Fantasy High School Part 4 PreCalc

I’ve been looking around at sample curriculum sequences due to odd  seeming topics I’ve seen at home via the Pre-Calculus class my older son is taking,  In the past I’ve noted that Algebra 2 is extremely non-standard when it comes to curriculum. The same goes for Pre-Calculus but I think after checking a bunch of samples, it particularly lacks coherence and integration with the classes that go before and after it. So I thought I’d dig into a reasonably typical representative curriculum:**Semester 1 **

• Functions Analysis - Unit 1- Linear and Quadratic Functions - Unit 2- Polynomial and Rational Functions - Unit 3- Inverse, Exponential and Logarithmic Functions - Unit 4- Conic Sections - Unit 5- Matrices - Unit 6
  Semester 2
• Trigonometric Functions - Unit 7- Analytic Trigonometry - Unit 8- Applications of Trigonometry - Unit 9- Vectors and Polar Coordinates - Unit 10- Sequences and Series - Unit 11- Limits - Unit 12 What’s striking about Semester 1 is that is mostly duplicates and spirals over topics that were just taught in a typical Algebra 2 class.  There isn’t potentially a new topic introduced until Conic Sections and/or Matrices.  And in many cases, Algebra 2 will have covered Conic Sections already as well. Based on some chapter samples, these really are review topics and don’t go any deeper than was done the previous year. The units on linear functions and then factoring quadratics are often particularly noteworthy in this regard. Then we come to Matrices. While Linear Algebra is definitely interesting it doesn’t in anyway connect with Calculus I. This material seems more likely to be forgotten after its introduced in a typically short and cursory unit in the middle of all the other topics.  What’s worse is there is no motivation for why its being taught which I expect most students to notice. Semester 2 is more promising and includes the needed trigonometry. There’s a review of Series and Sequences which may be justified by their central role in  Calculus. And then comes a unit on Limits. While this is probably an extension of work with asymptotes and very closely linked to the foundations of Calculus, the problem here is that almost certainly any Calculus class is going to repeat this material all over again. So in sum, more that 50% of the material probably doesn’t really make sense. That may be an opportunity because, as mentioned before Last Post there is constant demand for more topics on Discrete Math or Statistics etc.  Perhaps rationalizing this class is part of the overall solution. Or in the cold light of morning perhaps this also indicates more problems in the previous years classes. You don’t hear a lot of complaining about the spiral. Is it necessary right now because either the Alg I / Alg 2 classes don’t cover what they are intended to or the material doesn’t stick for enough students?