DescriptionThis video comes from The Private Universe Project in Mathematics and includes narrative voice-over and interview with researcher, Carolyn Maher interspersed with footage of students engaged with problem solving and discussion with researchers about their work on building towers with unifix cubes available as a math manipulative. It begins when the students are in 3rd grade where they work with a partner on the problem: How many different towers four blocks tall can you build when selecting from two colors? Students work on the task for about an hour on the first day. The task is challenging for them, and it pushes them to invent strategies and heuristics for problem solving. About five minute into the task, the students discover that they need to check for duplicates as they try to find all the possible combinations. This prompts them to develop ways of organizing the towers they build, as they try to convince themselves, their partners, and the researchers that they have found them all and have no duplicates. The researchers return the next day and ask the students to consider building towers three cubes tall selecting from two colors of cubes. They ask the students whether they think there will be more, the same amount, or fewer towers than when they are four cubes tall. Student responses may be surprising, and they are given opportuntity to explore whether or not their conjectures are correct, as well as discover reasons why. Next, the video shows the students as 4th graders working on the task to build towers five cubes tall selecting from two colors and convince others that they have found all possible combinations. As before, the challenging nature of the task gives students opportunity to spontaneously develop new strategies. Asking students to provide convincing arguments as justification for their solutions pushes them to move beyond trial and error. The researchers conduct interviews with students the following day to find out more about what they were thinking, and about the extent to which students are aware of their own thinking.
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: Workshops (web-based) utilize the video PUP Math Towers Publisher: Annenberg Learner Creator: Harvard-Smithsonian Center for Astrophysics Name: Private Universe Project in Mathematics Workshops Reference: http://www.learner.org/workshops/pupmath/about/overview.html