# Using formal underpinnings to teach basic concepts

I recently started tutoring a $9^{\text{th}}$ grader who had managed to rotely memorize some processes (thats how he got this far).

In short, I have someone that is trying to learn basic concepts (that we use a positional number system for example and what that means) at the same time as learning things that rely on that (scientific notation).

Is it standard practice in these cases to jump right to expressing numbers as $\sum\limits^{n}_{i}{a_i10^i}$ (in words of course) and how that can be generalized, or should I in essence do the 3rd? grade part first, and then do scientific notation normally?

Note: This is just one example. There are many others, and I am asking for a general rule for what to do in these cases.