Writing a Precalculus Assessment

• Include questions in multiple representations (graphical, analytical, tabular, verbal)

• Write questions that reflect learning targets and require conceptual understanding

• Include multiple choice and short answer or free response questions

• Determine scoring rubric before administering the assessment (see below)

• Offer opportunities to practice with and without calculators throughout the year

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Questions to Include

• Solving for missing sides and angles of triangles

• Error analysis of a student incorrectly solving for an angle in the Law of Cosines 
  (combining all terms, then dividing)

• Identifying how many triangles can be made with a given set of SSA conditions and explaining why

• Finding the area of an oblique triangle

• Selecting an appropriate law to use for a given set of conditions

• Finding component form of a vector given initial and terminal point

• Finding magnitude and direction of a vector from component form

• Finding component form of a vector given magnitude and direction

• Given the direction angle of a vector, identifying which statements about its component form are necessarily guaranteed

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Grading Tips

Look for more than just correct answers. Give students feedback on their justifications, communication, and mathematical thinking. We recommend that you prepare a rubric for the free response and short answer items before you begin grading your quizzes or tests. Know what information is necessary for a complete and correct response and award points when a student presents that information. Many of the “Why did I get marked down?” questions are eliminated when you share the components that earn  points.

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Reflections

This quiz assessed skills in a pretty straightforward manner. Students struggled with the signs of values in vectors, often using the horizontal and vertical components incorrectly when finding the direction. Students also had a hard time identifying the number of triangles that could be made. A picture that was not drawn to scale confused some students.

We chose not to include many problems that had students solve for an entire triangle, as this can take up a large chunk of time for some students. Instead, we asked about specific angles and sides. One of our favorite strategies for writing conceptual questions is to give limited information and have students reason with the parameters about the parameters of the equation, deciding which things can be known for certain and which things can’t.