DescriptionResearcher Amy Martino asked the students to assign a number name to the white rod when the orange rod was called ten. After discussing the problem with their partners, the students joined in a whole...
DescriptionDuring this session, researcher Carolyn Maher provided the students an opportunity to revisit the task that they had been introduced to during the previous session: Which is larger, two thirds or...
DescriptionThis one-on-one interview between Researcher Carolyn Maher and Stephanie was an 85-minute discussion that occurred in the 4th grade about two weeks after Stephanie’s second interview with researcher...
DescriptionIn this clip, researcher Amy Martino leads a class discussion that centers on the task: If I call the orange rod one, what number name would I give two whites? Some students suggest the number name...
DescriptionIn the fifth and final clip from this session, researcher Carolyn Maher asked Jessica to re-explain her original model. Jessica restated her argument, saying that the model showed that one half was...
DescriptionIn the first clip a visitor worked with Danielle and Gregory on the second task of comparing two third and one half. Danielle showed her using the twelve-centimeter long model, that three fourths was...
DescriptionIn the fourth clip from this session, Jessica reported that Jackie and Kelly’s argument was different than their original argument in which they had showed the difference between one half and one...
DescriptionIn this clip researcher Carolyn Maher asked Graham what his argument would be for why two fourths could be labeled one half. He replied that one half plus one half would equal a whole and that two...
DescriptionIn the seventh clip Amy, Jacquelyn, and James built another rod model at the overhead to show their solution to the problem: Which is larger one half or one quarter. Amy explained that they had tried...
DescriptionResearcher Maher began the session by discussing the relative size of fractions within different models. Using the analogy of two different sized dioramas of children in a fishing boat, the class...