For grown-ups
InventForge is struggle before instruction. The pair looks at three machines' throws with no formula, invents a measure of spread from simple parts, and tests it on new cases.
Only then does the textbook's measure arrive. At this age that is the mean absolute deviation, the average distance from the average (Common Core 6.SP.B.5c); the standard deviation is its high-school cousin. The app shows where the invented measure and the textbook disagree. The textbook's choice is a convention; other measures of spread serve too, and the app says so.
The cases are built to test a measure, not to trick a child. In the first three, every machine, player or team has the same number of values, so a simple measure can work. The big batch puts twenty loaves beside four, so a measure that adds up distances is fooled by size; the heater case keeps the readings in time order, so a measure that looks at jumps sees something the others miss.
Two lap cases test two kinds of measure. In one, a team runs seven steady laps and one that is a little slow: "biggest minus smallest" sees only that lap. In the other, one lap is very slow: the average distance is pulled by it, while the middle distance ignores it. Neither measure is simply right there; that is the point. After the tests, Margrave brings a case held back from the tests, where the child's measure and another reasonable one part ways, and the child decides whether to keep it or go back to the bench. The textbook's own measure gets such a case too. A measure the child keeps is shown in pencil beside the textbook's in ink.
Nothing is sent. The measures a child keeps stay on this device.
What it never does
- No accounts, no ads, no tracking — anything kept stays on this device.
- No streaks, timers to beat, points to chase or leaderboards.
- No chat, and nothing anyone types is sent anywhere.