DragonBox games teach kids algebra and geometry proofs without any prior understanding. website 
I have colleagues who rave about this particular program. With many dozens (hundreds?) of levels one becomes familiar with the numeric range that adults might find interesting after playing for a few minutes.
What level are you on now? Twelve? Then turn it up to 35. That's where it gets interesting.
These levels progress from matching coconuts to solving simultaneous equations. (I think?)
What this convinces me is that algebra is interesting in that it has been difficult to learn but amounts to so little from a natural complexity point of view. Sure it allows solving a large class of problems with pencil and paper but an even larger class of problems can be solved with computer simulation.
It might be that learning algebra the hard way, with pencil and paper, might include more understanding that just the manipulations.
See As We May Understand that suggests a simple tool may not be sufficient for understanding modern devices. It could be that algebra is as obsolete as the screw driver in this story. Who cares if it is easily acquired.
See Morse Code Teaching Machine that similarly progresses through levels. However, to say a telegrapher is one who knows code is to misunderstand completely the work they did at the dawn of the communication age.