Research suggests that "the most accurate predictor of a student's achievement in school is not income or social status but the extent to which that student's family is able to:
1. Create a home environment that encourages learning
2. Express high (but not unrealistic) expectations for their children's achievement and future careers
3. Become involved in their children's education at school and in the community”.
http://www.education.com/reference/article/benefits-parent-involvement-research/ (for further reading)
The Ministry of Education also has a section for parents.
MOE - parent section including information about the New Zealand Curriculum