# What does this symbol mean?

Another useful question is to ask students is “What does this symbol mean?”. Mathematics uses a lot of symbols and even a small symbol may be representing a very complicated concept. And, as was observed yesterday, the same symbol may be representing different concepts! In particular, the zeros in
$\lambda _1 v_1 + \lambda _2 v_2 + \dots \lambda _n v_n = 0 \implies \lambda _1= \lambda _2 =\dots = \lambda _n=0$
are different. One is a vector, one a scalar.

More generally, consider the symbols in the equation below taken from a course on fluid dynamics:
$\rho \frac{D\bf{u}}{Dt} = -\nabla p + \nabla \cdot \boldsymbol{\tau} + \rho \bf{g} .$
Asking the students what the symbols mean can be enlightening as to what they are having trouble with. The $\nabla$ behaves differently when combined with $\cdot$ (the dot). Do students know that? Some symbols represent vectors, some scalars. It’s hard to know whether students grasp this until I ask what the symbols mean to them.

Even asking a student to read out such an expression can be interesting. I have met students who are unsure of how to pronounce the Greek alphabet and will refer to — admittedly with some embarrassment — any symbol they don’t know as “that funny symbol”.

In conclusion, it is important to ask the students to describe what the symbols mean.