Yes, eventually it will because JavaScript knows about operator precedence too.
The problem that I have is with the steps that your planned program instructs the students to take.
6 + 2 * 3 being solved by:
- 6 = 6
- 6 + 2 = 8
- 6 + 2 * 3 = 12
That is not how things should be done, it is not how math should be taught, and you will damage students that try to learn math using that sequential technique.
I now need a break before I damage something around me.