DescriptionAfter the students have worked on the Towers Problem in the Towers series, researcher Alice Alston facilitates a group sharing session. She begins by asking how many towers the students have found and receives a reply of sixteen. She then asks if anyone has found a different number of towers, but no one reports having found a different number. The researcher asks if anyone thinks “there might have been seventeen” to which some students answer in the affirmative. The researcher then asks how they decided that there were not more than sixteen. Jamie explains that “if you got seventeen then it must have been that you would have had a match”. Milin shares that every tower has a “match”, a tower with the opposite color pattern. Jamie shows how the towers on her large recording sheet are arranged to display each tower and its opposite following it. The researcher asks if anyone used any other types of patterns. Dana answers that she created patterns with the different color cubes, apparently referring to patterns created within towers. Then the researcher asks Jeff and Brian if they thought there might be seventeen towers, and Brian replies that they thought there would be seventeen but that they “gave up” when then realized that the seventeenth tower was always a duplicate of one that they had found already. The researcher continues the discussion by raising the question of whether the number of towers they found is odd or even and whether or not that fact is important. Jamie says that since every tower has an opposite, they got sixteen towers, but without opposites they would only have had eight.
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Related Publication Type: Related publication Label: Ed.D. dissertation references the video footage that includes Towers Group Sharing, Clip 1 of 6: Discussing the solution and patterns related to it Date: 1992 Author: Martino, Amy Marie (Rutgers, the State University of New Jersey)
Name: Elementary students' construction of mathematical knowledge : analysis by profile Reference: QA.M386 1992
Source Title: B51, Towers Group Sharing (presentation view), Grade 3, October 11, 1990, raw footage. Identifier: B51-19901011-KNWH-PV-CLASS-GR3-CMB-T4T-RAW