Some kids are more hands-on — they need to touch things to get interested. Most robotic systems out there, like Lego’s Mindstorms EV3, are very comprehensive and has a learning curve that may be too steep for busy parents.
Lego has a much less well-known robotics-mechanical system called WeDo: https://shop.education.lego.com/legoed/en-US/search/navSearchResults.jsp?gradeLevels=Homeschool
And this is the starter kit for higher grade elementary levels : https://shop.education.lego.com/legoed/en-US/catalog/product.jsp?productId=9580
It may be more suitable for younger kids and parents who do not have time to learn something more sophisticated like Mindstorms.
For those of you that do not want to spend $90 for its software, you can use Scratch from MIT and add the Lego WeDo extension and install the device driver for Lego WeDo. You can buy the control hub, motors, lights, and sensors separately. For those of you that have a lot of those parts from your Lego Technic sets, all you are missing is the $50 USB Hub which you can purchase separately from Lego Education. With that control Hub and Scratch, you can program the lights, sensors, and the motors and use the rest of the Scratch commands to program the logic that goes with your Lego creation.
Once your child is in junior or high school, look for an on-campus robotics club that compete in the FIRST Lego League or something similar.