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*Indirect reasoning*in Subject11

DescriptionResearcher Carolyn Maher leads a whole class discussion after the students' exploration of the problem: Which is larger, one fourth or one ninth, and by how much? Several students described their...

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DescriptionIn the third clip David, Meredith, Erik, and Alan worked to build models on the floor using rods. David built a model to test his conjecture, while Erik continued working on the thirty-six centimeter...

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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...

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Date Created1993

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...

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TitleBuilding large models to show equivalence, an exploration, Clip 1 of 4: Is there a larger model?

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...

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Date Created1993

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...

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DescriptionIn the fourth clip from this classroom session, researcher Carolyn Maher led a whole class discussion. She told the class that she gave each of the two adults who were in the room half a chocolate bar...

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TitleBuilding large models to show equivalence, a generalization, Clip 1 of 3: Finding the smallest model

DescriptionAt the start of the session, researcher Carolyn Maher asked the students if they remember working on comparing two thirds and three quarters. She mentioned that she had seen students build more than...

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DescriptionIn the fifth clip, researcher Carolyn Maher called the class together. At the overhead, Erin, Jackie, and Jessica had built the six and twelve centimeter models. The researcher asked the class to...

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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...