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Prolegomena to Any Future Math Learning Environment

Main Actor

A student, Madeleine, who is trying to learn multivariable calculus.

Main Success Scenario

  1. Madeleine is enrolled in an advanced calculus course at university. She learns about PlanetMath from her instructor who recommends it as a place for extra practice with homework problems.  Madeleine creates an account, fills in basic profile information, and starts solving problems that the system supplies based on the information she supplied in her profile.
  2. The problems that the system supplies are automatically linked to reference resources in PlanetMath’s encyclopaedia.  This expository material gives Madeleine easy access to the relevant mathematical concepts, examples, and hints needed for solving the increasingly difficult practice problems. However, she eventually runs into a problem where neither the automatically supplied information, nor her current knowledge of the subject, is sufficient. She’s completely stuck on a problem having to do with water flow in a pipe!  Madeleine attaches a help request to the problem: “I understand that I have to use the two variables x and y to solve for water flow, but I don’t understand what the boundary limits of the equations would be: do I have to convert it to polar coordinates?”
  3. This request is noticed by Natalie, a mathematics graduate student who regularly looks at the feed showing “recent requests for help with advanced calculus.” She sees that the reference resources linked to Madeleine’s problem are probably not sufficient, and that Madeleine’s idea about using polar coordinates would work. Natalie makes some changes to the encyclopaedia indicating that converting to converting to polar coordinates can be necessary in pipe flow problems, and sketches an example.  Natalie then checks that this information links to Madeleine’s problem correctly, and alerts Madeleine to the changes.  With this new information, Madeleine is not only able to solve her problem, but can proceed with confidence: she had the right idea after all!

Post Revisions:

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