Where does the term 'Double Dutch' originate?

There are two theories:

1) 'Double Dutch' is also translated as 'Strange kind of talking'. In the early days of the 'New USA', as the English, French and Dutch settlers came to the country of unlimited possibilities, the children of the Dutch settlers were jumping their two ropes in front of their houses. During their jumping the children accompanied their jumping games with all kind of songs. Of course the songs were in Dutch; this couldn't be understood by the French or by the English children. That's why people called it 'Double Dutch'.

2) 'Dutch' is also translated as 'cheap'. In the early days of the 'New USA' jumping a long rope was practiced among the settler's children. But because of the frequent usage of the long rope it started to decrease / flatten in the middle. As the rope broke down or just before the rope broke down, the Dutch children folded the rope so they had two ropes without a weak part in between and they started jumping these 'two' ropes.