The Meanings of Equality

Using a computer algebra system (CAS) such as Mathematica to relate a mathematical narrative requires a more disciplined use of symbols and terms than is common in mathematical text. We distinguish 3 examples in the usage of equality, the process of naming a mathematical expression, the process of assigning a value to a variable in an expression and the conditional assignment of equality between the two sides of an equation in order to solve it. We show that Mathematica has 3 different constructions for describing these relationships and explain why we believe that fully integrating a CAS into mathematics education for scientists and engineers should provide a better understanding of these concepts than the traditional narrative in terms of mathematical text.