A year ago I embarked on a wild idea. Algebra II as a subject is taught in a broken way. The goals of the project:
- Students can recognize an equation of any function type at a glance
- Students are comfortable manipulating parent functions of any type
- Students aren't scared of decimals or 10-step solutions
- Students can connect algebra manipulation with a graph
- Students don't think there's anything special about an inequality
I wrote a plan and spent a school year making it up as I went along. What's practice look like? What do the assessments look like? How extensive will we study rationals?
It was an experiment in every aspect. I never knew what was going to happen more than a day or two in advance. As if changing the entire curriculum wasn't enough, I tasked these students with two ambitious projects. That I made up randomly.
All I can say is that the experiment was a complete success. The kind of algebra these students were doing at the end of the year was unthinkable a couple years ago in an academic-level class. In certain aspects we were beyond a PreAP level.
And now you can try it yourself!
My Algebra II resources have been very popular this year. If you've found your local Algebra II resources lacking, mine have been freshly updated with everything you need to approach Algebra II in this excellent way.
SBG Assessments? Check. Practice? Check. Activity Ideas? Check. Final Exams? A formalized outline of the curriculum you can use to start a meeting with your Algebra II team? Check.
Before you get too excited, there are some shortcomings. I did not meet all of my goals. You should know in advance that:
- I could've done a better job with inequalities, students were ok with the mechanic but I have this nagging feeling they never conceptually understood x = 3 vs x > 3
- I never got to conic sections, like, at all
- I don't like the names I used for my assessment standards, students were confused and the SBG system was kind of compromised as a result
- I covered systems of equations without ever calling them systems of equations
- I never stressed simplifying radicals, I had them fiddle with decimals instead
- I barely talked about factoring, my students even rejected it in favor of the quadratic formula, and I never touched it when dealing with rationals
- I could've included more material to enforce domain and range, I introduced it and tried to reinforce when discussing the boundaries of solution regions, but many students found it to be a struggle, and I have no idea why
- I didn't stress complex solutions a lot, and I never got into the mechanics of complex numbers
- I didn't discuss rationalizing denominators or complex conjugates
- I only scratched the surface of polynomials, it was relegated to a vocabulary unit
That means there's room for improvement. Due to the needs of my department, I won't be teaching Algebra II in the future. But, the experiment gave me a much better understanding about how the topics of algebra connect. As a result, the lessons learned here will have an impact on how I teach Pre-Cal and Calculus.
On the off chance you're going to TMC14, the results of this experiment will be discussed in the Algebra II morning sessions.