This case is becoming much less important as time goes by. This is because there is very much less corporal punishment in public school in the United States. At the time of the Ingraham decision, only 3 states and the District of Columbia banned corporal punishment in public schools. Today, 31 states do and the practice is not nearly as common as it once was even in most places where it is still legal.
If you need to argue that the case is important, you can argue that it helped to bring about a change in what Americans see as acceptable. It may have helped to make Americans more aware of the presence of corporal punishment in schools and, thereby, to have created a backlash against the practice.