My 4-year-old loves it. What can I say? She barely knows the alphabet yet she's learning algebra for fun!
I'll keep feeding it to her and keep you appraised.
I wonder what the big rush is with children, symbolic manipulation in a 4 year old's world has very little implication. Manipulating her environment through motor skils, developing ever more sophisticated interactions with other children, play etc, all seem to be much more useful. But anything that's fun is very likely good. I wonder how much of the fun is her reading back to you your enjoyment at seeing your offspring participate in algebra. The first rule of being a 4 year old is to please the parents. They, after all, provide everything.
My father got me playing around with programming when I was very young -- I think six or eight years old. Some of my first memories involve our VIC-20 computer.
While a lot of what I did was just typing in simple programs from a book, I did some experimentation on my own, and it became pretty obvious how variables, loops, and the rest worked.
When I hit school I was mathematically so far ahead of everybody else, not because I'm some kind of genius, but because I had already spent a lot of time unknowingly learning algebra.
This was a disadvantage, because the school system wasn't built to cope with a kid that understood algebra before he had memorized the multiplication table.
As an adult, however, I've enjoyed a pretty serious advantage when it comes to understanding abstract concepts, especially anything involving symbolic manipulation, and I think I can thank that VIC-20 BASIC manual from many years ago for it.
I wouldn't be too worried about starting a kid out 'too soon', provided that other areas of the child's mental development aren't neglected in favor of developing mathematical skills.
From fifth grade, I was bored out of my mind during math class. In sixth grade, my math teacher recognized my boredom to be a lack of challenge and decided she should do something about it. I was pulled into the vice principal's office at one point and asked to slow down my at-home learning because the teachers did not know what to do with me during class.
Eventually, we settled on a solution: I became the equivalent of a teacher's aid for my middle school class and tutored other kids who were having difficulty. This instilled a love for teaching that I carry with me to this day.
I don't think we should discourage children from learning at a fast pace as long as they appear to retain the information and it doesn't compromise other aspects of development. On the contrary, we need to find a way to help our education system cope with children learning things outside the classroom.
Indeed, the sheer brilliance of this game is the separation of the concrete blandness of raw numbers and plain symbolic letters (which she's already having enough meaning imputed upon while learning to read) from the pure symbology and entertaining rules applied thereto. That's why I'm a programmer: the joy of symbolic manipulation; this game starts her down the same track.
I gave some positive feedback, yes, but the bulk of that was just acknowledging her excitement in creating a new "monster" and next to nothing about the algebraic content. She took her own interest in the game far beyond any parent-pleasing feedback she got.
We're talking a couple hours of fun, and the chance that math won't seem so scary in high school.