Tuesday, July 20, 2010

How Much is Nothing?

[First some housekeeping issues and an apology.  A couple of you wrote that you did not like the white on black background.  I was trying to emulate a blackboard type of presentation.  Apparently blackboards work best in classrooms and not on blogs.  But my apology is for the changing fonts that happens at times in the blogs.  I don't know what is causing it and at times I seem to not be able to fix it. I've looked at Google help section and it doesn't help me.  So for the moment, let us try a new setting and see how that goes.  Thanks for your patients]

If I remember correctly I was in a first grade classroom teaching some music to the kids and was attempting to show beats in a measure of a song.  Now that i think of it, I was probably over their head--too soon for this type of instruction.  But I remember explaining the beats and counting through several measures.  At one point I came to a rest and said that there is no music on a rest.  It is nothing.  A hand went up and someone asked me, "How much is a nothing?"  I had misspoken and implied that a rest was nothing when indeed it does have a value.  I don't remember how I got out of this mess but we ended up singing which is what they liked to do.

But I have thought of that question over the years.  "How much is nothing?"  I was enamored to find in an early philosophy class that there was quite a to-do when philosophers and mathematicians (not much difference between the two long ago) agreed that nothing had value and a place.  What an interesting concept.

I tell you this little tale by way of an introduction of a suggestion that along with learning to read we need to teach the numbers--from nothing to a gadzillion to our children.  It is another way to communicate which our children need to learn.  And many do learn elements of numbers.  "How old are you?  I'm five."  "No you may not have a fourth cookie!"  "When you're sixteen and that's final."  Yes, we do pass on the rudiments of numbers, counting, time, and some calculations before the child gets to school.  We need to teach our children at an early age the value of numbers and arithmetic.

LIke the teaching of reading, the teaching of numbers is the process of putting meaning to an abstraction.  What does the symbol "5" mean to a five year old?  That little one doesn't remember five distinct years but she/he has been told that they are "five" years old.  And we count on their fingers until we get to five and the pinky.  They can now make an association with one hand and their age when the question comes at them.  It is a beginning.

I propose that teaching reading and numbers (or arithmetic) should be the initial subjects taught to our children.  Both are abstractions that have to be taught by association unlike speaking and listening which are acquired by association alone.  We may need to teach new words to our kids but they first come to school with an established vocabulary already.

Hmmmm.  I'm making an assumption here that may not be correct.  What if a child comes to school and only knows Spanish.  Now what?  So I guess we have to first teach listening and speaking words and forming associations of what those words mean.  Major mistake in my thinking here.....

Okay, so now we have to teach reading, writing, numbers and arithmetic and speaking and listening in English.  There is good research that suggests that perhaps teaching in the family language at first is better for the child as they learn learning skills.  I've not had experience with that problem--all my kids spoke English, sometimes at the same time!

I tell my readers that there are a number of methods of teaching reading, each method touts itself as the proper way.  And believe me, I don't want to get into the quagmire of how to teach arithmetic.....although much of that discussion tends to be directed at the more advance subjects in mathematics.  I've already ticked off several professors of mathematics who favor either the rote method or the other method of discovery.   I hope you will bare with me and just agree that we need to teach our children some form of mathematics that will give them good confidence in later life.  Agree?

The more I write of what subject to teach our children, the more I want to thank the primary teachers (kindergarten, first and second grades) for the work that they do.  Amazing.  My life as a fourth and fifth grade teacher was made much easier because of the work of these primary teachers.  Thank you all.