The word which best fits the definition a system in which a child's main education undertaken by a parent is homeschooling.
Homeschooling is when children's education is based at home with their parents' guidance rather than through enrollment in a public school or private school. In general, parents select to home school their children for social, academic, family, and/or religious reasons.
In a homeschool setting, parents are able to provide a more personalized lesson plan for their child. Public school teachers have a classroom of students with different abilities and levels of learning. The lesson plans won't be tailored for each individual student.
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