Monday, October 01, 2018

The Engine of the World

I remember when tenor Andrea Bocelli sprang out of nowhere as the heir apparent to the great Luciano Pavarotti.

For audiences, it always seems like that; suddenly this great supernova explodes into view, changing the sky forever. 

Of course it's not like that at all.

Fame may happen overnight, but the artistic growth and development of a phenomenon like Bocelli is often excruciating slow and painful. The degree of hyper-focus and self-centeredness required of great artists makes intimate relationships all the harder to create and maintain. No wonder addiction and madness are familiar attendants to those having regular intercourse with the Muses.

Yet somehow the fuse finally gets lit, the coming eruption only a matter of counting down. Those that survive ignition share with us glimpses of other worlds, uncommon truths and ephemeral realities, souvenirs of Heaven.

Dear Veronica, my dear children,

Every life is a wonderful story worthy of being told. Every life is a work of art, and if it does not seem so, perhaps it is only necessary to illuminate the room that contains it.

The secret is never to lose faith, to have confidence in God's plan for us, revealed in the signs with which He shows us the way.

If you learn to listen, you will find that each life speaks to us of love. Because love is the key to everything, the engine of the world. Love is the secret energy behind every note I sing.

And never forget that there's no such thing as happenstance. That's an illusion lawless and arrogant men invented so that they could sacrifice the truth of our world to the laws of reason.

Andrea Bocelli (2017 biopic: The Music of Silence)

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Saturday, September 01, 2018

2, 800, 44



Concerning the SAT Math Subject Test, the three most important numbers are:

2, 800, 44.

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2:

You should take the SAT Math Subject Test, Level 2 (SAT2M2). There’s virtually no reason for anyone to take Level 1.

Here’s why:

SAT Subject Tests allow students to pick the two subjects at which they most excel and then show off by getting very high scores on those tests. A very high score on Level 1 of the SAT Math Subject Test is meaningless, because it begs the question: “If this student is so good at math, why didn’t she take the SAT2M2?”

And that would be a good question. If you’re so good at math that you’ve chosen mathematics as one of your two subject test areas, you should certainly be taking the most advanced level of the math subject test, which is Level 2.

Opting for Level 1 of this particular test defeats the purpose of choosing this particular subject area in the first place.

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800:

A perfect 800 is the score you want on the SAT2M2. Fully 20% of students who take the test get this score. A much lower score, once again, kind of defeats the purpose of electing this subject in the first place.

By choosing math as one of your two subject test areas, you’re declaring yourself to be a hotshot math student. You should therefore be able to score in the top 20%, which means you want an 800 on this test, or darn close to it.

The good news is that this isn't that hard to do, as long as you’re truly good at math, make the best possible use of your calculator, and work hard to prepare (i.e. take lots of practice tests, assiduously critique the results, do careful error analysis, and review regularly).

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44:

This is the number of right answers you need out of the 50 questions presented on the SAT2M2.

Notice that you don’t need a perfect score to get a perfect score. Not even close. On average, you only need an 88% (44/50) to score a perfect 800. No one can tell the difference between someone who gets 88% of the answers right and someone who gets 100% of the answers right; on the SAT2M2, both students receive the same scaled score: 800. So you’re shooting for 44. Anything above that is nice, but superfluous.

What about the other six questions?

You get a pass on these six. You can skip them all, get them all wrong, or skip some and get some wrong. It doesn't matter.

Here’s why:

According to the most recently released official SAT2M2 practice tests, on average, you actually only need a raw score (correct answers – .25 * incorrect answers) of 43 to get a perfect 800 scaled score. If you skip all six questions, your raw score is 44. If you answer all six incorrectly, your score is 42.5, which rounds up to 43. If you skip three and get three wrong, your raw score is 43.25, which rounds down to 43.

No matter what you do with the other six questions, as long as you get 44 right answers on this test you’ll likely receive a perfect 800 as your SAT Subject Test score.

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You can probably do this.

Anyone who could score 700 on their own just sitting down and taking the test with no prep at all (requiring a raw score around 33: e.g. 35 right answers, five skips, ten wrong) can score 800 with strong preparation, plenty of practice, good calculator skills, and the right calculator programs.

And once again, if after a year of high school precalculus you can’t just sit down and get a 70% on this assessment (35/50), you might want to pick another subject test.

For more SAT2M2 advice and resources, click here.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, August 01, 2018

The Matchless Enthusiasm of Martin Gardner

The hyper-competitive struggle for survival against the old Soviet Union made American math and science education a top priority during the Cold War decades of the 20th century.

Many Baby Boomers (like me) remember with fondness the fascinating articles published monthly in Scientific American magazine. One of the most interesting features of the magazine in our time was Martin Gardner’s column on recreational mathematics, which ran for 25 years. 

Among the many necessary qualities of truly great teachers, enthusiasm might be listed first. An instructor’s genuine, overflowing enthusiasm is that which excites students' souls and convinces them that the required academic work and sacrifice will be amply rewarded. The etymology of the word “enthusiasm” (en-theos: literally, "in God") points straight at the Divine, and no one could excite the soul with the beauty of mathematics like Gardner could.

A 1998 article by the master preserves for modern readers the flavor of Gardner’s contagious enthusiasm and gold-medal exposition that so characterized his column, presenting to Gardner fans and neophytes alike the pure noetic joy that accompanies deep dives into the realm of creative mathematics.

Reflecting the timelessness of the subject, the article reads as if it were penned yesterday, fresh and new. It’s not long, and is well worth a bit of your time:

A Quarter-Century of Recreational Mathematics.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Sunday, July 01, 2018

Calculator Policies: SAT and ACT

SAT and ACT policies regulate the types and models of calculators allowed for use in solving math problems on standardized tests administered by each organization.

For a while, the SAT had a more or less unrestricted calculator policy whereas the ACT had a tightly controlled one, allowing only those user-installed programs comprising 25 or fewer lines of code. Aside from being unduly onerous, the old ACT policy was obviously unenforceable, and has recently been changed to essentially match the unrestricted SAT rule.

In a nutshell, here's what you need to know:

All features, apps, and user-installed programs are permitted for use, without restriction, on any model of the Ti-84 graphing calculator family (including the powerful Ti-84 Plus CE model) on the SAT, the SAT Math Subject Test (Levels 1, 2), and the ACT.

Below are links to current policies:

SAT Calculator Policy (updated: 2023)

ACT Calculator Policy (updated: 2023)

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, June 01, 2018

Fractal Coloring Book

Adult coloring books have become popular in recent years. A number have been published already, and more are finding there was to amazon all the time. Below are my favorites:

Coloring Mandalas for Meditation was a hit with my daughter and her friends at Wesleyan who needed to periodically take a break from the stress of studying.

Adult Coloring Book: Fractals by Ben Trube not only offers beautiful fractal designs to color, but also provides a visceral experience with fractals and the math behind them.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.