Unpacking the New Mathematical Practices of AP® Precalculus


Precalculus Practices

On May 16, by the College Board announced its latest mathematics course—AP® Precalculus. It has been more than 25 years since the last such announcement—AP® Statistics. Thus, this new course is a major landmark in U.S. mathematics. One of my favorite features of the course are the Mathematical Practices of AP® Precalculus. These essentials are high-level skills that build on one another:

  • Procedural and Symbolic Fluency

    This first core competency for students involves algebraic acumen: They learn how to manipulate formulas, equations, and expressions—with and without technology. This algebraic fluency provides a foundation to prepare them for success in calculus.

  • Multiple Representations

    This is so central to our approach that we call multiple representations by name in the title of our textbook. This AP® Precalculus skill is the ability to interpret and translate across mathematical models: graphical, numerical, algebraic, and verbal. Students read tables and graphs, parse equations, and make sense of written problem statements, and then convert the information into other forms to solve the problem at hand.

  • Communication and Reasoning

    This practice is about students making their thinking seen and heard by others. Students explain what they did, how they reached their conclusion, and why they know their conclusion are valid. They describe attributes and characteristics of functions and know when to use them to model real-world situations. They learn how to articulate their underlying assumptions and recognize the assumptions within a given problem

When I first saw these AP® Precalculus Practices, it struck me how closely they align with the six core competencies of quantitative reasoning, which are interpretation, representation, calculation, analysis, assumptions, and communication. I thought, Wow! This new course teaches both precalculus and numeracy. That is, the College Board not only has created a course that will prepare students for success in calculus but also one that will prepare them to apply mathematics in other college courses, in their chosen careers, and in everyday life. Hmm. This may help answer the question, why another AP® math course?

Greg Foley is the coauthor of the upcoming Demana AP® Precalculus text and MyLab course.

About the author: Dr. Greg Foley is the Morton Professor of Mathematics Education at Ohio University. Foley received BA and MA degrees in mathematics and a PhD in mathematics education from the University of Texas at Austin. He has taught arithmetic through graduate-level mathematics and coauthors Advanced Quantitative Reasoning: Mathematics for the World Around Us and Precalculus: Graphical, Numerical, Algebraic.

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About the Author

Gregory Foley

Author & Morton Professor of Mathematics Education at Ohio University