More thoughts on Algebra for the 8th Grader:

I teach 8th grade Algebra (for the past 5 years), so the Algebra II list is not immediately relevant to my anecdotal experiences. It has been ages since I have thought about logrihms. I do think a WHOLE LOT about Algebra I, though and have slowly been developing a love/hate relationship with certain topics:

Love:

I love the "magic" of algebra in describing so many different type of patterns of growth. Most of my students enjoy working with this as well. They are developmentally intrigued by the ways algebra helps them describe these patterns outside of simple tables or vague words. In other words, they like the elegant way equations and graphs work together. Linear growth is a natural for them: it is easily seen and predictable. They like that!

Data is a topic Leinwand put into his talk: I think it very very important, particularly logic around reading graphs, tables, and such. I also see that my students need a lot more work with interpreting graphs and basic statistics.

Less Love:

Exponential functions, particularly quadratic, are fun to a point and then quickly become tedious, particularly when dealing with quadratic formula. We spend a good amount of time in Winter and Spring on factoring quadratic equations, really like working out puzzles and trying to make sense of them in various "real world" situations, but I feel I start losing a lot of my students around quadratics. It all starts to feel increasing procedural, even when I emphasize algebra tile models and pattern recognition. Attention wanes.

Then we come to inequalities, which are relatively easy and accessible for them.

Hate: 

We end the year in a whimper with rational expressions. All the procedural knowledge a student got during our work with factoring quadratics comes into play, plus concepts of fractions. Some students are totally "there", some struggle but "get it" and many simply "give up". Add it some absolute value stuff and it all gets messy for them. I have yet to find a way outside of thinking of these expressions as "puzzles" (Sudoku) to make this topic approach real to them. I also am ignorant of their use in higher math. This is an area of growth for me, to be certain!