Take some online classes on programming! There are plenty of free classes you can take online now through Coursera, edX, or Udacity. The classes are offered for

Take some online classes on programming! There are plenty of free classes you can take online now through Coursera, edX, or Udacity. The classes are offered for the benefit of the students more than anything else, but they do offer certificates (the vast majority of them at least) of completion as well as paced assignments which are graded. This may be more along the lines of traditional proof that you are being productive that your parents are looking for. Additionally, if they are worried about you going to college, most colleges have a process by which you can take an exam for credit for courses which you purport to already be knowledgeable in. It's possible that if you learn the material from an online course, you could end up translating that knowledge to credit wherever you go to school. If you make this argument to your parents, you may be able to continue learning what you're interested, furthering your education, and appeasing them all at the same time.