Curriculum is a current focus of mine. In recent years, I worked through thought experiments on Algebra II and Calculus curriculum. What happens if you ignore a textbook publisher? What if you start with the standards and find a spiraling pattern that makes sense? Can you find the themes? How will what you teach in September help your students in May?
Viewing your course in broad strokes has proven to be very valuable. In Algebra II I only got one year to play with it, unfortunately there was no follow up. Calculus is very much a continuing experiment. Upon taking over in 2014, I knew it was a five year project minimum. Deploying a curriculum of my own design was going to be a really big piece.
With another round of AP scores to analyze, what needs to change in that vision?
More pressing, what has crafting a vision for Calculus taught me about Pre-Calculus?
Pre-Calculus has some themes: raw algebra, trig, polynomials, and a random bin of parts. Can we tie those together better?
At TMC 16, on Sunday July 17, I'm going to offer an opportunity to participate in this thought exercise. Does the curriculum we work through have to be something we actively teach? Do the standards have to match the one from our state? I don't think so.
I've worked through 8th grades standards and Algebra I standards before, neither are things I've ever taught. If you want to broaden your horizon of how math concepts go together, I think it's well worth the trouble to read about all the things you don't teach.