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

• A scenario that requires interpreting a constant rate of change and writing a linear equation, interpreting the slope and y-intercept in context

• Novel applications of the distance and midpoint formulas; consider giving an endpoint and midpoint and having students find the other endpoint, or solving for missing coordinates given a distance between two points

• Given a volume, working backwards to find a missing dimension

• Writing equations of two lines that are parallel/perpendicular, then justifying that they are parallel/perpendicular in at least two ways (graphical, analytical)

• Describing a range of numbers using set, interval, and algebraic notation

• Writing equations of circles or identifying center and radius from a given equation

• Describing the effect of scaling a variable in a non-volume equation (like kinetic energy KE=½ mv^2)

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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

Although students were familiar with this content from previous years, we found that the style of questions was new to students and provided a window into their conceptual understanding more so than traditional assessments. Overall students did well on the test, though some struggled to apply the learned concepts to new scenarios (the physics equation!) Students came away realizing that memorization of definitions and procedures would not be enough to be successful on an assessment.