Monthly Archives: December 2015

CBE is not for me, in verse

“Mathematics, take a break, the doggerel has come back !”

Today I start to fill my pail.
Through the next test I will sail.
Common sense must then prevail:
I’ll clear my brain of what’s now stale
To make some space inside the pail.
For competence, the holy grail,
Ensures that I will never fail,
Though moving forward like a snail.
* * * * * * * * * * * * * * * * * * * * *
The whole damn thing’s to no avail.

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Filed under education, testing, tests, Uncategorized, verse

What exactly is Base 10 arithmetic ?

Teacher: “Now we’re going to learn about base 10 arithmetic”.
Wise guy: “Is that where 3 + 4 = 12, or is it where 3 x 4 = 12 ?”.

I did a search on the net and found the term “base 10” all over the place. What does it mean?

An apparently annoying question:
“Does the 1 in 10 stand for the number 10’s in 10?”.

The interpretation of 10 in the system described as “Base 10” depends on the base of the system, so what is it? How do I find out?

We have here a logical problem. The term “Base 10” as a definition is self referential. It is more subtle than this definition of a straight line:

“A straight line is a line which is straight”.

The problem arises from the almost universal confusion between the two things:
1: The name of a number, in this case “ten” is supposedly implied
2: The symbols representing a number, in this case 10 in the base ten system”

So the answers to the questions “What is it? How do I find out?” above are “Unknown” and “You can’t”

Writing “Base 10” when you mean “Base ten” is probably the first step in making math meaningless.

 

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Filed under abstract, arithmetic, confusion, definitions, language in math, math, teaching

divide by zero: why not?

Optional thought: Just read it.

Resource Room Dot Net Blog

Student couldn’t *quite* remember how she had remembered why you can’t divide by zero, and she started by saying “I knew 0 / 9  was zero because …”   and she drew a 9 and the “gazinta” and the 0, and yes, you could put a “zero” on top and do standard long division.

So, taking that cue, I put the zero on the out side and asked, “what would you put on top so that 0 x that was 9? ”  And since nothing made sense…

A nice visual…

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A. N. Whitehead on negative numbers (1911)

This is really worth reading. It is from his book, “Introduction to Mathematics”, published in 1911.

whitehead intro to math negative nos

 

 

 

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Filed under abstract, arithmetic, Number systems, teaching, Uncategorized