School Reform: Rise of the Machines

What does the future of education look like? Picture 100 students sitting at terminals. Five teachers circulate, monitoring student progress. Onscreen, a virtual tutor with human-like charisma assesses what little Billy knows about, say, the Pythagorean Theorem. It detects a gap. It accesses a database containing Billy’s entire educational history – test scores, skills, deficiencies, everything. Because Billy learns best through games, a geometry game appears onscreen. It’s designed incrementally so that Billy always wins, and always learns the material.  This utopian or dystopian vision is still a long way off, however. In the meantime, reform-minded school systems are tinkering with the great-grandparents of these machines – databases for collecting and crunching information about the educational progress of every child, in every classroom, everywhere. Armed with more precise data, states, cities, and schools will be better able to determine who's learning what, who isn't, and what to do about it. The stakes are undeniably high. Failure in school is a statistically significant predictor of problems in later life, including long-term unemployment, drug abuse, and incarceration. High school graduation rates in US public schools are dismally low and skewed steeply by household income. In other words, the public school system is a factory for producing social inequality. Leading reform efforts in the State of New Jersey is Chris Cerf , recently appointed Acting Commissioner of Education by Governor Chris Christie. A former New York City Deputy Chancellor under zealous school reformer Mayor Michael Bloomberg, Cerf is pursuing system-wide change on a template that mirrors Michelle Rhee's recent efforts in Washington, DC, and City Hall's in New York. As in those cities, changes in the New Jersey Department of Education will be swift, acute, and sometimes unpopular. Popularity is not the point, Cerf argues. The point is “maximizing the number of children who get a quality public school  Teacher quality and student data tracking are the twin fronts in this war, and it is a war. Data-driven reformers have identified teacher quality as the single most important predictor of student success in school. They are going after teacher-tenure laws that make it difficult to fire veteran teachers, regardless of ability, and pushing for  higher teacher salaries and merit-based pay –raises tied to student performance.

Pythagorean Theorem Formula | TechCull.Com

If you have just taken up a basic geometry course, one of the first relations in Euclidean geometry that you will come across is the Pythagorean theorem formula. It is a fundamental theorem related to right angled triangles that is of immense value to geometry and mathematics in general. In this article, I explain what is the formula for Pythagorean theorem.

This theorem which details an important property of right angled triangles is named after the Greek mathematician and philosopher Pythagoras who discovered it. However there is evidence that this theorem was known to ancient Indian and even Babylonian mathematicians. An ancient Indian text called the Apastamba Sulba Sutra dating back to about 600 BC has a numerical proof of Pythagorean theorem formula. Many indirect evidences of knowledge of the theorem have been found in ancient Egyptian scrolls and Babylonian artifacts. After that brief discussion of the history of the Pythagorean theorem let us move towards the statement of the theorem and formula. Read more on history of Pythagorean formula.

Pythagorean Theorem Formula Explained

To understand the statement of Pythagorean theorem formula, on must understand what is a right angled triangle. For those of you, who are new to geometry, let me give a brief introduction. I assume you understand what is meant by angles. Angles are a quantitative measure (measured in degrees) of separation between two lines starting from a common point. A triangle is a closed three sided, two dimensional geometrical object.

With three sides, a triangle has three angles and their sum in two dimensional geometry is always 180 degrees. A right angled triangle is a special type of triangle that has one of its angles to be exactly 90 degrees. Traditionally, the side that is exactly opposite to the right angle is called the hypotenuse. The Pythagoras theorem statement is as follows:

For any right angled triangle with length of sides being denoted by a,b,c (c being the length of the hypotenuse) the following relation always holds:

a

This is the Pythagorean theorem formula. In other words, the theorem can be restated as follows: For any right angle triangle, the square of the hypotenuse is exactly equal to the sum of the squares of the other two sides. (By square of side length, we mean the length multiplied by itself).

There is one more way of simply stating the Pythagorean theorem: ‘If you draw squares on all sides of a right angled triangle (with same length as the triangle sides), then the area of the square drawn on hypotenuse will be equal to the sum of the areas of squares drawn on other two sides.’ There are multiple proofs of this theorem ranging from the very simple to the complex. You should know at least one proof.

The Pythagorean theorem, a 4,000-year history

This book is designed for readers who are inspired, or who want to be inspired, by the numbers that Eli uses to tell his story.

A short history of Greek mathematics

One is the construction of the five regular solids, the other is the Pythagorean theorem, Euclid I. 47. Timaeus, in the dialogue of Plato above cited, ...

Hands on history, a resource for teaching mathematics

(The book by Heath [4] remains an excellent source for this history.) However, the proofs of the Pythagorean Theorem by Pythagoras (as reconstructed) and by ...

The Math Book, From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

The Pythagorean theorem states that for any right triangle, ... Although Pythagoras is often credited with the formulation of the Pythagorean theorem, ...

History of mathematics, a supplement

Lˇı and D`u's Chinese Mathematics; A Concise History does not commit to a pre- Pythagorean date for the treatment of the Pythagorean Theorem in the Nine ...