The problem in Algebra 2: too many topics, too many formulas that mean too little to most students.
We propose a partial solution: teach fewer topics, in more depth, to inject meaning into the course; provide access to all students through carefully selected tools, and still try to challenge the strongest students.
Blog post: In Defense of Algebra 2
Naoko Akiyama and Scott Nelson had designed a one-hour presentation based on the Math 3 curriculum which we've all taught, and which was largely developed by me at the Urban School of San Francisco. I later joined them to expand the presentation into a 3-hour minicourse, which we presented at the California Math Council, Southern Section (Palm Springs, November 2001) and National Council of Teachers of Mathematics (San Antonio, April 2003.) I updated it in 2011 to present at an NCTM summer institute.
Also available on this site :
Iterating Linear Functions from The Mathematics Teacher (with Jonathan Choate), and Algebra: Themes, Tools, Concepts (with Anita Wah). Also there: a bit on iterating non-linear functions and chaos.
Sequences and Series from Algebra: Themes, Tools, Concepts
Intro to linear programming: Letters and Postcards
A visual explanation of completing the square.
More on parabolas and quadratics.
Animation to explain the sine curve.
Electronic Graphing (scroll down to "Super-Scientific Notation" for an intro to logarithms.)
Perspective (lab on inverse variation, similar triangle review.)
Worksheets and games about complex numbers.