Every parent, guardian or other person having custody and control of a child between the ages of six and 16 years shall cause such child regularly to attend the public schools of the district or a day school in which there is given instruction equivalent to that provided in the public schools for children of similar grades and attainments or to receive equivalent instruction elsewhere than at school. N.J.S.A. 18A:38-25
The italicized bit, or to receive equivalent instruction elsewhere than at school, is what permits homeschoolers to homeschool. Over the last 15 or so years, there have been several attempts by NJ state legislators to change the law by either increasing the age of compulsory attendance or increasing the State’s oversight capacity.