Towards more meaningful math notation
By Murray Bourne, 11 Jun 2007
Students struggle a lot with the way mathematics is written.
For example, most students don’t have too much of a problem with:
5(a + b) = 5a + 5b
Then they see this and it is also OK:
5(ab) = 5ab
In most cases you can substitute various values of a and b and the students can see that it works. Fair enough. Then the student does twenty (mind-numbing) examples of such bracket expansion and they feel they have got it.
Later, they come across things like:
sin(a + b)
And then their math teacher goes ape when the student expands it like:
sin(a + b) = sin a + sin b
Perfectly logical, in the minds of the student.
Similarly, it is logical to have the following, isn’t it?
log(a + b) = log a + log b
Oh, and then we have functions. You know, like this:
Is that the same as
f × x? (That is, f multiplied by x?)
I wish to propose an alternative notation for concepts where you cannot expand in the way you do with simple algebra. It might look something like this:
This would send a much clearer message to students that the particular function or operation does not work in the same way as simple algebra works.
Now, the proposed rectangle would be a nightmare given that we need to type mathematics (actually, everything is a nightmare when you are trying to type mathematics…).
So a more computer friendly option would be to (exclusively) use [ ] - square brackets - for such concepts, like this:
sin[x + y]
log[x + y]
Would this work? Would it confuse everyone even more? I feel that if such a notation were to be universally adopted, then less confusion would arise.
[I wrote about notation before in Phase shift or Phase Angle?].
See the 59 Comments below.