1, 1, 2, 3, 5, 8, 13, 21 ...are a sequence of numbers known to mathematicians as the Fibonacci sequence. At first glance, the numbers seem random. However, if we take a closer look, the numbers have a very distinct pattern. The pattern starts with 1, followed by another 1, and the subsequent numbers are derived by adding the previous two numbers. For example, 1, 1 , (1+1 = 2), for the sequence 1, 1, 2; then (2+1=3) for a sequence of 1, 1, 2, 3; then (3+2=5) for a sequence of 1, 1, 2, 3, 5; then (5+3=8) for a sequence of 1, 1, 2, 3, 5, 8, …, and so on. This unique set of numbers were discovered by an Italian mathematician, Leonardo Pisano Bogollo (c. 1170 – c. 1250)] also known as “Fibonacci” .
Fibonacci first thought of the sequence as a solution to a problem involving the growth population of rabbits in a book entitled, Liber Abaci (The Book of Calculation), published in 1202. Fibonacci posed the following question: “...suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits. Suppose that our rabbits never die and that the female always produces one new pair (one male, one female) every month from the second month on. ...How many pairs will there be in one year?” The answer, he would discover, would be 377. In a years’ time, the rabbits would produce pairs of offspring that would mirror this sequence of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377.
3.14159265 (affectionately known as pi – pronounce “pie”) is a single number that cannot be expressed exactly as a fraction m/n, where m and n are integer and its decimal representation never ends or repeats. The constant gets its name from the Greek word περίμετρος (perimeter) – where the Greek symbol pi is the first letter in the word perimeter. Mathematically, pi is defined as the as the ratio of a circle's circumference C to its diameter d.There is an abundance of evidenced to suggest that the conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3 + 1/7 in the designs of the Old Kingdom pyramids in Egypt. In fact, The Great Pyramid at Giza, constructed c.2550-2500 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π . There are also textually approximations that date from around 1900 BC that include the Indian text Shatapatha Brahmana - which gives pi as 339/108 (approximately 3.139).
Additionally, the Old Testament makes references to pi in 1st kings 7:23. ''And he made a molten sea, ten cubits from the one brim to the other: it was round all about and his height was five cubits: and a line of thirty cubits did compass it about''....from this we can deduce another approximation of Pi - having a diameter of ten cubits, and a circumference of thirty cubits, implying an approximate value of three.
As Wikipedia points out, “…the concept of π has become entrenched in popular culture to a degree far greater than almost any other mathematical construct. It is, perhaps, the most common ground between mathematicians and non-mathematicians.” It’s no wonder it has it own special day – March 14.. (3.14) However, it is the next set of numbers that will prove the most interesting of all.
In this sequence the number 1 is the ranking of United States (US), in terms of Gross Domestic Product (GDP). GDP is a measure of a country's overall official economic health. Technically speaking, GDP is the total market value of all final goods and services produced in a country in a given year. In 2008, The World Bank estimated the US GDP at 14.6 Trillion dollars . While the closet country, China, was estimated to be just over 5 trillion. Not to mention, 403, the next number in the sequence, is the number of Billionaires within the United States of America - which is more than all other developed nations combined . China is in second place with 64. In other words, The United States is a very rich nation!
In 2006, The United States placed 32nd – our final number in the sequence – in the Program for International Student Assessment (PISA). PISA, is a system of international assessments that measures 15-year-olds’ performance in reading, mathematics, and science literacy every 3 years. PISA, first implemented in 2000, is sponsored by the Organization for Economic Cooperation and Development (OECD), an intergovernmental organization of 30 member countries.
In 2006, fifty seven jurisdictions participated in PISA, including 30 OECD jurisdictions and 27 non-OECD jurisdictions. A December 2007 report, “Highlights From PISA 2006: Performance of U.S. 15-Year-Old Students in Science and Mathematics Literacy in an International Context,” published by The US Department of Education, gives a striking account of United States’ performance in math.
It also reported, “When comparing the performance of the highest achieving students—those at the 90th percentile—U.S. students scored lower (593) than the OECD average (615) on the mathematics literacy scale. Twenty-nine jurisdictions (23 OECD jurisdictions and 6 non-OECD jurisdictions) had students at the 90th percentile with higher scores than the United States on the mathematics literacy scale.”
Other measures that were illuminated in the PISA report were the, “Differences in Performance by Selected Student Characteristics.” In other words, the report was broken down by sex (or what most may call gender) and racial/ethnic background. In fact, the report states “On average, Hispanic students scored higher than Black (non-Hispanic) students, while White (non-Hispanic) students scored higher than Asian (non-Hispanic) students. This pattern of performance on PISA 2006 by race/ethnicity is similar to that found in PISA 2000 and PISA 2003 (Lemke et al. 2001, 2004)”
The 2007 Trends in International Mathematics and Science Study, (TIMSS), reported on a similar metric: socio-economic status. The report stated, “fourth-graders in schools with 50 percent or more students eligible for free or reduced-price lunch scored lower, on average, while those in schools with lower proportions of poor students scored higher, on average, than the U.S. national average.”
I draw attention to this because Dr. Deborah Nightingale, Professor of the Practice of Aeronautics and Astronautics and Engineering Systems at MIT, talks about characteristics of good metrics:
o Metrics are meaningful, quantified measures
o Metric must present data or information that allows us to take action
o Metrics should be tied to strategy and to “core” processes -indicate how well organizational objectives and goals are being met
o Metrics should foster process understanding and motivate individual, group, or team action and continual improvement.
However, if we take a look at the scores from the same report, we will find the Chinese Taipei scored 549, Korea 548, Hong Kong – China scored 547, Macai-China 525, and Japan 523 – all well above the national average of 498. The United States scored below the standard at 474. Although the jury is still out, one can conclude that ethnicity is not a deciding factor – if it were, either whites would dominate in this category or Asian would do just as well in the United States - instead we find this not to be the case.
Recall from earlier, the TIMMS report stated “fourth-graders in schools with 50 percent or more students eligible for free or reduced-price lunch scored lower, on average, while those in schools with lower proportions of poor students scored higher, on average, than the U.S. national average.” And yet the United States is the riches nation in the world – with more billionaires than all other developed nations combined. It would stand to reason that United States should lead all nations in every category – if money was truly a factor
Do you think the color of someone’s skin, the chromosomes in their genes, or the money in their bank accounts really matter when measuring someones intellectual ability; or is it something else. I would argue that the propensity to learn is a function of one's ability to master a subject's objectives, concepts and principles.
Any thoughts?
As for me, I think we need to get back to the basics!
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