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DescriptionThe third of 6 clips focuses on the four 11th grade students as they map the numbers of pizza choices to the rows of Pascal’s Triangle and attempt to make sense of the addition rule with the...

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DescriptionIn the second clip, David and Meredith worked on building models to represent their solution to the problem: Which is larger, two thirds or three quarters, and by how much. David first built two...

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DescriptionIn this short clip, James explains to Robert B. Davis his solution to the problem: Which is larger, one fourth or one ninth, and by how much? After some questioning, he explains that the train (i.e.,...

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DescriptionIn the fourth clip Erik repeated the explanation of his model to the classroom teacher. His model consisted of a train of three orange and one dark green rod and lined up four blue rods. He lined up...

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DescriptionIn the last of five clips from a single class session, the researcher reviews with the students how to place whole numbers on a number line. The students are then asked to decide about the placement...

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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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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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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 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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Date Created1993

DescriptionThis is the third in a series of four clips from this session. The researcher, Carolyn Maher, asks the students where they would place the number “one” on the number line that Alan had made. The...