DescriptionIn the sixth clip in a series of seven from the seventh of seven interviews, 8th grader Stephanie first revisits her investigation of the number of duplicates that would be produced when building...
DescriptionIn the second of 6 clips, the four 11th grade students generate an exhaustive list of pizza options choosing from 4 toppings. They recognize that the 16 choices correspond to the fourth row of...
DescriptionThis clip is the first of six featuring four grade 11 students, Robert, Stephanie, Shelly, and Amy Lynn, as they construct and justify solutions to the Pizza Problem. This clip focuses on Stephanie...
DescriptionIn this fifth of six clips, four 11th grade students reconsider Pascal's Triangle as it relates to the Pizza Problem and connect this problem with the Towers Problem. As the students summarize their...
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...
DescriptionIn clip 4 of 5, fifth grade student Matt shares his understanding of Milin’s inductive argument with Robert and Michelle R. who, up to this point, found twelve, four-tall towers. Stephanie...
DescriptionIn the first of seven clips from an after-school enrichment session in an urban middle school, two 7th grade boys, Ariel and James, are exploring ideas about functions. Researcher John Francisco...
DescriptionIn the final clip of the series of seven from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, revisits his method for solving a specific example of the Ladder...
DescriptionIn the fifth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues his work on the Ladder Problem. Researcher John Francisco challenges...
DescriptionIn the fourth of seven clips from an after-school enrichment session in an urban middle school, Ariel, a 7th grade boy, continues his exploration of ideas about linear functions. Researcher John...