They're at it again

[unixronin]

The school just sent a letter home with a booklet of vocabulary words ... from the math program.  It contains things like "number sentence".

You'd immediately recognize what they call a "number sentence".  It looks like, for example, "2 + 3 = 5".

There's a perfectly good word for that already.  We call it an equation.  What asshat thought it was a good idea to go muddying the water by making up inaccurate terms like "number sentence"?  (The previous iteration was "number fact".)

Precision and accuracy are important in mathematics.  There are reasons why we use terms whose meanings are precisely defined.  Equations — or mathematical statements in general — have different structure and obey different rules than sentences, and different sets of operations can be performed upon them.  Calling them sentences confuses the issue to no purpose.

Instead of kludging together some artificial term that vaguely approximates what something is, why not just teach the correct word and its meaning in the first place?  We don't teach children to talk about "milkable dogs" when we mean a cow, so why are we making up crap like "number sentence"?  Talking about a number sentence is like talking about a feathered cat.  If it has feathers, it isn't a cat, it's a bird; and if it's made up of constants, variables, and mathematical operators, it's not a sentence, it's an equation.  (Or an inequality, or an identity, or one of several other kinds of mathematical statement.)

And we wonder why our schools are failing.

Comments

[unixronin.livejournal.com]

Also, finally, note that not all number sentences are equations. By definition, an equation involves a relationship of equality. But "x + 3 < 5" is a 'number statement' that's an inequation.

Sure. I didn't mean to imply that all mathematical statements are equations. But the specific one they used in their example was.

Personally, I would prefer they got rid of the phrase 'number' altogether, as well as 'sentence'. Call them what they are: not equations, not sentences, but declarations. I declare that "x + 3 < 5". What numbers will make me be telling the truth? Which will make me a liar?

I prefer "statement" myself. Anyone should be able to understand that a mathematical statement, just like a linguistic one, can be true, false, or even complete nonsense.

[cipherpunk.livejournal.com]

Statement, declaration — I'm not picky between the two. :)

However, it's very important to me that "number" be dropped as an adjective. "x + y = z" is not a number declaration. There's no requirement that the letters be numbers at all; only that they support an additive property and can be tested for equality. Admittedly, you'd have to get into some very advanced math before "x + y = z" could be viewed as no longer about numbers, but...

I much prefer if kids are taught math starting from logic and patterns. I don't care if a fourth grader can multiply together three-digit numbers or do simple algebra. I care a lot if a fourth grader can listen to a statement I make and point out "you know, I don't think it quite works that way."

"If it's raining, the sidewalk is wet. The sidewalk is wet, so it's raining." That's the sort of fourth-grade math skills I think are very important, and very under-studied in schools today. I think a fourth grader ought to be able to say "no, I don't think that's sound," and ought be able to say "... but it might be raining anyway."

[genuine-snark.livejournal.com]

The specific example isn't important though. Things can have different categories at different levels of generality.

1 + 2 = 3 is a number sentence that communicates an equation and a fact. "Your eyes are like a pair of shining diamonds" is a word sentence that is a simile that communicates a compliment.

FWIW, in poking around on this, I found lots on mathematical logic involving sentences and whatnot. A logical sentence basically amounted to a mathematical statement with no free variables (which may be in sharp contrast to cipherpunk's definition w/ x + y = z).

This really looks like a higher-level concept finding its way into elementary math. I just have to wonder why this is a bad thing, assuming they still learn the math too. I bet some of the "new math" set theory was pretty damned useful to computer science years later.

[perspicuity.livejournal.com]

some people probably find it objectionable, because it's new to them, and out of context, doesn't make sense. of course, it's possible the context is never revealed during the teaching either.

in thinking about this... math IS a language. a simple 4 banger calculator (+ - * /) and numbers and = is pretty easy to represent as a formal grammar (BNF say). that said, grammars have atomic units - tokens. tokens are then built up to form sentences. number sentences if you will.

later, they learn that number sentences can be (if i got this right), form portions of equations... equations however, are not number sentences, nor degrade that way, even if you happen to construct an equation that looks like a number sentence. the grammar, and thus the parsing (and parser) just don't grok that :>

i think the difficulty is overloading the word sentence, and thinking "natural language". which is incorrect. this has nothing to do with that.

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