Acceleration or Enrichment – The Tower Built on Sand

At Payton, we seem to be moving rapidly through difficult content, in order to prepare our students for AP Calc. The aim, within the next few years, is for every student to study Calculus by the end of their time with us. Students are now even able to take Algebra 1 and Geometry combined into a one year course (where traditionally it would take 2), in order to get them ready.

I have been mulling over this, reading this article and this report about the phenomenon of increasing numbers of high school students taking college-level Calculus courses, in America.

Some factoids:

  • In the 1980’s, 5% of high school students took Calc. Only those students who were planning to do intensive STEM degrees at college. Now it is more like 20%.
  • 80% of AP Calc students take it because it looks good on their college application.
  • 90% of AP Calc students re-take calculus in college anyway.
  • 47% of Asian American students take AP Calc. Only 8% of black students do.

Overall message: in order to learn Calculus, you have to want to learn it. Too many students are now taking AP courses, and for the wrong reasons. Simultaneously, not enough students from disadvantaged areas are taking AP courses, since their teachers do not have the required subject expertise.

Some ideas:

  • There is a difference between acceleration and enrichment. Rushing through the foundations of Math, in order to get to Calculus before the end of high school, often creates “a tower built on sand” – students might be able to differentiate a polynomial, but they don’t really understand what a polynomial is or why calculus is beautiful and important.
  • When these students re-learn Calculus at college they often lose confidence – unable to understand the content when presented at a greater pace and more formally. They are lacking the fundamental prerequisite understanding.
  • Seeing the idea of Calculus in high school is beneficial for students, but there is no need to do a formal exam in it.
  • How would you differentiate (x^3 -1)/x? If you are an expert, you would simplify first. If you are a student, you would just use the quotient rule.
  • In order to get students ready for Calculus, often teachers in middle schools who lack subjects expertise are teaching Algebra. Is this what’s best for the students?

What can we do at Payton?

  • Encourage colleges to no longer value AP courses. Unsure of how feasible a task this is for one school.
  • Only encourage students to study Calculus if it is suitable for them. (What does this mean? How can we do this with equity?)
  • Offer a wider variety of Math courses for older students. Probability? Geometry? Coding? Number theory? Graph theory? Interdisciplinary projects? Problem-solving? Financial Math? History of Math? Calculus is great, but so are many other ideas. (We would have to work hard to ensure these are not seen merely as the cop-out options for students who are not “clever enough” for Calculus).
  • Can we survey the current students, both those who are doing AP Calc, those who are about to do it, and those who are doing Pre-Calc in their senior year? What are their thoughts and motivations?

The overall picture of the High School math journey.

Group A – stronger mathematicians. Group C – weaker.

What should a pre-calc course include?

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