To date, I haven't heard of any "educational game" that satisfies my criteria for learning.

Elsewhere I describe what I call "JITED: Just-in-time education". By JITED, I mean that our precollege schools too often teach essential subjects (such as medial reading and arithmetic) "just-in-time" -- further delay would severely conflict with other "just-in-time" essentials.

But perhaps I learned "my method" (as Sherlock Holmes put it) from my gardner father: PLANT NOW; HARVEST LATER.

And that staging of tasks parallels staging in the history of mathematics, of science, etc. For, simple ideas grow into sophisticated or complex subjects. Hence, OUR TEACHING RUNS OPPOSITE TO HISTORY!

Therefore, beginning in 1955, I conceived the notion of "mathtivities" and "scitivities". MY INTENT being A CHILDPLAY ACTIVITY THAT GENERATES A STRUCTURE IN LABELS A CHILD OR TEEN CAN UNDERSTAND. Yet, BY RELABELING, THE ACTIVITY BECOMES AN IMPORTANT STRUCTURE OF MATHEMATICS OR SCIENCE!!!

A PROTOTYPE of this is any early mathtivity of mine, described herein, Pecking Order.

The structure, built by Preschool Kids, parallels the pecking order of chickens in a farm barnyard. But it is equivalent, nonmathematically, to THE HIERARCHICAL STRUCTURE used in The Business World and in The Military. And merely by RELABELING (as a girl changes costumes of a Barbie Doll or a boy changes uniforms of a G.I. Joe Doll) PECKING ORDER TRANSFORMS INTO 40+ fields of MATHEMATICS and LOGIC.

Can a game do that?

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In some instances, herein, you find PROTO-MATHTIVITIES or PROTO-SCITIVITIES, with material wherewith to form MATHTIVITIES and SCITIVITIES.

Have you ever watched great African-American tap dancers in bravura performance? One will execute an amazing flight of steps, then yell at another, "CHALLENGE! CHALLENGE!", daring the other to do as well. There's a documentary film, Tap, produced by Gregory Hines, with the young xxx, among others, that delightfully displays this. And there's a segment of the "Bill Cosby Show" with a CHALLENGE-session. (I apologize for not remembering the name of the old tapper who made it vivid.)

I CHALLENGE you to transform PROTO's into MATHTIVITIES or SCITIVITIES.!