Double Standards

Today I looked at my list of new math students and saw a familiar face. Later that face was erased. I do not know why, but I suspect that the young person's parents asked for a change.

Schools are weakening. Parents are part of the weakening process. In the case above, there are two children in a family of educators. The older is the wonder child, brilliant, magical—a gift. The second child is finding his way and wonders if will ever measure up in the eyes of his parents.

Of course. He already has. A parent's love is unconditional, but does he know this?

Parents want the best for their children, but what they do not realize is the constant, unconscious set of  messages they send: our number two child is different, unsure, less self sufficient. To make up for their anxiety at having to work harder to convince a second, third or fourth child that he or she is valued, parents go out on a limb to pull strings, sometimes hoping that the younger child knows about this. They want to be seen as parents who are "fair" and parents who "really care."

But the truth of the matter is that children know that the best thing would be for parents to stay out of the way and to let children weather the realities that life creates.

When it comes to secondary and higher education, it is not about the parents but about the children. If a struggle presents itself, then celebrate, rather than weaken the situation, which, in the long run, weakens the child.

But, and I say this with trembling knees, maybe parents intend this all along. After all, the firstborn has traditionally been a special child, and parents seem to do what they feel is dignified and noble to ensure that the world is aware that this first offspring really is a gift.

God help us!

Amy Tan TED Talk

http://www.ted.com/talks/amy_tan_on_creativity.html

trick of 9's is not a trick

Suppose for positive integers a, b, c, d, … , we have a + b + c + d + … = 9k for some positive integer k.

For a multi-digit number, say four digits, we can write the number as

1000a + 100b + 10c + d, which can also be written

999a + a + 99b + b + 9c + c + d.

Clearly 999a + 99b + 9c is divisible by 9,

and

a + b + c + d was given to be divisible by 9, so

since all of the individual summands is divisible by 9, then the sum must be divisible by 9.

This same logic can be used on any multiple digit number whose individual digits add to a multiple of 9.

EXAMPLE:

1278

1 + 2 + 7 + 8 = 18 = 9(2).

1278 = 1(1000) + 2(100) + 7(10) + 8

= 1(999) + 1 + 2(99) + 2 + 7(9) + 7 + 8

= 9(111) + 9(22) + 9(7) + 9(2)

= 9(142).