Stormfields

Cucumber Day in Calculus, 2014 Edition

FracTad's Fractopia

If I’ve used an activity for three years in a row, I guess it’s a tradition! My calculus students have done this one for several years now, and it’s always been a hit.

To introduce the concept of volumes of rotated solids, I have my students slice cucumbers into disks and measure the volume of each slice. Then they add them up to approximate the total volume. It’s a nice way to help them visualize objects in 3D. You can read about what we do in a couple of earlier posts, here and here.

Here are the basics of the lesson:

1. Review the formula for the volume of a cylinder:

Volume Formula

2. Pair up the students, and distribute the cucumbers.

I used small seedless cucumbers that came six to a pack, and were relatively similar in size:

Cukes

Have a discussion on whether we can use the cylinder volume formula to…

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It’s Time to Connect With John Wesley

Progarchy

Disconnect-cover InsideOut Music  recently signed John Wesley to its label, and his new album, Disconnect , will be available March 31 in Europe and April 1 in the U.S.  I’m not pulling an April Fools’ joke when I say that it is my favorite album of 2014 so far (despite stiff competition from  the likes of John “KingBathmat” Bassett , Gazpacho , and Transatlantic ).

Who is John Wesley? Hailing from Tampa, Florida, he’s an enormously talented guitarist and vocalist who has toured with Porcupine Tree, Fish, and Steven Wilson. Check out Porcupine Tree’s DVD, Anesthetize, to see how integral he was to their live show. As a matter of fact, after watching that DVD, I wondered why Steven Wilson didn’t go ahead and make Wesley an official member. His guitar playing and vocals added a new and exciting dimension to Wilson’s songs.

Approaching Wesley’s new solo work, I had low…

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Integrity’s Minstrel: John Bassett. Unearth (2014)

Progarchy

Unearth-Album-Cover A review of John Bassett, Unearth ( Stereohead Records ; release date: March 31, 2014).

I’m honestly not sure if my admiration for John Bassett knows many—if any—bounds.

When we first announced progarchy’s birth in the fall of 2012, Kingbathmat’s label reached out to us immediately.  As objective as I’m trained to be in my own actual day-to-day profession (though, I’ve become firmly convinced that so-called objectivity is highly overrated), it’s hard not to be grateful when someone, some band, or some label contacts us.  After all, it’s automatically a profound sign of trust, though always based on a leap of faith.

As reviewers and lovers of music, we’re, of course, not for sale.  Still, we are rather human.  Kindness and relationships make a difference in the ways we perceive artists.  In no genre of music is this more true than in prog, as the audience matters so deeply to…

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The Five Biggest Myths About Secession

Pileus

With the ongoing tension over Russia’s annexation of Crimea, now would be a good time to talk about the biggest myths people believe about the origins of secessionist movements around the world (even though Crimea is a case of irredentism not secessionism).

  1. Myth: Secession is contagious. Back in the 1990s, journalists worried a lot that the disintegration of the Soviet Union, Czechoslovakia, Yugoslavia, and Ethiopia heralded some broader worldwide trend toward the splintering of the state. Even some scholars indulged talk of our “neomedieval” future of microstates. Now, with secession referendums in Scotland and Catalonia on the docket, a secessionist party gaining support in Quebec, that online referendum in Veneto, and recent events in the post-Soviet space, I’m seeing similar questions about whether this is a new “trend.”

    Fact: Secession happens because of particular circumstances, not contagion. Scholars have looked at the evidence every which way, and in no…

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A Couple of Reading Recommendations

FracTad's Fractopia

I’ve been on Spring Break this week, and we’ve stayed home this year, which has been nice. I’ve had a chance to catch up on some reading, and I really enjoyed two books in particular – one nonfiction, and one fiction. Both will appeal to teachers and lovers of mathematics.

First, the nonfiction book: Amanda Ripley’s The Smartest Kids in The World and How They Got That Way. I’ve read many books about education, and how American schools are failing our students, but this one is the most eye-opening and refreshing take on that subject I’ve seen. Ms. Ripley shares her data and conclusions through the personal stories of three American high school students who participate in foreign exchange programs. Kim leaves Oklahoma to spend a year in Finland, which has been in the news lately because of its students’ extraordinary performance on the PISA (Program for International Student…

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Math Is So Romantic

FracTad's Fractopia

I’ve been using a new review technique with the students in my Calculus class – speed dating! I wish I could take credit for it, but one of the incredibly creative teachers in the Harpeth Hall math department, Maddie Waud, introduced me to it. The first time I tried it, I was very pleased with how seriously my students took it, and after they finished, they all agreed it was helpful.

To set up a classroom for a speed dating session, divide all the desks into pairs facing each other. I put mine in a large circle.

Speed Dating1

Speed Dating2

At each pair of desks, place a problem for the partners to solve.  There are 18 students in the class, so I wrote up 9 problems. If there an odd number of students, the teacher can fill in and give whoever the solo student is some hints to solve her problem.

Problem

Give the students…

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Why So Little Decentralization?

Pileus

Many scholars (forinstance) have noted a trend around the world of greater decentralization, at least on certain dimensions. Many non-federal, unitary states have tried to devolve some spending and decision-making authority on local or regional governments. Virtually every democratic government nowadays at least feigns some interest in decentralization.

Yet what strikes me is how little decentralization there has been, especially in the developing world. Some developing democracies that are sometimes described (or describe themselves) as “federal” or “semi-federal” include Mexico, India, Indonesia, Brazil, Argentina, Venezuela (before it went authoritarian some time in the 2000s), South Africa, Malaysia, Pakistan, Iraq, Nepal, and Nigeria. Yet none of these countries, other than Mexico, affords its constituent state or regional governments autonomy commensurate with that found in federal and semi-federal “Western liberal democracies” like Spain, Canada, the U.S., Switzerland, Belgium, Germany, Austria, Australia, and Italy. For instance, in Brazil, states do…

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