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 second 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 linear functions. In responding to...
DescriptionIn the last of five clips from a follow-up interview about his participation in Informal Mathematics Learning (IML), an after-school enrichment program, Ariel, an 8th grade student in an urban middle...
DescriptionIn the sixth clip in a series of nine from the first of seven interviews focusing on Early Algebraic Ideas about the binomial expansion, researcher Carolyn Maher asks Stephanie to justify her...
DescriptionIn the sixth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie uses her numerical...
DescriptionIn the fifth clip in a series of seven from the third of seven interviews in which 8th grader Stephanie explores Early Algebraic Ideas about Binomial Expansion, Stephanie is asked by researcher...
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 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 the fourth of six clips, the four students develop the structural isomorphism between adding an additional pizza topping choice and the addition rule for successive rows of Pascal’s Triangle and...
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...