MGTutoring.com. A Rational Perspective on Education.

May 11, 2011

Some Tidbits of Math History

Filed under: History,Mathematics — Administrator @ 8:51 am

There is some interesting material about math symbols at The History of Mathematical Symbols by Douglass Weaver and Anthony D. Smith.

For example, they say:

Percent has been used since the end of the fifteenth century in business problems such as computing interest, profit and loss, and taxes. However, the idea had its origin much earlier. When the Roman emperor Augustus levied a tax on all goods sold at auction, centesima rerum venalium, the rate was 1/100. Other Roman taxes were 1/20 on every freed slave and 1/25 on every slave sold. Without recognising percentages as such, they used fractions easily reduced to hundredths.

In the Middle Ages, as large denominations of money came to be used, 100 became a common base for computation. Italian manuscripts of the fifteenth century contained such expressions as “20 p 100″ and “x p cento” to indicate 20 percent and 10 percent. When commercial arithmetics appeared near the end of that century, use of percent was well estasblished. For example, Giorgio Chiarino (1481) used “xx. per .c.” for 20 percent and “viii in x perceto” for 8 to 10 percent. During the sixteenth and seventeenth century, percent was used freely for computing profit and loss and interest. (NCTM p146,147}

May 6, 2011

OMG. Squared.

Filed under: Mathematics,MGTutoring — Administrator @ 12:32 am

While tutoring a student at Barnes & Noble, a girl started talking to me. Come to find out, she was a student of mine about 15 years ago, when she was in 7th grade. She said I inspired her to study math — so now she has a Masters in math from *Rice* and is going to go for her PhD at *Rice*!!! Wow!!! I’m floored!!!

April 12, 2011

How Not To Teach Math

Filed under: Education,Logic,Mathematics,Philosophy — Administrator @ 11:02 am

No wonder Dan Meyer is a heralded educator: he’s a pragmatist who would have our kids’ minds be crammed into and restricted to the immediate moment.

  Would he have us look at the universe, look at broad abstractions and large contexts, a la the Greeks and Galileo? No! Heck no! He says to look at the local basketball court — where you can find an application of math no one cares about and no one uses. Such examples are easily dismissed as artificial, since no one ever uses algebra and parabolas to shoot a basket — first-hand experience in the class room tells me so. And such examples are as narrow as the book examples Mr. Meyer is trying to oppose. And such examples do not naturally lead to further thought and investigation.

He responds to Platonism by giving us Pragmatism — but they are two sides of the same false coin. We need a rational approach, a la Aristotle, Archimedes, Newton, Galileo and Gauss.

March 10, 2010

A Math Problem

Filed under: Mathematics — Administrator @ 9:07 am

If:
2 + 3 = 10
7 + 2 = 63
6 + 5 = 66
8 + 4 = 96

Then:  9 + 7 = ????

It took me, what? 15 seconds? 30 seconds? 3 minutes?. It was fascinating how my subconscious grasped the answer, but then it took 1/4 second to 2 seconds for me to identify explicitly the pattern needed to get the answer and to put the answer into words.

(HT: my brother)

January 25, 2010

TAKS Practice Material

Filed under: Education,Mathematics — Administrator @ 10:31 am

On the Internet there is a plethora of practice material for the math portion (and science, reading, etc.) of the TAKS test. The Texas Education Agency, TEA, has made available pdf files of some recent tests and also has a number of tests archived. This material would be good for preparing for the TAKS test and for practicing algebra and geometry.

Pearson has made available some pdf files of study guides and has some online, interactive study guides. (If those links do not work, start on the TAKS Study Guides page, then click on “Interactive Study Guides,” or click on “Printed Study Guides” followed by “Study Guide PDFs.”)

January 18, 2010

The Graphing Calculator

Filed under: Mathematics,SAT, ACT, ETC. — Administrator @ 10:25 am

Mathbits has some good information on how to use the TI-89 and how to use the TI-83/84. Valuable stuff for those taking math or getting ready for the SAT or ACT.

Update (1-21-10, 9:32 AM): I highly recommend that you be fluent with a graphing calculator for the tests. The test makers might say that the calculator might help, might not, and might slow you down, but they are talking to a general audience, including people who do not know how to use a calculator, people who are trying to use one they are unfamiliar with, and people who do not know how to use the graphing calculator effectively on the tests. The fact is that the calculator can make some of the questions, even some of the ones rated “hard,” virtually brainless; it makes it possible to get some easy points on the SAT, ACT, TAKS, and AP exams.

January 14, 2010

Differentials and Error Analysis

Filed under: Mathematics,Physics,Science — Administrator @ 3:48 pm

Differentials, an aspect of calculus, are important for working with errors of measurement and the propagation of error.

Dr. Donald Simanek discusses their use in Error Calculations Using Calculus. Dr. Mike Coombes discusses their use in Error Propagation Using Calculus Solutions. And Dr. Rhett Allain uses them in the interesting Error Propagation And the Distance To the Sun.

I have not read the articles/essays closely, so I don’t know if there are any mistakes in them. But they illustrate the general idea.

January 13, 2010

Measurement Humor

Filed under: Humor,Mathematics,Science — Administrator @ 8:33 pm

I received this in an email from a parent of a student I have tutored:

New IEEE standard values:

Non-Conventional Units of Conversion

Ratio of an igloo’s circumference to its diameter = Eskimo Pi

2000 pounds of Chinese soup = Won Ton

1 millionth of a mouthwash = 1 Microscope

Time between slipping on a peel and smacking the pavement = 1 Bananosecond

Weight an evangelist carries with God = 1 Billigram

Time it takes to sail 220 yards at 1 nautical mile per hour = Knotfurlong

16.5 feet in the Twilight Zone = 1 Rod Serling

Half of a large intestine = 1 Semicolon

1,000,000 aches = 1 Megahurtz

(more…)

January 8, 2010

The First American Arithmetic Text

Filed under: Education,History,Mathematics — Administrator @ 9:30 am

On p. 143 of Old textbooks: spelling, grammar, reading, arithmetic, geography, American history, civil government, physiology, penmanship, art, music, as taught in the common schools from colonial days to 1900 ((c) 1961, University of Pittsburgh Press, printed by American Book-Stratford Press, Inc.), author John Alfred Nietz wrote:

The first seven arithmetic textbooks published in the Americas were in Spanish, four in Mexico and three in Lima, Peru. The first mathematics textbook was the Sumario Compendioso (1556) written by Juan Diez Freyle, and the first separate arithmetic was the Arte Para Aprender Todo El Menor Del Arithmetica by Pedro de Paz (1623), both published in Mexico. Incidentally, the first university in America was founded in Mexico by 1554, in which later the first lecturer in mathematics was Juan Negrete.

Wow. Fascinating.

December 21, 2009

Statistics and Current Events

Filed under: Mathematics,Science,Statistics — Administrator @ 8:48 am

In “Fables of the Reconstruction (Or, How to Make Your Own Hockey Stick),” the blogger Iowahawk says:

What follows started as a comment I made over at Ace’s last week which he graciously decided to feature on a separate post (thanks Ace). In short, it’s a detailed how-to-guide for replicating the climate reconstruction method used by the so-called “Climategate” scientists. Not a perfect replication, but a pretty faithful facsimile that you can do on your own computer, with some of the same data they used.

A good read. And fun with stats. Check it out.  (HT: Geoffrey K.)

On a related note, read “The ‘Science’ of Global Warming” (Macleans.ca, Thursday, December 3, 2009 10:00am) by Mark Steyn. He writes:

Yet perhaps the most important revelation is not the collusion, the bullying, the politicization and the evidence-planting, but the fact that, even if you wanted to do honest “climate research” at the Climatic Research Unit, the data and the models are now so diseased by the above that they’re all but useless. Let Ian “Harry” Harris, who works in “climate scenario development and data manipulation” at the CRU, sum it up. Mr. Harris was attempting to duplicate previous results—i.e., to duplicate all that science that’s supposedly settled, and the questioning of which consigns you to the Climate Branch of the Flat Earth Society. How hard should it be to confirm settled science? After much cyber-gnashing of teeth, Harry throws in the towel:

“ARGH. Just went back to check on synthetic production. Apparently—I have no memory of this at all—we’re not doing observed rain days! It’s all synthetic from 1990 onwards. So I’m going to need conditionals in the update program to handle that. And separate gridding before 1989. And what [#%] happens to station counts?

“OH [#&] THIS. It’s Sunday evening, I’ve worked all weekend, and just when I thought it was done I’m hitting yet another problem that’s based on the hopeless state of our databases. There is no uniform data integrity, it’s just a catalogue of issues that continues to grow as they’re found.”

You cannot do good statistics with bad data. Nor can you do science.   (HT: Harry B.)

In stats and science, reality must come first.

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