Assessment of Knowledge of Curriculum Big Ideas Martin Kozloff Copyright 2006 Task 1

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Assessment of Knowledge of Curriculum

Big Ideas

Martin Kozloff

Copyright 2006
Task 1.

Give examples of two big ideas in subject matter of your choosing. Explain how these big idea will assist students to organize, retrieve, and apply knowledge. [Make sure that your examples are the correct type; e.g., a concept. And make sure that your examples of big ideas are general enough to organize much material, because that is what they are for.]

1. Core concept.



2. Propositions, principles, or rule-relationships.



3. Theories and models


Task 2. Persian Wars

Your job is to develop several big ideas that will help students understand why or how 300 Spartans were willing and able to fight so bravely, knowing they could not defeat the enormous Persian army, and would surely be killed. Write what you would say to your students to introduce a unit on the Persian Wars, just as Mr. Lee presented a model of conflict to introduce a unit on the American Revolution. Here are your resources.

Persian Wars.

Little Greece Huge Persian

The Persian King Darius invaded Greece in 490 BC. His enormous army fought the much smaller Greek force at the battle at Marathon (490 BC).  Darius and his army were driven into the ocean and went back to Persia.

Darius's son, Xerxes, tried again (480 BC) to conquer Greece.  The Greeks sent a few thousand hoplites (heavily armed infantry) to Thermopylae (hot gates)--a narrow mountain pass in northeastern Greece.  The point was to stall the Persians long enough that the Greek city states to the south could prepare for later battles when the Persians broke through and came south. If the Greeks had not held off Xerxes at Thermopylae, the Persians probably would have conquered the unprepared Greek cities. That would have been the end of western civilization. There would have been no ideas of democracy, philosophy, and science to pass on to the Romans.

The leaders of the Greeks at Thermopylae were King Leonidas of Sparta


and his 300 Spartan hoplites. The Spartans were known as the toughest soldiers around. They never gave up and they never left a wounded comrade behind.

For several days, Xerxes sent waves of Persian soldiers against the Greeks, but the Greeks beat them back. However, Leonidas and his Spartans knew they couldn't endure. There were about 300,000 Persians and a few thousand Greeks. So, Leonidas sent everyone home to prepare for later battles, leaving the 300 Spartans to hold on.

A traitor named Ephialtes (probably a goat herder from the hills around Thermopylae) told the Persian King Xerxes of a path around the mountain that would enable Xerxes to encircle the Spartans. Here's the account of the historian Herodotus of the Spartan's last stand.

At sunrise, Xerxes made his libations and...made his attack.... (T)he Greeks, knowing that their own death was coming to them from the men who had circled the mountain, put forth their utmost strength against the barbarians; they fought in a frenzy, with no regard to their lives...Most of them had already lost their spears by now, and they were butchering Persians with their swords... (T)he Greeks retreated into the narrow part of the road, and...defended themselves with daggers--those who had any of them left--yes, and with their hands and teeth, and the barbarians buried them in missiles, some attacking them in front...while those who had come round the mountain completed the circle of their attackers.  (Herodotus.  History.)

The tomb at Thermopylae. The Spartans' message to the world.

"Go, stranger, and tell the Spartans that we lie here in obedience to their laws." [Simonides of Creos.]

Other writings of the Greeks Concerning the Spartans.

For no man ever proves himself a good man in war

unless he can endure to face the blood and the slaughter,
go close against the enemy and fight with his hands.

Here is courage, mankind's finest possession, here is
the noblest prize that a young man can endeavor to win,
and it is a good thing his city and all the people share with him
when a man plants his feet and stands in the foremost spears
relentlessly, all thought of foul flight completely forgotten,
and has well trained his heart to be steadfast and to endure,
and with words encourages the man who is stationed beside him.

Here is a man who proves himself to be valiant in war.

With a sudden rush he turns to flight the rugged battalions
of the enemy, and sustains the beating waves of assault.
And he who so falls among the champions and loses his sweet life,
so blessing with honor his city, his father, and all his people,
with wounds in his chest, where the spear that he was facing has transfixed
that massive guard of his shield, and gone through his breastplate as well,
why, such a man is lamented alike by the young and the elders,
and all his city goes into mourning and grieves for his loss.
His tomb is pointed to with pride, and so are his children,
and his children's children, and afterward all the race that is his.


It is beautiful when a brave man of the front ranks,
falls and dies, battling for his homeland,
and ghastly when a man flees planted fields and city
and wanders begging with his dear mother,
aging father, little children and true wife.
He will be scorned in every new village,
reduced to want and loathsome poverty; and shame
will brand his family line, his noble
figure. Derision and disaster will hound him.
A turncoat gets no respect or pity;
so let us battle for our country and freely give
our lives to save our darling children.

Young men, fight shield to shield and never succumb

to panic or miserable flight,
but steel the heart in your chests with magnificence
and courage. Forget your own life
when you grapple with the enemy.
Never run
and let an old soldier collapse
whose legs have lost their power. It is shocking when
an old man lies on the front line
before a youth: an old warrior whose head is white
and beard gray, exhaling his strong soul
into the dust, clutching his bloody genitals
into his hands: an abominable vision,
foul to see: his flesh naked. But in a young man
all is beautiful when he still
possesses the shining flower of lovely youth.
Alive he is adored by men,
desired by women, and finest to look upon
when he falls dead in the forward clash.

Let each man spread his legs, rooting them in the ground,

bite his teeth into his lips, and hold. [Tyrtaeus of Sparta c. 630 BC]


1. What big ideas (e.g., Greek concepts, such as definition of a man, a good man) are revealed in the writing on the tomb of the Spartans and in their poetry?

2. Write a procedure by which you could communicate that big idea to your class. Use quotations from the above or other materials to exemplify the big idea.

Task 3. Convection cells

Convection cells are a big idea that can connect a lot of material (material that only seems to be different) in sciences courses or science lessons. Examine the materials, below. Then write out what you would say to teach the big idea of convection cells, and prepare graphics (from the materials below, if you wish) you would use to introduce the big idea of convection cells. [Hint: Definition. Diagram. Examples.]


A convection cell is a phenomenon of fluid dynamics which occurs in situations where there are temperature differences within a body of liquid or gas.

Fluids are materials which exhibit the property of flow. Both gases and liquids have fluid properties, and, in sufficient quantity, even particulate solids such as salt, grain, or gravel show some fluid properties. When a volume of fluid is heated, it expands and becomes less dense, and thus more buoyant than the surrounding fluid. The colder, more dense fluid settles underneath the warmer, less dense fluid and forces it to rise. Such movement is called convection, and the moving body of liquid is referred to as a convection cell.

A rising body of fluid typically loses heat because it encounters a cold surface, because it exchanges heat with colder liquid through direct exchange, or in the example of the earth's atmosphere, because it radiates heat. At some point the fluid becomes more dense than the fluid underneath it, which is still rising. Since it cannot descend through the rising fluid, it moves to one side. At some distance its downward force overcomes the rising force beneath it and the fluid begins to descend. As it descends, it warms again through surface contact, conductivity, or compression, and the cycle repeats itself. (The heating through compression of descending air is what is responsible for such welcome winter phenomena as what is known in Western North America as a chinook or in the Alps as a foehn.)

Altocumulus cloud as seen from the space shuttle. Altocumulus is formed through convective activity.

Convection cells can form in any fluid, including the Earth's atmosphere, boiling water or soup (where the cells can be identified by particles they transport, such as grains of rice), the ocean, the surface of the sun, or even a farmer's field, where large rocks have been seen to be forced to the surface over time in a process either analogous to or directly related to convection (the connection is not yet clear).

The size of convection cells are largely determined by the fluid's properties, and they can even occur when the heating of a fluid is uniform.

Convection cells on the Sun with North America superimposed

The Sun's photosphere is composed of convection cells called granules, rising columns of superheated (5800 °C) plasma averaging about 1000 kilometres in diameter. The plasma cools as it rises and descends in the narrow spaces between the granules.

convection - energy transport - fluid dynamics

What it shows:

Hot fluid rises, cool fluid sinks. Here is a desktop convection cell modeling the processes in the atmosphere, oceans or stellar interiors.

Setting it up:
The heater is a small hotplate set at around 200W output. The aluminum block needs to be chosen to match the height of the heater (or adjusted to do so) for good thermal contact. The translucent nature of the fluid makes back lighting probably the best option - there is too much reflection off of the glass wall in front lighting. A camera setup is required - play around with the aperture to get the best contrast.

Heat Transfer

The transfer of heat is normally from a high temperature object to a lower temperature object. Heat transfer changes the internal energy of both systems involved according to the First Law of Thermodynamics.

Heat transfer from a cold to a hotter region


R Nave

Heat Conduction

Conduction is heat transfer by means of molecular agitation within a material without any motion of the material as a whole. If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones. For heat transfer between two plane surfaces, such as heat loss through the wall of a house, the rate of conduction heat transfer is:

Heat Convection

Convection is heat transfer by mass motion of a fluid such as air or water when the heated fluid is caused to move away from the source of heat, carrying energy with it. Convection above a hot surface occurs because hot air expands, becomes less dense, and rises (see Ideal Gas Law). Hot water is likewise less dense than cold water and rises, causing convection currents which transport energy.

Convection can also lead to circulation in a liquid, as in the heating of a pot of water over a flame. Heated water expands and becomes more buoyant. Cooler, more dense water near the surface descends and patterns of circulation can be formed, though they will not be as regular as suggested in the drawing.

Convection cells are visible in the heated cooking oil in the pot at left. Heating the oil produces changes in the index of refraction of the oil, making the cell boundaries visible. Circulation patterns form, and presumably the wall-like structures visible are the boundaries between the circulation patterns.

Convection is thought to play a major role in transporting energy from the center of the Sun to the surface, and in movements of the hot magma beneath the surface of the earth. The visible surface of the Sun (the photosphere) has a granular appearance with a typical dimension of a granule being 1000 kilometers. The image at right is from the NASA Solar Physics website and is credited to G. Scharmer and the Swedish Vacuum Solar Telescope. The granules are described as convection cells which transport heat from the interior of the Sun to the surface.

In ordinary heat transfer on the Earth, it is difficult to quantify the effects of convection since it inherently depends upon small nonuniformities in an otherwise fairly homogeneous medium. In modeling things like the cooling of the human body, we usually just lump it in with conduction.

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