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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...
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...
TitleIntroducing fraction equivalence and an exploration of fraction comparison, Clip 3 of 4: Proportional Reasoning Continued
DescriptionThe students work on the task: If the orange rod is called fifty, what number name would I give the white rod? Sarah and Beth offer an answer immediately, and are questioned by researcher Amy Martino...
TitleIntroducing Fraction Equivalence and an Exploration of Fraction Comparison, Clip 2 of 4: An introduction to proportional reasoning.
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...
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?...
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...
TitleEarly algebra ideas about binomial expansion, Stephanie's interview seven of seven, Clip 7 of 7: Finding a general direct "rule" for the number of Unifix-cube towers, selecting from two colors, for any height.
DescriptionIn the final clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie responds to questions from researcher Carolyn Maher about problems that she and her classmates had...
TitleWord problems with addition and subtraction, Stephanie's group, Clip 9 of 9: Reasoning about the solution to problem 4 with the teacher
DescriptionIn the final clip of the series of nine in a first grade classroom, four children: Stephanie, Gerardo, Sean and Aaron, explain their reasoning about problems 4 of a set of 6 problems to their teacher,...
TitleNight session, Pascal's identity, clip 2 of 7: making sense of factorial notation and "why you multiply"
DescriptionThis is the second of seven clips from the night session. In it, Jeff, Michael, and Romina, along with Ankur (who has just arrived), use the analogy they call “people on a line” to investigate...