This would be a good chance to talk about systems and feedback since these two scenarios would result in different types of feedback, one positive and one negative (I’m not saying which is which).

Technology / Programming

Setting up an Excel spreadsheet with all the numbers in it would give practice with Excel, make it easier for the student to see the result of small changes, and even to graph changes. They could try varying albedo or the solar constant by 1% through 5% to see if changes are linear or not (though they should be able to tell this from the equation).

A small program could be written to simulate time. This is a steady-state model, but you could assume a certain percent change per year and see how that unfolds. This would probably be easier as an Excel spreadsheet, but the programming would be useful practice.

Of course this could also be the jumping off point for a lot of research into climate change, but that would be a much bigger project.

References

Yochanan Kushnir has a page/lecture that treats this type of zero-dimesional, energy balance model in a little more detail.

Citing this post: Urbano, L., 2011. Global Temperature Model: An Application of Conservation of Energy, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: assignments, climate, excel, fundamental principles of physics, my diagrams, physics, programming, projects, radiation, research projects, temperature

… despite being weightless, they still have mass.

(article, headline)

Citing this post: Urbano, L., 2011. Pope blesses astronaut ..., Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: physics

Razib Kahn has a fascinating interview with Milford Wolpoff, one of the main scientists behind the research that argues that humans are not all part of a single family tree, descended from a single ancestor who moved out of Africa about 200,000 years ago.

This section focuses on the theory, and has a nice explanation of what mitochondrial DNA is (and why it’s important):

It gives an excellent perspective on how science works, and how scientists work (scientists are people too with all the problems that entails).

The entire thing is a bit dense, but it’s one of the better discussions I’ve seen describing the process of science in action, with little hints at all the challenges that arise from personality conflicts and competing theories.

Citing this post: Urbano, L., 2011. Human Evolution not Drawn as a Tree?, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: anthropology, archeology, earth science, genetics, heridity, phylogenetic tree, racism, science

“It’s like finding out Santa Claus doesn’t exist.”

That was my student’s response on discovering that jacklopes do not actually exist.

She’d been planning on doing her Independent Research Project on jacklopes. She’d already invested some time in doing some internet research, and this morning she came up to me and asked, “Are jacklopes real?”

A jackalope on the wall of a restaurant near the west entrance to Death Valley (image by SedesGobhani via Wikimedia Commons).

I told her they weren’t, but she had to go look them up herself in actual hardcopy, the Wildlife Fact-file binders that we keep on the reference shelf. They weren’t in there.

I offered that she could still do her IRP on jackalopes, just focusing on the cultural meanings and reasons behind the phenomenon. Also she could discuss the potentials for genetically engineered organisms.

She’s still considering it.

Citing this post: Urbano, L., 2011. Jackalopes, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: IRP, journal

MediaBistro has a series of posts for National Novel Writing Month to inspire and assist the serious writer.

Tips and links range from how to start a writing bible, to the correct writing posture. I’m partial to tip on how to turn your computer into a typewriter, although it’s something that’s never worked for me:

The free Q10 program will convert your distracting computer into an old-fashioned typewriter–focused by real typing sounds and disconnected from the Internet.
-Boog (2010) in GalleyCat

Citing this post: Urbano, L., 2010. Writer's Resources, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in Language Arts, UncategorizedNo Comments » - Tags: language, online resources, websites, writing

Mirable by Janet Kagan

One of my favorite books that ties in with the study of the life sciences is Janet Kagan’s Mirable. It’s a series of stories about colonists trying establish themselves on a new world. Because of an accident on the trip over from Earth, the plants and animals they try bring with them (or propagate from their recorded DNA sequences) tend to randomly, and all too frequently, produce offspring that are hybrids of all sorts of phylogenetically unrelated organisms. The hybrids then produce other hybrids until, eventually, they produce another “Earth-authentic” species. This was supposed to be a feature to add redundancy to their gene banks. The impetus for the stories comes from the fact that some of the hybrids are unexpected and quite interesting, like the kangaroo-rex.

M. A. Buss' model of the kangaroo-rex. Note the sharp pointy teeth and claws.

Kagan writes a good story, entertaining, light hearted and easily accessible to early adolescents, but I particularly like her model of education on the new world. Since they need as much genetic diversity as possible, even people who don’t want to raise children need to have them. So kids are sent to live at a boarding school that’s really a hotel, which they run. Sounds a lot like Montessori’s Erdkinder.

The kids get training and regular visits from experts in a variety of fields. They get to help of the protagonist with her projects by tracking animals in the field and running genetic sequences through their equivalent of GenBank.

The best science fiction provides interesting models of society. Mirable, I believe, is a model of a society designed around the ideas of Peace Education. The Montessori spirit runs throughout the stories not just in the education system, but in the way characters interact one another, even in times of conflict.

I’m an unabashed advocate for using science fiction in the classroom because it delves into such wide ranging parts of the curriculum, Natural World, Social World, Language and, in this case, Peace Education. Of course the stories have to be chosen well. Mirable is one of perhaps only two books (the other is The Chrysalids by John Wyndham) that I use when we study the life sciences.

Citing this post: Urbano, L., 2010. Montessori Science Fiction, Retrieved May 19th, 2012, from Montessori Muddle: http://MontessoriMuddle.org/ .
Attribution (Curator's Code ): Via: ᔥ Montessori Muddle; Hat tip: ↬ Montessori Muddle.

Posted in UncategorizedNo Comments » - Tags: books to read, genetics, literature, novels, peace education, science, science fiction