I'm not sure what would make you uneasy about that, almost all infant learning happens this way. The education system we understand is a trade off of educating the masses vs cost, nothing about the education system that we went through was determined to be the best system for everyone (thus you could argue, for anyone though obviously some do excel) and there is no real basis to believe that initially abstracting the pedagogical outcome of a topic from learning the underlying mechanics would have any detrimental effect on the learners long-term understanding.

If you extend this concept out you could very well have large impact in the adult learning sector, where often the students have grown to develop a bias towards certain subjects or areas (math especially) which makes them quite difficult to engage. The barriers could potentially be reduced using the same abstraction mechanic.

I remember you said once that rote practice and drilling of arithmetic helped even higher math. I agree. How is drilling mental math any less mechanical than the unconscious familiarization/ingraining of algebraic concepts of this app? In both cases there is an intangible benefit beyond the process.

For the brain, prior meeting in a simpler guise is useful in reducing friction when incorporating new concepts. I imagine it like starting off with good weights when doing a search with no global.

  * How is drilling mental math any less mechanical
    than the unconscious familiarization/ingraining
    of algebraic concepts of this app?

There is a difference in that with mental arithmetic you have, or can have, a direct connection with an underlying reality. This seems to be entirely divorced from any reality, and the rules can, if you don't already know what's going on, appear completely arbitrary.

I can picture asking an adept "why do you put the same thing on each side?" And getting the answer - "Cos that's just how it works."

It -is- how it works. In algebra at least.

Yes, it is how it works, but it's not just how it works. There are reasons for the rules, and underlying models for the rules. It's not arbitrary, it has evolved over centuries to have purpose.

It's not "just" how it works. When you have the equals sign between two expressions you are saying that instantiation of the variables must result in quantities that are the same. When you modify one side then you must make the same modification on the other side in order to retain that property. there are reasons for things to be the way they are.

It's not "just" how it works.

Disagree strongly. It's not useful as an entire stand-alone, but having a friendly environment that doesn't let you screw up to badly is a great way to start learning by doing. There is a good feedback loop here where getting stuck with what you're doing or not being able to move those skills onto paper or into real world problems ends up motivating learning. The point is to be a tool supported by other resources not to replace all of classroom learning.

I don't think its intended to teach algebra independently. The article addresses the roles of teachers in potentially using this in classes, to "teach the whys of algebra". And this applies to both the whys of the rules, and the possible real world applications.

I think the main reasons that people are turned off of algebra are that they think it is hard and it is boring. An thats the hurdle that must be jumped. This gets around both of those problems. They learn it without realizing that they are learning it. And once they know the rules, it is relatively simple to show how this fun game that they just learned actually has real world applications.

I might have been a massively nerdy little kid, but I remember learning the basics of algebra back in the 6th grade and doing problems and thinking how FUN it was. I didn't get how most kids in my class didn't think that this was a new exciting puzzle. Its exciting to see something that manages to put that sense of fun back into math.