Nice article about Algebra vs. Arithmetic
If you are anything like me, this is something you've try to articulate. Here's a great article on that arcane topic!
What is algebra? | profkeithdevlin:
Is mastery of algebra (i.e., algebraic thinking) worth the effort? You bet -- though you'd be hard pressed to reach that conclusion based on what you will find in most school algebra textbooks. In today's world, most of us really do need to master algebraic thinking. In particular, you need to use algebraic thinking if you want to write a macro to calculate the cells in a spreadsheet like Microsoft Excel. This one example alone makes it clear why algebra, and not arithmetic, should now be the main goal of school mathematics instruction. With a spreadsheet, you don't need to do the arithmetic; the computer does it, generally much faster and with greater accuracy than any human can. What you, the person, have to do is create that spreadsheet in the first place. The computer can't do that for you.