Math Forum Discussions

Bill Marsh

Posts: 154
From: Port Angeles, WA
Registered: 12/22/08

Re: Defining Decimals
Posted: Feb 20, 2009 3:56 PM

Plain Text

Wayne Bishop presumes to tell me:

'Come on, Bill. The only reason you keep arguing for defining decimals too early is to support calculator use in the early grades, possibly even kindergarten forward, fuzzy math biblical precepts to avoid learning arithmetic properly.'

Wayne has no way of knowing what he asserts he knows about what I think or about my motives for thinking anything.

Wayne's attempts at insult are at the same level as the curriculum we are discussing, too childish to require comment here. What is harder to work out is how many of the misstatements in what he goes on to say result from his inability to deal with new material or new ways of looking at things and how many are deliberate distortions.

Let's start by stipulating that I do believe in using calculators in K-8, and that I do wish to introduce decimals before addition of fractions. It does not at all follow that I believe either because of the other, or that, if I did, that the other would be the only reason I believe in the first.

I support early use of calculators because using them properly can make math more interesting and fun for kids while greatly extending the range and verisimilitude of the applications they can make of some of the math they are learning to do. I would also suggest using calculators to motivate the learning of standard algorithms. If I were to use a calculator with third graders to add or multiply numbers, I would make sure that they knew that they would be learning how to do what the calculator is doing in a grade or two. When they get to that learning, I would try to motivate them in part by setting the goal of understanding how computers (can) do arithmetic.

(In this line I favor teaching the doubling and halving method of multiplying numbers and then showing them how it looks in binary. Anything we can do to help people understand computers is good.)

I support early introduction of decimals so third graders can engage in real measuring and to help them develop a good concept of non-whole numbers.

Wayne then tells me:

'As I suspect you actually understand, 0.123 means what you want it to mean only by looking at that portion of the number line that is the sum of some segments obtained by repeatedly subdividing the identified identified segment into tenths.'

Wayne follows Wu by starting with one way of doing something, then dogmatically claiming and perhaps believing that it is the only way. This happens on both sides of the math wars, sually in the weaker form of merely claiming there is only one best way.

Wayne goes on at length about adding lengths, though almost word for word using my explanation of a zeroing in process. He speaks of subdividing into tenths, as I did, but then adds a lot of complication.

It is possible to get a meaning for 0.123 by adding different lengths than Wayne uses, by the way. You can start at the upper end of the unit interval with a length of .8, then add on its left (in the usual number line orientation) a length of .07 and then bonding on a third length of .007.

A good way to see that addition is not, contrary to Wayne's assertion, needed in this definition, is to consider dictionaries. We know that the d- section can be divided into twenty-six parts, one of which is the du- section. We can subdivide twice more to get to the dumb- section.

Which is a good place to end this note.

Bill Marsh