Here are some ideas about how a graph could know about data and ask questions.

Interesting point reporter. The grapher should be able to tell Pedagogica 'interesting' data for any graph of data or a function. These interesting data would include local and absolute max and min, curvature at max and mins, axis crossings, points of max and min slope, noise, frequency spectrum, the derivative and integral functions, and crossings of multiple datasets. These data would allow Pedagogica to ask intelligent, data-sensitive questions about the graph, such as "where is the maximum?" or "where is the graph increasing the most?" The user would be able to point to a place on the graph and click to indicate a response.