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*Indirect reasoning*in Subject1

DescriptionDuring this clip, the students discuss a task that had been posed by Erik: If I call the blue rod one, what rod will I call one half? A lively discussion centering on the definition of one half...

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DescriptionAmy Martino leads a whole class discussion during which they talk about ways of writing number sentences for two problems: 1) How many one sixths are in one? and 2) How many one twelfths are in one?...

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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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DescriptionResearcher Amy Martino posed two related tasks to the students that highlighted the difference between additive and multiplicative reasoning. First, she asked the students: If we call the orange...

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DescriptionResearcher Amy Martino led a whole class discussion that focused on solutions to the task: I'm going to call the orange and light green together one…Can you find a rod that has the number name one...

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DescriptionResearcher Amy Martino posed two related tasks to the students. In this clip, the students work on designing a rod that can be called one half when the blue rod is called one. Erik and Alan discuss...

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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...

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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...

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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...

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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...