Barbara Wendell wrote:


> I teach 8th grade science and am continually amazed
> at the number of students who write the following:
> 
> I would minus this number by the first number to get
> my answer.
> 
> First of all the word minus cannot be used in this
> fashion but the "by" issue is one that confounds me.
> Am I crazy in thinking that this is incorrect?  You
> u would only use the word by if you were talking
> about multiplication.  In my mind, the only correct
> options are:  1) I would subtract the first number
> from this number to get my answer or 2) I would take
> the difference between these numbers to get my
> answer.
> 
> It's driving me crazy.


Good question, Barbara.  The word "by" can be used for division
as well (which is, of course, defined in terms of multiplication
anyway) such as in "Divide 14 by 2."  As far as I know, "by" is not
used with addition and subtraction.  I've yet to have seen anyone say
that this word can be used with addition and subtraction; if were 
considered acceptable to do so, I most likely would have seen it already.

I definitely agree that you cannot minus one number by another.  "Minus"
can be used as a verb but only in sentences such as "Five minus two equals
three."  

I teach college math but not K-12 math.  But I have seen many students abuse
mathematical language and notation, but I don't recall anyone saying what you
have described here.  The most common errors I see are equals signs being used
to mean "the next step is" rather than to mean that the numbers are the same
and the word "equation" being used instead of "expression."  I also see "solve
expressions" all the time, and I try to tell my students that you evaluate
expressions and solve equations but that you cannot solve an expression.
Sometimes it works, but my efforts fail more often than they succeed.  

I think the problem is that they have trouble understanding the precise
meanings of words in mathematics and the precise rules for their use
and that they have trouble understanding the need for this precision in
mathematics.  And they have trouble with language anyway; I don't think it
is a coincidence that they struggle with grammar and punctuation and writing 
style and also struggle with mathematical notation and language.  

Jonathan Groves