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 this final clip, an exuberant Stephanie presents her understanding of the “doubling rule” to the group of students ( Matt, Michelle I, Michelle R, Milin and Robert) who assembled around a...
DescriptionThis is the fifth of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) have been discussing Pascal’s Triangle. The researcher rewrites row 3 of Pascal’s...
DescriptionIn the final clip the students generalize the exponential structure of the Pizza Problem and describe the relationship between two consecutive rows of Pascal’s Triangle with reference both to the...
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...
DescriptionIn the second clip in a series of eleven from the sixth of seven interviews, 8th grader Stephanie continues her exploration of early algebraic ideas about binomial expansion with researchers Carolyn...
DescriptionThis is a raw footage video. On February 26, 1993 fifth graders, Stephanie, Michelle, Milin and their classmates, worked on the Guess My Tower task in a class session, about a year after the “Gang...
DescriptionIn the first of five clips, Milin and Michelle I, two fifth grade students are attempting to find all possible towers three cubes tall when selecting from two colors as the sample space for Question 1...
DescriptionIn the 2nd of 5 clips, Stephanie and Matt, two fifth grade students are attempting to find all possible towers four cubes tall when selecting from two colors as the sample space for Question 2 of the...
DescriptionIn this full-session, raw footage video, students have come to school in the evening for a night session. The group, made up of Jeff, Michael and Romina begin discussing the coefficients of the...