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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.
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still. "number sentence"... alludes to parsing, and perhaps "numberical string"... computational algebras.
nd if it's made up of constants, variables, and mathematical operators, it's not a sentence, it's an equation
or a program :)
people generally not expert in their field like to make up new language. the experts naturally, hate this.
dogs ARE milkable ;) but they's not cows.
cats however, should never have wings.
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http://www.youtube.com/results?search_query=terc+investigations
this -> http://www.youtube.com/watch?v=Tr1qee-bTZI
good thing it's not terc at least :)
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Heck, I'd settle for the past tense of 2 + 2 = 4.
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Dixitque Deus fiat lux et facta est lux!
(… hey, you asked!)
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http://en.wikipedia.org/wiki/Number_sentence
http://www.google.com/search?q=%22number%20sentence%22
mmm
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"Number sentance"? I can't wait until some yo-yo here at work tries that line on me or my deparment.
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For one, they can be inequalities.
3 + 6 < 10
For another, they don't need to be true, though I suppose that can be said of equations as well:
7 + 9 = 17
That's a number sentence.
As said before, it's basically a parsing thing. They're probably starting by explaining to the kids how to form a valid syntactical construct (the sentence) in the first place.
Hard to say, without seeing the curriculum, but you might be getting angry at them teaching more or at a deeper level than they taught you.
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By definition, an equation is a relationship between equals.
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You're probably right about truth not being intrinsic to the definition of an equation (or a sentence). I'm guessing the "number fact" implies truth though.
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When I talk to fourth graders about math, I tell them that math is a language. Like any language, it's used to express ideas -- and sometimes you can even tell jokes with it. My usual joke involves giving them a new definition of prime numbers: "A number is prime if it can't be evenly divided by any other prime number." I show them how this is a circular definition, and after a while they all see how weird it is, and how strange. I tell them that's the set-up to the joke. The punchline is, "2 is a prime number."
I spend the next half hour showing them that this "punchline" suddenly makes everything make sense, and this really weird-looking "setup and punchline" gives the exact same answers as their more pedestrian "a number is prime if it cannot be evenly divided by any numbers besides itself and one".
In Day Two, I show them some other mathematical "jokes". Mandelbrot sets -- want to see what happens when you blow this up a KAJILLION times? Ha! It looks just like itself! And so forth, and so forth.
So... I'd actually defend them if they want to talk about "number sentences." It's probably an attempt to convey to kids the idea that math is a language, not just a bunch of facts. Of course, it's probably an incompetently executed attempt, but... I admire what they're trying to do. I think the "number sentence" idea isn't a good way of doing it, but I admire what they're trying to do.
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.
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?
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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.
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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."
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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.
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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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I think another aspect of this is to limit the new vocabulary [jargon] that is used in a new field. If we teach a vocabulary that borrows from what the instructors are familiar with, and understand, we reduce the anxiety in both the instructor and students. Precision of expression can be learned later, if needed. My children learned very early to be precise in their requests and statements. That has spilled over into their education experiences outside of the home.