DescriptionIn the first of five clips, four twelfth grade students develop their initial strategies for approaching the Taxicab Problem. They determine the shortest distances to the three given points: A, B and...
DescriptionThis is the last of seven clips from the night session. The students (Ankur, Jeff, Michael, and Romina) explain to Brian, a late-comer, the meaning of Pascal’s Identity (the addition rule for...
DescriptionResearchers Carolyn Maher and John Francisco conduct a group interview with Romina and Jeff as second-year college students who have been participants in a long-term study on development of...
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...
DescriptionThe small group interview with 4 students (Jeff, Michelle, Milin, and Stephanie) lasted about an hour and occurred after the students worked in the classroom on building towers of height five...
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...
DescriptionThe small group interview with 4 students (Jeff, Michelle, Milin, and Stephanie) lasted about an hour and occurred after the students worked in the classroom on building towers of height five...
DescriptionIn the last of three clips in a first grade classroom, Jeff, Milin and Jamie begin by reading problem 4. Jeff, without referring to the stones or cubes, immediately states that Grandpa would have six...
DescriptionIn the first of three clips in a first grade classroom, teacher Angela Marinaro introduces the day's activity and distributes a packet of problems to each child. She first asks the students to...
DescriptionIn the second of three clips in a first grade classroom, Jeff, Milin and Jamie begin by reading problem 2. Jeff and Milin use Unifix cubes and Jamie counts out stones to model the problem. The two...