Science cannot and does not operate apart from a belief system. Not even good science was able to convince the teacher her conclusions were wrong.
Science is absolutely independent of ANY belief system. I guarantee you that if a Buddhist, a Christian, a Muslim, an agnostic, or an atheist drop a ball from the same fixed height and measure how long it takes to fall to earth, they'll all get the same answer (within statistical error).
The teacher is an excellent example of NON-science.