My Latest Theory On Special Education

My Latest Theory On Special Education
By Lance Winslow

A couple of use ago, I was talking to a special ed postgraduate student. They were working on a way to help special ed kids get to the next step of cognition. The theory was to help their brain connect to other parts of the brain by teaching new skills, and things which they normally wouldn't have learned. Why do I think this is a great idea, well, because it works with all humans regardless of their cognitive ability or IQ. Let me explain.

When I was a young man about 10 years old, my dad taught me how to fly. Learning how to fly is different than just about any other activity that a young person might do. All of the sudden you are introduced to a much larger 3-D environment, you begin to see the world in a different way, and your mind starts remapping your environment as you know it. Once you learn how to fly and enjoy that activity it is as if it opens your mind to so many more possibilities, thoughts, ideas, and ways of looking at things.

My postgraduate special ad researcher acquaintance also noted that when they taught autistic kids to ride a bicycle that suddenly these new skills they needed for balance, judging distance and motion assisted them in coming out of their shell, and they then related to the world in a different way, one they had not been accustomed to before. So maybe it's important that we show our special kids all sorts of new activities. I have another acquaintance that takes autistic and special kids down the Rogue River through the rapids. The kids absolutely love it, and they learn new skills in the process.

Now then, my latest theory on special education would go something like this. Not only should we expose kids that we perceive to be normal to many diverse activities such as karate, sports, computers, art, dance, etc. But we should also do the same for kids within the autistic spectrum, and all of the kids in the special education classes.

It may very well be that much of what we are doing is harming the special education kids as we isolate them from new experiences, something which they could greatly benefit from, perhaps even more so than the other kids - in which case it is our own fault, not theirs - as we perpetuate a self-fulfilling prophecy in their education. Indeed I hope you will please consider all this and think on it.

Lance Winslow has launched a new provocative series of eBooks on the Future of Education. Lance Winslow is a retired Founder of a Nationwide Franchise Chain, and now runs the Online Think Tank; http://www.worldthinktank.net

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The Theory of Quadratic Equations

The Theory of Quadratic Equations
By Srinivasa Gopal

A quadratic equation is a polynomial equation of second order. A quadratic equation has two roots. The roots can also be equal and identical. Let us write the quadratic equation in two forms

AX * X + BX + C = 0 an example of a quadratic equation would be 5X*X + 3 *X + 2 = 0

Rewrite this as ( X-R1) * (X-R2) = /0. The above step is termed as factoring.

The polynomial form of the equation is X*X + B/A * X + C/A = 0

The factored equation can be split as X * X -X( R1 + R2) + R1R2 = 0.

Comparing Similar terms we can see that -(R1 + R2) = B/A

R1R2 = C/A

(R1 + R2) = -B/A

Let us investigate the discriminant b *b - 4 * a * c

b = -a ( r1 + r2)

c = AR1R2; 4*A*C = 4 * A* A* R1 * R2

b*b = A*A(R1 + R2) * (R1 + R2)

DISCRIMINANT = A*A(R1 + R2) * (R1 + R2) - 4*A*A*R1*R2

= A*A ( (R1+R2)((R1+R2) - 4R1R2)

= A*A ( R1 - R2) * (R1 - R2).

Notice that this is a perfect square of A(R1-R2). So if the discrimant becomes negative it means that the quadratic equation does not have real roots as squares of real numbers are also perfect squares.

Let us add A( R1-R2) to -b which is A( R1 + R2), and the sum is 2AR1. Dividing this by 2A would yield R1.

Similarly let us subtract A( R1-R2) from -b ie., A( R1 + R2) - A (R1-R2)

which is equal to A(2R2) or 2AR2. Dividing this by 2A would yield R2.

So R1 is (-B + squareroot( discriminant) ) / 2A and R2 is (-B - squareoot( discriminant) / 2A

Let us take some common factoring problems that you would encounter

say x * x + 5*x + 6 = 0.

First step evaluate the discriminant = SQUAREROOT(25 - 24) = 1, which means that there are real roots.

The roots of the equation are (- 5 + 1)/ 2 is equal to -2 and ( -5 -1)/2 equal to -3.

The equation can be factored as (X+2)(X+3) = 0.

Let us take another example

3 * x * x + 9 * x + 6 = 0, rewriting this as x * x + 3*x + 2 = 0.

discriminant = sqrt(9-8) = 1
R1 = -1 and R2 is -2. So the factored form of the same equation is

(x + 1)( x+ 2) = 0.

A quadratic equation can also be plotted on a graph. It will yield the equation of a parabola.

The author is an Ezine Expert on issues related to science, IT and Cricket. Known as Srinivasa Gobal to my friends and family prior to 1992 and known as Srinivasa Gopal and Gopal Srinivasan later during 1999- 2008.

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