Talk:Word problem (mathematics education)

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As it was written, this article is childish. All mathematical problems are expressed primarily in words. Any impression to the contrary is found only among those whose acquaintance with mathematics comes only from having been required to learn it from textbooks, and even then it's based only on misperceiving what they've read. A student sees a problem written thus:

x² + 3x + 2

and thinks this is a problem posed in "equations" (a common misnomer among non-mathematicians). Such a student has failed to notice that somewhere above this "equation" there were some words that said "Factor the following polynomials" or "Find the derivative of each of the following functions of x", etc. If those words say "Factor the following polynomials" and one of the polynomials is x² + 3x + 2 then one problem has been posed; if they say "Find the derivative of each of the following functions of x" then quite a different problem has been posed. That difference sometimes goes unnoticed among those who hate being required to take a math course, and that's a big source of missing the point. Michael Hardy 00:01, 16 Aug 2003 (UTC)

I now see that the only page linking to this one is about the "word problem" in group theory". That problem most certainly is not called the "word problem" because of its being expressed in words! Michael Hardy 00:03, 16 Aug 2003 (UTC)

Well, that's my understanding of what word problems are. They're used primarily in high school mathematics. You know, like the ol' "A train is heading blah blah blah", and the whole idea of the question is to test your understanding of the mathematical ideas behind the question...

That's a good explanation, I think I'll add it, if you don't mind me unredirecting. There's nothing stopping the article from having a groups explanation as well... Dysprosia 00:18, 16 Aug 2003 (UTC)

"Used primarily in high school mathematics"?? That is utter nonsense! As I said, all mathematics problems are expressed in words. That fact fails to be obvious to students only because they have failed to understand, but it becomes more clear as you get into more advanced work. Look at Walter Rudin's book Principles of Mathematical Analysis. Michael Hardy 14:43, 2 Sep 2003 (UTC)

This nonsense that there are some mathematical problems that are not expressed primarily in words arises only in the most elementary courses -- through about second-year calculus or so. After that it would become obvious that all mathematical problems are necessarily expressed verbally. But I suspect that most people who don't figure that out when they are in secondary school or earlier will never reach more advanced courses. Michael Hardy 14:59, 2 Sep 2003 (UTC)

Michael, as I see it, there are two outcomes to this issue: either we can get it to an acceptable, NPOV article, or we can leave it as a solid redirect. If we want to go down the first path, sure, that's fine talking about the misconceptions about "word problems", but I don't see what was so wrong about the addition re math. modelling.

As it stands, "childish misunderstanding" and "That difference sometimes goes unnoticed among those who hate being required to take a math course" is not NPOV. "The impression to the contrary is found only among those whose acquaintance with mathematics comes only from having been required to learn it from textbooks" is unsubstantiated, and probably inaccurate too (Kids who are taught math in one manner, ie., rote learning of shifting of symbols may get this impression too).

If we can't work this out, then I'm happy to leave it as a redirect. But we're both intelligent people, so I'm sure we can! :) Dysprosia 22:42, 2 Sep 2003 (UTC)

You began with this:

A word problem is sometimes used to describe a mathematical problem posed descriptively

First a grammatical point: The term "word problem" may be used to describe something, but you wrote, not the that term is used to describe something, but that a word problem is used to describe something.

However, modelling problems often involve some kind of specific mathematical concept underlying it - these modelling problems are often described entirely in words without needing to resort to "equations".

Why restrict this to "modelling problems"? Where is there any mathematics problem that does not involve specific mathematical concepts? What about this problem: Prove that every metric space that is complete and totally bounded is compact. There is no mathematical notation used, but it's not a "modelling" problem.

(As for the POV problems -- I'll try to find a way to rephrase it while still being realistic.) Michael Hardy 00:18, 3 Sep 2003 (UTC)

I didn't restrict it to modelling problems, I simply added the fact that the term "word problem" could include math modelling questions as well. You are right, such other questions do not involve modelling also and should be added.

As for the grammar, yes, I'm still learning. That is why you're such an asset here! :) Dysprosia 04:45, 3 Sep 2003 (UTC)

Word Problem:

How many

            drops

of rain

                       are falling

at this moment in this city in this storm?

                       How many

on this patch of asphalt

from now to now?

Count them.

[edit] Just commenting

As I read through this article, I could not help but feel that this point: 'No doubt the term "word problem" is sometimes regarded as meaningless' was being driven home rather forcefully. The iteration of the point that "In fact, all mathematical problems are expressed primarily in words", including the use of bold to highlight all makes it feel as though someone has an axe to grind. I am not disputing the point, but the repetition of the statement feels forced. Does anyone have any thoughts on this, (or should I butt out)? Laconic 18:19, 22 Jun 2005 (UTC)

I put that there. I have a times been quite irritated by the proposed dichotomy, according to which there are some mathematical problems that are expressed in words and others that are not. This weird notion is in fact widespread among people who don't get along well with mathematics. Michael Hardy 19:50, 22 Jun 2005 (UTC)

While I quite agree with Michael, that all mathematical problems are expressed in a combination of words and mathematical notation. I still think most people "know a word problem when they see it", however (kind of like what the Supreme Court justice said about porn), and it's still possible to come up with a reasonable "definition". I find in my classes, from college algebra to differential equations, students invariably have far more problems with "word problems" than with more computational problems. The distinction to me does not have to do with whether "words" are being used or not. This distinction is that a problem is described verbally in a way that conceals the mathematical expression of the problem. The problem is that students are not accustomed or skilled in translating descriptive statements of a situation into precise mathematical expression. Anyone who has taught college algebra knows what I mean. I believe Davis/Hersh had something to say about this in the Math Experience. 198.59.188.232 02:32, 24 October 2005 (UTC)

You're talking only about problems posed as exercises in textbooks, not about math problems generally. And I think you're mistaken in thinking that the problem is primarily with translating words to symbols. The problem is that when they're in symbols then the student can often solve them without understanding them, by applying algorithms they've been given. Words, on the other hand, require understanding. Michael Hardy 18:43, 24 October 2005 (UTC)