Are Mathematical and Scientific Models different?

When students fit functions to data they are rarely challenged with the question “why does this function fit?”  A good mathematical model for physical data demands an explanation.  This is the power of science …it is an explanatory power.  Responding to the question “why does a mathematical function fit the data?” means providing a scientific model which explains.   In this way mathematical models support scientific models and vice versa.  This is what I understand by STEM. It is, here, the deep underlying connection between mathematics and science.