Abstract = Spoilers

Although it feels like you're giving away the whole story -- because you are -- the Abstract should be all spoilers.
Although it feels like you’re giving away the whole story — because you are — the Abstract should be all spoilers.

I was trying to explain that the abstract of a lab report was a really brief summary of everything in the report.

One of my students said, “Oh, so it’s like spoilers.”

And they were right.

If you didn’t know, spoilers are little bits of information that give away the plot. While you don’t want any spoilers if you have not seen the movie, in a lab report you what to give away the plot because since it’s a short, concise summary, it’s what most people will read.

So now my middle-schoolers are submitting lab reports with a section called “Spoilers” on the cover page.

Natural Selection by Alfred Russel Wallace

Everyone knows about Charles Darwin, but hardly anyone remembers Alfred Russel Wallace, who came up with the idea of natural selection at the same time as Darwin. Darwin’s publication of the On the Origin of Species was spurred on by Wallace. Flora Lichtman and Sharon Shattuck shed a little light on Wallace with this video:

Indeed, from the introduction of On the Origin of Species:

I have more especially been induced to [publish], as Mr. Wallace, who is now studying the natural history of the Malay archipelago, has arrived at almost exactly the same general conclusions that I have on the origin of species. Last year he sent to me a memoir on this subject, with a request that I would forward it to Sir Charles Lyell, who sent it to the Linnean Society, and it is published in the third volume of the Journal of that Society. Sir C. Lyell and Dr. Hooker, who both knew of my work—the latter having read my sketch of 1844—honoured me by thinking it advisable to publish, with Mr. Wallace’s excellent memoir, some brief extracts from my manuscripts.

— Darwin, 1859. On the Origin of Species.

↬ The Dish

Global Shipping Patterns Then and Now

Ships tracks in black, plotted on a white background, show the outlines of the continents and the predominant tracks on the trade winds. Image and caption from Sapping Attention.
Ships tracks in black, plotted on a white background, show the outlines of the continents and the predominant tracks on the trade winds. Image and caption from Sapping Attention.

For an interesting historical contrast — that highlights the change from wind to engine powered ships and the opening of the Panama and Suez canals — above is Ben Schmidt’s image created from the log books of U.S. ships in the 19th century, while below is a figure by Ben Halpern showing modern shipping patterns.

This map shows the frequency of shipping traffic along shipping routes around the world, ranging from low (blue) to high (red). Image and caption from SeaWeb.
This map shows the frequency of shipping traffic along shipping routes around the world, ranging from low (blue) to high (red). Image and caption from SeaWeb.

The first image also clearly shows the triangular trade routes between the Americas, Europe and Africa.

Schmidt also has some wonderful videos showing, among other things, the routes of whaling ships that are pushed farther and farther out as they drive whale populations toward extinction.

Discovering Progressive Education

Joshua Davis has a fascinating article on a math teacher who borough collaborative, self-motivated learning to students at a school in a drug-war-torn Mexican city. The results were excellent.

Davis also cites a study by Gopnik and others that showed that:

kids given no instruction were much more likely to come up with novel solutions to a problem.

↬ Ms. Douglass.

The Economic Benefits of Messing with Nature

“… we argue that destroying and replacing the free gifts of nature can be an economic benefit.”
— Gowdy et al. (2012): The Parable of the Bees: Beyond Proximate Causes in Ecosystem Service Valuation via Krulwich Wonders.

Robert Krulwich has a fascinating article that summarizes a research paper that looked into what happened when people had to replace the honeybees to pollinate fruit crops in China. Apparently, from a purely economic standpoint, humans did a better job — they pollinated more flowers — and because people had to be hired to do this, it helped the economy as well.

Despite the economic benefit, summarized by the alarmist quote above, the authors of the article actually use this example to argue that it is foolhardy to use this type of economic analysis for deciding what to conserve.

We do not argue that the positive economic benefits justifies eliminating natural processes. On the contrary, the Maoxian [, China] case illustrates the danger of allowing the logic of the market to drive conservation policy.
— Gowdy et al. (2012): The Parable of the Bees: Beyond Proximate Causes in Ecosystem Service Valuation.

↬ Dr. Sansone

Experiments for Demonstrating Different Types of Mathematical Functions

This is my quick, and expanding, reference for easy-to-do experiments for students studying different types of functions.

Linear equations: y = mx + b

  • Bringing water to a boil (e.g. Melting snow)
  • Straight line, motorized, motion. (e.g. Movement of a robot/Predicting where robots will meet in the middle)
  • Current versus Voltage across a resistor as resistance changes.

Quadratic equations: y = ax2 + bx + c

Exponential functions: y = aekx

  • Cooling water (ref.)

Square Root Functions: y = ax1/2

Trigonometric Functions: y = asin(bx)+c