If you want to reach new askers, "ask" yourself this:
Why hasn't the /ask page meaningfully changed since 2010?
Here's a screenshot of the ask page circa 2009 from the wayback machine, next to what it looks like right now today in 2016.
I'd argue that the ask page is the one page on Stack Overflow that has changed the least in the last 5 years. Given the increasing volume of questions, and the importance of question quality to the whole Q&A ecosystem— that's … strange.
If you want to reach new askers, you need a better /ask page. A whole lot better. How can this page interactively teach new users how to ask better, and raise the bar for the quality of the questions being asked?