Is 'Find x' Really About Calculating the Value of x?

  • Context: MHB 
  • Thread starter Thread starter I like Serena
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the phrase "Find x" in mathematical problem statements. Participants explore the implications of this phrase, questioning whether it strictly means to calculate the value of x or if it encompasses a broader understanding of the term "find." The conversation touches on language nuances, humor in misinterpretation, and the importance of precision in mathematical communication.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Meta-discussion

Main Points Raised

  • One participant suggests that mathematics should focus on answering precisely what is asked, exemplified by the equation $x^2=4$, expecting the answers $x=2$ and $x=-2$ without extraneous information.
  • Another participant emphasizes that the phrase "find x" could be interpreted as "discover which number x is," suggesting a distinction between locating and calculating.
  • A participant notes that in their language, the equivalent phrase translates to "what is x" or "determine x," raising questions about the clarity of the phrase in English.
  • One participant shares an anecdote about a math teacher who valued precision in problem statements and would treat ambiguous answers as correct, highlighting the potential for misinterpretation in mathematical communication.
  • Humor is introduced through a deliberate misinterpretation example, illustrating how language can lead to unexpected interpretations in problem-solving contexts.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of "find x," with some arguing for a strict calculation meaning and others suggesting a broader understanding. The discussion remains unresolved regarding the implications of the phrase and its usage in mathematics.

Contextual Notes

Participants note the ambiguity in language and the potential for misinterpretation in mathematical statements, emphasizing the need for clarity in problem phrasing. The discussion reflects on personal experiences with teaching methods that address or exacerbate these ambiguities.

I like Serena
Science Advisor
Homework Helper
MHB
Messages
16,335
Reaction score
258
I was just wondering... my avatar is intended as a joke, but...

As I see it, mathematics is about being nitpicky.
That is, considering carefully what a question is, and answering exactly what was asked, not something unrelated, and not a long story that doesn't even contain the answer.
So if someone asks for which values of $x$ the equation $x^2=4$ is satisfied (within the context of the real numbers), I expect the answer $x=2$ and $x=-2$.
I don't expect a dissertation on algebra in general, nor do I expect that it's also possible that $y$ might be $3$.

If someone asks me to "find an apple", I might search for one, and point out where one is, which would be a geographic location.

From Dictionary.com:

[fahynd]
verb (used with object), found, finding.
  1. to come upon by chance; meet with:
    He found a nickel in the street.
  2. to locate, attain, or obtain by search or effort:
    to find an apartment; to find happiness.
  3. to locate or recover (something lost or misplaced):
    I can't find my blue socks.
  4. to discover or perceive after consideration:
    to find something to be true.
  5. ...


Am I missing something?
Can "Find x" actually mean "Calculate the value of x"?

Or otherwise, how is it that in mathematics there are so many problems statements saying something like "Find x", when that is never what is intended?
It seems to me that "Find x" should be more related to treasure hunting, where the treasure is marked with an "x".
 
Last edited:
Mathematics news on Phys.org
Meaning #4 is the pertinent one, here.
 
Deveno said:
Meaning #4 is the pertinent one, here.

I'm guessing, since I'm not natively English speaking, that "find x" is a proper way to put the question.

Shouldn't it still be "find the value of x" then, or something like that?

In my own language, we use something that translates to "what is x" or "determine x".
 
The intended meaning is: "discover which number $x$ is" (that is, assign it a value from the real numbers, or rational numbers, etc.).

The "joke" lies in conflating this with meaning #2: to locate.

This form of humor is called "deliberate misinterpretation", as in the following:

A programmer's wife asked her husband to go to the grocer's, "Get a loaf of bread. Oh, and if they have eggs, get a dozen".

He returned with 12 loaves of bread.
 
My old math teacher had this rule he set himself.
Whenever his problem statement would be ambiguous, and people answered differently than intended, he would treat it as a correct answer.
This was sometimes abused, but he was very meticulous and kept himself objective.
He probably considered it his own fault for not being meticulously precise, which is what he was trying to instill on everyone.
And how could he do that, if he didn't set the example himself.

The other side was that if students were sloppy and/or wrote ambiguous answers, he would meticulously deduct 0.1 points - each and every time.
This doesn't sound like much, but if it happens about 50 times, it will guarantee an insufficient grade.
That happened to me when I first entered his class, which hit me hard at time, proud as I was of my math skills.
In retrospect, I've learned a lot from him, and after a while (it took about a year) my grades soared up higher than they were before.

I imagine that if he had phrased "find x" in one of his problem statements, and someone would answer with something like my avatar, he would smile grimly, and treat it as a correct answer.
Of course in any subsequent examinations there would never be a "find x" any more.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 12 ·
Replies
12
Views
4K
  • · Replies 7 ·
Replies
7
Views
3K
Replies
2
Views
3K
  • · Replies 10 ·
Replies
10
Views
3K
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K