Category Archives: Analogy

Analogical Mapping and Classroom Representations

Lately, I’ve been thinking a lot about mappings–particularly the kind of mappings we make across mathematical representations like algebraic notation.  Part of this is to build toward a cluster of automated mapping systems that allow for flexible enforceable mappings across structures–I’ll write about that project later.
Here, I’m just going to muse a little bit on the difficulty of pinning down some analogies that are very common in math classes, yet on their surface seem challenging for mapping processes (at least, the ones I know of) to handle.  I’m going to talk just about number lines and arithmetic notation, but the same points seem to hold for a wide variety of situations.

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