One of the strangest tutoring jobs I ever had was for a family of radical unschoolers.
Unschooling is like homeschooling, but without a traditional curriculum. To some extent, I agree with unschoolers, in their desire to concentrate on the interests and abilities of the students, and in removing any artificial application of elements of classroom learning, like busywork or homework. But I disagree with extreme unschooling in that I think it's sometimes necessary, unfortunately, for kids to have to learn things that are important but that they may not enjoy.
I think most unschoolers are more reasonable about it, in that even though all the emphasis is on children pursuing their own interests, they also include traditional subjects and learning along with that.
The family I got a tutoring job for were the more extreme unschoolers I've ever met. I was hired as a math tutor. The mother wanted me to make math "fun" for them -- rather than actually "teach" them anything. It was for a couple of girls, one was the daughter of the woman who hired me and the other was her friend; they were about 9 or 10 years old, sometimes with younger sisters too.
I have some multiplication games I like to play, but which require knowing times tables. Well, when their mother found out I wanted them to learn times table, she put a stop to that! They were actually forbidden to memorize anything. (That's why I refer to them as extreme, radical unschoolers.)
So I had to find some ways of tutoring them in math without doing anything that was like normal schoolwork.
I did find a couple of ways of doing that!
Most of the time, I spent teaching them about geometric reflections and other transformations. We used a lot of graph paper, and talked about what happens when you look at things in a mirror, and how shrinking and growing affects shapes. That worked out quite well! They found it fascinating to see how things change like that. And that was just what the mother wanted: for me to get them interested in math, but without letting them study anything.
Another thing I did with them was extremely large numbers. That was another thing they found exciting. I even managed to slip in a bit of arithmetic!
It was very tough trying to figure out how to teach math without actually teaching math. I'm not sure what made her think of hiring a tutor when she was so strongly opposed to any sort of traditional teaching. But I have to admit it was an interesting tutoring job, having to come up with things to do with them that were completely different from anything I had ever done before while tutoring math for regular families. And it's not a bad thing to practice finding ways of making subjects interesting.