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Transcript and student work are also available.

Robert B. Davis Institute for Learning. (1993). Building large models to show equivalence, an exploration, Clip 1 of 4: Is there a larger model? [video]. Retrieved from

A92A93-FRC-CMPRF-CLIP001

During 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 three quarters, and by how much. The students were encouraged to build more than one or two models. The video data lent insight into the reasoning of four groups of students, whose ideas about this task will be traced below. Erik and Alan began to work on the problem by building the models that they had found the day before. First, Erik built the twenty-four centimeter-long model, and the researcher asked him to reconstruct the other model that they had found. After some trial and error, they succeeded in building the twelve centimeter-long model, first by using a train of two yellow rods and a red rod, then modifying that train to an orange rod and a red rod. Erik and Alan explained to the researcher that the first model showed that the difference between the two lengths was one twelfth or two twenty fourths, and that the first model showed that the difference was one twelfth. Alan then stated that the larger model was the only model that could show the difference in twenty-fourths. He explained that if one wanted the smaller model to contain twenty-fourths, the white rods would need to be split in half.

The researcher then challenged Erik and Alan to find another model. Erik proposed using a train of three orange rods. He then tried using a longer train of orange rods. During his exploration, he stated that the brown rods were equivalent to ten white rods, and that the orange rods were equivalent in length to twelve white rods. Alan used reasoning to show Erik the flaw in his assumption. He told Erik to line up white rods against the orange rod, and Erik concluded that the length of the orange rod was equivalent to ten white rods.
Erik then built a model using three orange rods and a dark green rod. He found that the blue rods could then be called fourths, and showed Alan what he had found. Alan then challenged him to find thirds. In a discussion, Alan showed Erik that no rod could be one third of the train that he had built. He said that the orange rod was ten white rods long, implying that the train was more than thirty white rods in length, and therefore none of the rods, the largest of which was the orange rod, could be called one third of the train. Erik agreed.
Erik then checked what Andrew and Jessica were building. Andrew had built a train of two oranges and a red rod followed by another two oranges and a red rod. Erik used Alan’s argument, telling Andrew that his train was too big and that it couldn’t be divided into anything. Andrew countered Erik’s argument by saying that if one could make a train to represent a whole, then one could make a train to represent a third or a quarter. Erik then left Andrew to join the researcher and Alan at David and Meredith’s table.

http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000067459

doi:10.7282/T3NV9GV1

The video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.