What’s going on in this (reconstructed) student work? Tell a story in the comments.

And then go thank Christopher Danielson for sharing this stuff.

  • Classic! Interesting how 2^(-3) becomes -8 vs -6…, and then distributing the negative to the exponents is wowsers. Poster work for instrumental understanding.

  • Jim Doherty

    Yeah…. sadly the 2^(-3) is not a terribly surprising result. Most kids just try to cram in the fact that negative exponents do ummm, something to the base. Without some conceptual hangar to place this fat they are left wildyl guessing. The final step, however, is a surprise to me. It’s pretty clear that the negative sign was just distributed here but I have no idea why that would happen. I was waiting for the shortcut of simply reciprocating the entire fraction. This one was a surprise. Christopher – had you seen this particular mistake before? What in the student’s previous work can prepare us to analyze this problem?