Writing an AP Calc Assessment
Include multiple choice and free response items
Write questions that reflect learning targets and success criteria
Determine scoring rubrics for FRQs before administering the assessment
Require multiple forms of communication: numerical, graphical, analytic, and verbal
Questions to Include
Questions to investigate application of the basic rules for derivatives
Derivatives that can be found using multiple methods
Derivatives with independent variables other than x
Interpretations of the graph of f’(x)
Application of the definition of derivative
Writing equations for tangent lines and interpreting the line in context
This quiz contained numerous derivative problems solved by quick application of the basic rules. Some solutions, however, could be achieved by using multiple strategies. To best assess student thinking, we required that they show work on selected problems. We wanted to know when students used the quotient rule or, instead, took advantage of simplifying a rational function before proceeding.
Notation is still a work-in-progress at this point, but we are clear about our expectations before each assignment, quiz and test. Be sure to align your grading policy to the expectations you have communicated to your students.
Most students labored through the quotient rule when presented with an easily simplified rational expression. Of course, this presented many opportunities for errors (with both calculus and algebra). Point out the advantages of simplifying!! Remembering the format for the quotient rule is a year-long challenge for some students. The internet abounds with songs and phrases for remembering the correct formula if this works for your teaching style.