Question

I have a concern about notation in the math group regarding exponents.

"x2" does not equal "x^2"

yet is is continually assumed that whenever someone writes x2 they mean "x^2". This can lead to forming bad habits. How can we fix this?


Here's why I'm concerned: "x2" means "two times x" because algebraically, when multiplying to quantities x and 2 together, "2x = x2" or equivalently, "two times x equals x times two". Multiplication is commutative. This is a very important property and I fear sloppy notation is making it only more confusing to students.

Answer 1

As another math teacher, my initial impression is that you're making a bigger deal of it than is necessary. It's merely a matter of communication. The students typing it know that the 2 should be written as a superscript, and the teachers reading it are smart enough to figure that out based on the context.

Answer 2

I feel my concern is justified. Think of it from the perspective of a student who has a hazy concept of multiplication vs. taking an exponent.

consider x23 + x32

Does "x23" mean "x squared times three" \[\huge x^23=3x^2\] or "x to the twenty third power" \[\huge x^{23} \] or "twenty three times x"? \[\huge 23x\]

Same question for "x32"

For a student who is experiencing confusion about these things, I think it is not a good strategy to treat these shortcuts as some of shorthand -- they are ambiguous and in mathematics, ambiguity of notation is not a good idea.

If a student writes x2 in place of \(x^2\), unless x = 2, they are incorrect.

Do you allow your students to use notation in this way?

Answer 3

Of course not, but they also don't type mathematics in my classroom. The notation is incorrect and admittedly horrible, but it's not destroying any conceptual understanding. It's simply a deficiency in the communication of math via the medium of typed text. The way to deal with it is to always clarify the problem before attempting any explanation, or to model correct notation, either using the ^ or with latex.

Answer 4

ok teach, i'm just gonna shoot it to you straight. Most students who take online courses on flvs such as me get lazy when they ask a question on yahoo answers or something.somone may write x2 instead of x^2 and assume they everyone knows its an exponent.But things like this only happens online rather than in a classroom. It's just a habit that people got used to and fortunatley, almost everone understands what it mean even when it may be written incorrectly.

Answer 5

I think the majority of students know they are writing it incorrectly when they do this.
I still think we should correct them when they do, or at least clarify the problem. I just don't think it's a huge problem, at least in most cases, and I don't think we need to do anything drastic about it.

Answer 6

@trueseminole This is a (good) explanation of the phenomena, but in my mind it's not a good excuse. My full time job is teaching online math courses, so I'm aware of the text shortcuts that happen. :) I try wherever possible to circumvent them as early as possible.

In my classes, I have a clear style guide for students to follow and I try to teach them how to use LaTeX.

In OS, I try to help the student use the equation button or use the sketch tool or attach a screenshot to make their question (and ensuing mathematical solution) as clear as possible.

Answer 7

lmao, i cant type anymore my computer is slow, but yeah, I get you.

Answer 8

@trueseminole I agree with @SmoothMath -- I'm not calling for drastic action, but exactly what we've been doing -- modeling good use of notation and always trying to clarify the question with the student before diving into it. :)

Answer 9

Yeah, and I hope that most teachers on this site do that because I do think it's important.

Answer 10

\[\text{A long time ago } x^2 \text{actually was written as } x2\]

Answer 11

The exponents were just written behind the variable.

Answer 12

Nowadays of course the notation has changed.
And I forget when the notation for x2 meaning x squared expired.
But yes it has been forever since that changed so I don't know exactly why people are still using that notation. I really don't think they are using that notation because it used to be used. They are using it just because they don't know how to write "x squared".
So really the above is just a history thing I like to present sometimes when this discussion is brought up.

Answer 13

That's cute.

Answer 14

as a math teacher myself, i believe that students need to learn the right way. however, it is already in the internation lazybones online math notations (I.L.O.M.N) that x^2 is written as x2. the only ones who wouldnt be able to understand these are those who learn from real time classrooms. and i believe those people are smart enough not to mistake x2 as x^2 in real life.

Answer 15

You're awesome.