Pre-History: "Boy lazy. He no wait sky fire. He rub sticks. Make flame."

Stone Age: "Man-child is lazy. He uses bow-drill to start fire. He is losing the old ways."

Medieval Era: "Methinks yonder child dost laze about. He summons flame with flint and steel."

Age of Enlightenment: "My son has grown complacent from the new technology of sulfur matches."

Victorian Era: "The kid can't even be bothered to strike a match. He just flicks his lighter."

Modern Era: "Kids today are dependent on calculators. The can't do math the old-fashioned way."

## Thursday, August 9, 2007

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## 5 comments:

What is the TERC era?!

i don't think you're giving

mental arithmetic anything like

its due. if a student can't,

for example, work out equations

like 10000*100 = 1000000 mentally,

i can confidently predict that

their calculator work will be

so error-prone as to be worse

than useless. likewise for, say,

division by -1 (or what have you --

any but the most radical technophiles

among math teachers will probably

have favorite examples of

"calculations that ought never

be done on the calculator").

I have myself winced as I watched a teenager reach for a calculator to figure out what 1/3 of 3 was, so I get where you're coming from. I just differentiate between the understanding the concept and actually cranking out the algorithm. Neither of your examples really require the use of either the standard multiplication or long division algorithms. What I am suggesting is that just as accountants obtained figures with an abacus, so can most people be taught to generate useful answers with a calculator. The real math can be left to those of us who love it.

Is it possible that the use of a calculator will allow more students access to the "real" math?

I'm not sure I agree with the first comment that "...work will be

so error-prone as to be worse

than useless." While I agree that estimation skills are necessary to determine if an answer is reasonable, I don't think the work with a calculator is useless.

I struggle with finding a balance between calculator/by hand work.

I think people get confused about what math is. Cranking out a long division algorithm isn't math at all. In fact, you don't even have to understand Indo-Arabic numerals or realize that the symbols are related to numerosity. You can be taught to generate correct answers with a simple times table and a list of steps. This makes the algorithm a tool. You can't hold it in your hand like a hammer or a calculator, but it's a tool nonetheless. The "real" math is discovered by asking the right questions and discovering the answers. It's something that humans do naturally, but it still helps to have a good teacher to guide the way. The reason I favor a calculator is that provided you understand what you are doing, which can be a big "if," it is a far more expeditious and pleasant way to do arithmetic. When arithmetic becomes a chore, math stops being about discovery and starts being about drudgery. My "M for Mature" post goes into greater detail.

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