Thursday, December 30, 2010

Math != Calculating

This is an interesting talk:

Math >> Calculating

1. Pose the right questions.
2. Real world problem --> math formulation
3. Computation
4. Math formulation --> real world problem and verification

Maybe not spend so much time on step 3?  Use computer programming to nail down understanding!  These are very interesting ideas.


Thursday, December 2, 2010

Adding and Subtracting Rational Expressions

To simplify a rational expression:
Step 1:  Factor all denominators as a means to easily determine the LCD.
Step 2Multiply by the appropriate factors to obtain equivalent terms with a common denominator. 
Step 3Add or subtract the numerators and place the result over the common denominator. 
Step 4:  Simplify the resulting algebraic fraction.

A more involved example follows:

It is always a good idea to state the restrictions.  Remember that the restrictions are the values that produce zero in the denominator.


Mandelbrot Explorer using Flash

Give the below flash movie a minute to download. Move the looking glass over the picture and release it to zoom.

The orbit is displayed, real time, in the corner.

Monday, November 29, 2010

Trigonometric Function Explorer using Flash

Above you should see a flash movie that I have made.  This is a test post to see if I could emed a flash component into blogger.  The swf file has been saved in Google docs and shared with everyone. Success!

Wednesday, September 15, 2010

Top 100 Most Influential People of the Last Millennium

 From the
 On October 10, 1999, the American cable network A&E started counting down a list of the 100 most influential people of the millennium compiled by a staff of 360 journalists, scientists, theologians, historians, and scholars.
As many as 250 people were chosen to be on the list, but only 100 made it, these are the 100 people that did the most to shape the world we live in today.

1 The List

  1. Johann Gutenberg
  2. Isaac Newton
  3. Martin Luther
  4. Charles Darwin
  5. William Shakespeare
  6. Christopher Columbus
  7. Karl Marx
  8. Albert Einstein
  9. Nicolaus Copernicus
  10. Galileo Galilei
  11. Leonardo da Vinci
  12. Sigmund Freud
  13. Louis Pasteur
  14. Thomas Edison
  15. Thomas Jefferson
  16. Adolf Hitler
  17. Mahatma Gandhi
  18. John LockeJ
  19. Michelangelo
  20. Adam Smith
  21. George Washington
  22. Genghis Khan
  23. Abraham Lincoln
  24. St. Thomas Aquinas
  25. James Watt
  26. Wolfgang Amadeus Mozart
  27. Napoleon Bonaparte
  28. Johann Sebastian Bach
  29. Henry Ford
  30. Ludwig van Beethoven
  31. James Watson & Francis Crick
  32. René Descartes
  33. Martin Luther King, Jr.
  34. Jean-Jacques Rousseau
  35. Vladimir Lenin
  36. Alexander Fleming
  37. Voltaire
  38. Sir Francis Bacon
  39. Dante Alighieri
  40. The Wright brothers
  41. Bill Gates
  42. Gregor Mendel
  43. Mao Zedong
  44. Alexander Graham Bell
  45. William the Conqueror
  46. Niccolo Machiavelli
  47. Charles Babbage
  48. Mary Wollstonecraft
  49. Mikhail Gorbachev
  50. Margaret Sanger
  51. Edward Jenner
  52. Winston Churchill
  53. Marie Curie
  54. Marco Polo
  55. Ferdinand Magellan
  56. Elizabeth Stanton
  57. Elvis Presley
  58. Joan of Arc
  59. Immanuel Kant
  60. Franklin Delano Roosevelt
  61. Michael Faraday
  62. Walt Disney
  63. Jane Austen
  64. Pablo Picasso
  65. Werner Heisenberg
  66. D.W. Griffith
  67. Vladimir Zworykin
  68. Benjamin Franklin
  69. William Harvey
  70. Pope Gregory VII (the oldest person on the list)
  71. Harriet Tubman
  72. Simón Bolívar
  73. Diana, Princess of Wales (youngest on the list)
  74. Enrico Fermi
  75. Gregory Pincus
  76. The Beatles
  77. Thomas Hobbes
  78. Queen Isabella
  79. Joseph Stalin
  80. Queen Elizabeth I
  81. Nelson Mandela
  82. Niels Bohr
  83. Peter the Great
  84. Guglielmo Marconi
  85. Ronald Reagan
  86. James Joyce
  87. Rachel Carson
  88. J. Robert Oppenheimer
  89. Susan B. Anthony
  90. Louis Daguerre
  91. Steven Spielberg
  92. Florence Nightingale
  93. Eleanor Roosevelt
  94. Patient Zero
  95. Charlie Chaplin
  96. Enrico Caruso
  97. Jonas Salk
  98. Louis Armstrong
  99. Vasco da Gama
  100. Suleiman I

Saturday, September 4, 2010

NASA Photo Archive

A great resource for historical images found on Flickr:     NASA on The Common photostream:

A Delta II rocket.

More images can be found here:  NASA Images


Monday, August 9, 2010

Average Mathematics Scores by Country 2007

This does not seem so bad to me.  Here is the original link

Table 1. Average mathematics scores of fourth- and eighth-grade students, by country: 2007

Grade four Grade eight
Country Average score Country Average score
TIMSS scale average 500 TIMSS scale average 500
Hong Kong SAR1 607 Chinese Taipei 598
Singapore 599 Korea, Rep. of 597
Chinese Taipei 576 Singapore 593
Japan 568 Hong Kong SAR1, 4 572
Kazakhstan2 549 Japan 570
Russian Federation 544 Hungary 517
England 541 England4 513
Latvia2 537 Russian Federation 512
Netherlands3 535 United States4, 5 508
Lithuania2 530 Lithuania2 506
United States4, 5 529 Czech Republic 504
Germany 525 Slovenia 501
Denmark4 523 Armenia 499
Australia 516 Australia 496
Hungary 510 Sweden 491
Italy 507 Malta 488
Austria 505 Scotland4 487
Sweden 503 Serbia2, 5 486
Slovenia 502 Italy 480
Armenia 500 Malaysia 474
Slovak Republic 496 Norway 469
Scotland4 494 Cyprus 465
New Zealand 492 Bulgaria 464
Czech Republic 486 Israel7 463
Norway 473 Ukraine 462
Ukraine 469 Romania 461
Georgia2 438 Bosnia and Herzegovina 456
Iran, Islamic Rep. of 402 Lebanon 449
Algeria 378 Thailand 441
Colombia 355 Turkey 432
Morocco 341 Jordan 427
El Salvador 330 Tunisia 420
Tunisia 327 Georgia2 410
Kuwait6 316 Iran, Islamic Rep. of 403
Qatar 296 Bahrain 398
Yemen 224 Indonesia 397
   Syrian Arab Republic 395
   Egypt 391
   Algeria 387
   Colombia 380
   Oman 372
   Palestinian Nat'l Auth. 367
   Botswana 364
   Kuwait6 354
   El Salvador 340
   Saudi Arabia 329
   Ghana 309
   Qatar 307

Color swatch indicating that average score is higher than the U.S. average score (p < .05) Average score is higher than the U.S. average score (p < .05)
Color swatch indicating that average score is not measurably different from the U.S. average score (p < .05) Average score is not measurably different from the U.S. average score (p < .05)
Color swatch indicating that average score is lower than the U.S. average score (p < .05) Average score is lower than the U.S. average score (p < .05)
1 Hong Kong is a Special Administrative Region (SAR) of the People's Republic of China.
2 National Target Population does not include all of the International Target Population defined by the Trends in International Mathematics and Science Study (TIMSS).
3 Nearly satisfied guidelines for sample participation rates only after substitute schools were included.
4 Met guidelines for sample participation rates only after substitute schools were included.
5 National Defined Population covers 90 percent to 95 percent of National Target Population.
6 Kuwait tested the same cohort of students as other countries, but later in 2007, at the beginning of the next school year.
7 National Defined Population covers less than 90 percent of National Target Population (but at least 77 percent).
NOTE: Countries are ordered by 2007 average score. The tests for significance take into account the standard error for the reported difference. Thus, a small difference between the United States and one country may be significant while a large difference between the United States and another country may not be significant. The standard errors of the estimates are shown in tables E-1 and E-2 available at
SOURCE: International Association for the Evaluation of Educational Achievement (IEA), Trends in International Mathematics and Science Study (TIMSS), 2007.

Thursday, July 15, 2010

Absolute Value Inequality: A Graphical Approach

An absolute value inequality, such as,

\left| {x + 2} \right| < 3

can be solved as follows:

  - 3 < x + 2 < 3 \\
  - 3 < x + 2 < 3 \\ 
  - 5 < x < 1 \\ 

We can visualize these solutions if we graph the function,

f(x) = \left| {x + 2} \right|

in the rectangular coordinate plane and determine where the graph lies below the horizontal line given by y = 3.  In other words, for what x-values is

f(x) < 3

This idea is illustrated below:

Furthermore, we could use the same graph to visualize the solutions to,

\left| {x + 2} \right| > 3

We can see that the solutions are,

x <  - 5\,\,\,or\,\,\,x > 1

Now take the time to compare this visualization to that given on Wolfram Alpha.  Remember, it is always helpful to understand the geometric interpretation whenever possible.

Thursday, May 13, 2010

Math Education in the Real World

Here is a nice talk... "students come pre-installed with viruses..."

Thursday, April 8, 2010

The Future of the Lecture?

Here is a link that I found interesting regarding the future of education.

A Parody of the Future of Education

It is worth thinking about.

Monday, February 15, 2010

CAUTION: Multiplication before addition or subtraction.

Be aware that "they" like to dangle addition or subtraction in front of us like follows:

5 - 2(x + 7) = 11

It is very much tempting to subtract 5 - 2, isn't it? DO NOT DO IT... the order of operations requires that we multiply (or distribute) before subtraction. The solution follows:

Screen Capture

Use the Snipping Tool in Windows Vista for quick and easy screen captures. It is included, so to find it click the Start menu and type "snipping" in the search box.

Here is a link to more detailed instructions.

Saturday, February 13, 2010

Solving Linear Equations

Another video posted on YouTube. It seems that YouTube is more mobile friendly than blip. Here is another video test.

Stop Motion Tutorial

This is my first attempt at a stop motion video tutorial. Just a test really. I am solving a linear equation that happens to be an identity.

Wednesday, February 3, 2010

Copyrights Made Easy

The creative commons website offers easy to use tools for determining which attribution is best for you. Visit the site:

Click license, and after answering the questions click the Select a License button. It then shows which license is best and provides HTML that can be cut-and-pasted into your website as follows:

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

Tuesday, February 2, 2010

Free Digital Textbook Initiative Review Results

The California Learning Resource Network reviewed several free textbooks and compared the content to the current California content standards.  Have a look:

Free Digital Textbook Initiative Review Results