Invite people to the WHY of your ministry instead of the WHAT of your ministry.
People are drawn to the WHY. The WHY is what grabs people's heart.
A great example of this is Dr. Martin Luther King Jr.'s famous speech in Washington, D.C. Why did 250,000 people show up on a hot August day in 1963? It was because they believed in the WHY of his message. He didn't say "I have a plan." He said, "I have a dream." People were drawn to the truth that all men should be treated equal.
Instead of communicating the WHAT first - "We need someone to teach a 3rd grade class," communicate the WHY first - "If you're someone who wants to see the next generation follow Jesus, then join our team."
The WHAT is how the WHY is accomplished. But the WHY is why people volunteer. This one simple tweak will cause more people to be drawn to your team.