what approaches can you recommend to make science and technology education more relevant?

Answer 1

You could try the discovery approach.

Answer 2

Relevant to whom? students in elementary school, middle school, high school? College? Graduates? The general population?

If you mean elementary school: I would suggest having the students participate in fun experiments such as what happens when you mix vinegar and baking soda or dissecting a worm and showing how that works or looking at xrays of broken bones to show how technology can see that.
If you mean middle school: I would suggest dissecting a frog for the class, using a cow lens to read papers to show how lenses work, you can ask students to take off glasses and show how they cannot function as well without them (same for hearing aids).
In high school: students can dissect their own frogs, they can travel to a hospital to learn about the equipment used, they can watch videos of the space shuttles shooting off, they can study the effects of plants and how they grow in different conditions.
In college: take away their computer for a month
In graduate school: study medical advances and how less death results (think childbirth or amputation), look at the advances in mental health (think lobotomies and jails vs chemical stability, MRI scans, etc), and so on
As for the general population: point out how often they use traffic lights, electricity, drive their cars...etc

the key to making science and technology relevant is to show how it is used in every day life as well as how it has been used to help people...
Hope that helps