Fraction A Day - Day 9 - An Extremely Hard Problem

As mentioned yesterday I said I would work on the problem using Etoys (the above images are from the that project).  The image show notes (using "text box" from the connectors category of the supply bin) about questions I have and some design issues.

In doing this I am thinking I may want to switch things around.  The study interview started with what is 1/2 + 1/3, but that was to assess understanding, I am thinking I should create a version where the experiences lead to this.

This problem was based upon the problem on page 40 of: The Development of the Concept of "Fraction" from Grade Two through Grade Twelve. Final Report. Part One, Part Two and Appendix. - Robert B. Davis 


Also saw an article in the NY Times  Brain Calisthenics Help Break Down Abstract Ideas which mentioned  a 2010 study, researchers at UCLA and the University of Pennsylvania had sixth graders in a Philadelphia public school use a perception-training program to practice just this.  (more detailed version here)