The Problem with the Pacing of Precalculus

By Ruyi Wang

Of the 13 chapters in the Precalculus With Limits textbook, only Chapters 10 (Topics in Analytic Geometry), 11 (Analytic Geometry In 3 Dimensions), and 12 (Limits and an Introduction to Calculus) did not substantially overlap with content in any chapter of Algebra 2 & Trigonometry. Putting Stratford's school year trimesters into consideration, the course does not introduce significant new material until the final trimester. Although Precalculus has an important role, the way its material is distributed shifts much of its focus toward review even though there is ample space to introduce new material that will better aid Calculus study.

Of course, including review in the course right before Calculus, which is often referred to as a big transition point in math, is reasonable. Calculus expects algebraic manipulation, trigonometry, and other skills to be mastered beforehand. Someone who cannot proficiently apply these topics will likely struggle even more once moving forward. The success of a student in the standard math trajectory does rely heavily on their proficiency in the fundamentals of Algebra. A review that is valuable to one student can be repetitive to another. Is it really worth spending two-thirds of the year on? 

I think the problem becomes more noticeable when the actual AP Calculus BC course comes in to play. While Precalculus seems to slow down and recollect, Stratford's combined Calculus AB and BC course covers a huge amount of new material in a relatively short time. Precalculus slows down the progression and then that forces the following course to speed it back up. If Precalculus is supposed to make Calculus easier, it seems strange that the two are so drastically different in terms of pacing. 

Rather than cutting down the review in Precalculus, the full year can be reconsidered to better balance review with new material. That might support both students who need review and students who are ready to move forward to more preparation. Even introducing just one or two topics of Calculus in Precalculus could give students more time to understand them before using them in practice. That way, Calculus BC would not need to move much faster, and Precalculus would no longer feel slow at times. Based on comparing the two textbooks and personal experience from taking the course, I think Precalculus has room to introduce more new material without eliminating the review that some students need.

For some students, Precalculus can act as a barrier from getting directly to Calculus, or shut out the possibility of exploring other fields of advanced math study. A more effectively structured course could use the same amount of time to expose students to what can come after the Algebra checkpoint. As only one of many possible directions, Calculus should not necessarily be regarded as the endpoint of all mathematics in high school. While Calculus remains important for engineering applications such as structural design and aerospace technology, other areas of advanced mathematics can also prove valuable in coding, finance, data analysis, and artificial intelligence. Data Science, Discrete Mathematics, or even Game Theory are all compelling alternatives that are often overlooked because Calculus is widely considered the peak of mathematical accomplishment. Perhaps three trimesters could also be used to broaden students’ understanding of what advanced mathematics can offer, whether or not Calculus is their end goal.