They were, and still are, called Stonemasons, and not Builders, quite simply because they transform and place stone. Whether the finished article is a house or a monument or a wall is immaterial.
Nowadays we live in a society that takes pretty good care of everyone, but back in the "good ole days" if you couldn't find work you and your kids would starve/freeze to death. If a stonemason came to the end of a big job on a church or townhall, and had lined up another project in another town, but it didn't start for a month, what do you think he did?:-
1) went on a holiday to the Maldives for four weeks
2) took small jobs to tide him over wherever he could find them, i.e. fixing a hole in a farmer's wall, building a funerary monument for the local esquire or even filling in the great bog pothole at the end of the vicar's drive..
Returning to the OP's original question the vast majority of people couldn't afford to send their chidlren into education or even to pay a Master craftsman to apprentice them. Trade's tended to stay in the family so a child was likely taught by his father, an uncle or an in-law.
If the OP's family were masons throughout the 1700s it sounds like they would have been able to provide all the on the job training you could ever need. Why pay someone else to teach your kid when you can do it yourself?