Burndown chart doesn't include subtasks

Our Product Owner at Widespace usually looks at the Burndown Chart to keep track of the progress of the sprint. When we have few but large Stories or Issues, it becomes hard to see the progress being made, since the values are only decremented when the whole task is completed.

We try to split the tasks up with several sub-tasks, and complete those as we make progress. However, these sub-tasks don't contribute to the red line on the Burndown Chart. Shouldn't they? If not, how do you recommend we structure our issues to better keep track of their progress through the Burndown Chart?

(As an aside, it was really hard to report this issue. I have an account through the company, but I couldn't seem to report an issue from there. I had to create a new account, just to do that.)