We use the cursive book pictured. It does not go in alphabetical order, but goes from easiest letters to form to the more difficult ones.
We use the Handwriting Without Tears program, which is the same one your child used for printing. The cursive they are learning is different from the cursive I learned and probably that you learned. It is not slanted, doesn't have as many loops, and doesn't have extended beginning and ending strokes.
So far we have learned the a and the c. We will work our way through the book and then eventually take our spelling tests, complete papers and write stories in cursive.
At conferences at the end of October, your child will be showing you a sample of his/her cursive of the letters the students have learned so far.