We start student computing with some very simple programs.  About once a week we have an “eExercise” such as graphing a surface z=f[x,y] and its tangent plane.  In these basic programming assignments, we strive to show how the paper and pencil procedure written as Mathematica commands gives the solution, but typically with the addition of Mathematica graphics.  The program can then be used to solve difficult examples with graphics that could not be done "by hand."

Several times at the end of a collection of ideas there is an eExam that requires students to apply conceptual ideas to a new program.  They develop a general formula and then can see if it produces the correct graph, so there is a way to check their own work.

Some eExams are:

The formula for the steepest tangent to z = f[x,y].

Gas, brakes, and turns: Animating motion along a curve showing the components of acceleration that speed up, slow down, and turn.