Yes. You do need auto insurance when driving with a learner’s permit. This insurance must adhere tot eh laws of the state in which you are driving. In general, however, a person with a learner’s permit will be automatically covered by the insurance of their parents, as long as the parents are in the car and the person is obeying the laws of driving under a learner’s permit.
This statement is a large generality. You should check with your individual agent as car insurance laws and insurance varies by state.