Recommended Reading
Algebra is a killer subject, probably *the* killer subject for mathematics at school. Many students can't do it; even those who can do it and get the answers, usually don't know why they are doing it. If you come at algebra as a game for moving symbols around, confusion is very likely to follow.
Algebra is an amazing piece of technology, for solving problems in the real world. More than that, it's a special, mathematical way of thinking about the world. It is sad that few people ever get access to this experience of algebra. (For mathematicians, algebra is a lot more than that - a rich and complex, abstract world of its own, but that is a different story.)
The key thing is to keep hold of what the x's, y's and z's stand for - what they mean. Basically you're setting up a relationship between several quantities. Being able to see this relationship in several ways is critical: as symbols, as a picture (graph), as a table of numerical values; if the quantities have a physical meaning, that tells you other things about the relationship (for example, negative time or negative length may or may not be meaningful in a physical situation).
Each view of the relationship is good for particular purposes; when they combine together you can have a powerful feeling of understanding. Computers and calculators are really helpful for this - because drawing graphs by hand or working out numerical values is very tedious and the computer can do the drudge work. But computers don't just replace your mental effort, they can provide new ways of experiencing mathematics that could not exist before now.
Here is one of my favourite books on this subject: Changing Minds: Computers, Learning and Literacy by Andrea diSessa (published in 2000). It's an 'academic' book and may be hard to get into. You can read the first chapter online for free: http://www.soe.berkeley.edu/boxer/Chapter1.pdf .
At least, read pages 12 to 16 about Galileo - how his development of a science of mechanics was made more difficult because he did not have the right language to express relationships between speed, distance, time, and acceleration. The way that algebra captures the relationships, and gives the mind a new way of thinking, is so beautiful, it's really stunning.
