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PUP Math Towers of Hanoi
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Abstract:
This video comes from The Private Universe Project in Mathematics and includes excerpts from interviews as well as narrative voice-over, interspersed with footage of students engaged with problem solving. A class of Kenilworth sixth graders investigate the Tower of Hanoi problem that was posed by researcher, Robert B. Davis. He tells the students about an order of monks in the city of Hanoi, who were concerned about when the world was going to end, and so they made a puzzle like this which has 100 disks in it [illustrates a model of the discs]. Davis explains how the monks were very focused on working to solve that puzzle. When they have it done, that is supposed to be when the world ends. The students were challenged to find out when the world would end and began by moving discs of the tower model according to the rules described and clarified by the researcher. The students speculate as to the outcome and then explore cases for the number of moves required for towers built with certain number of rings. They record, share and check their findings. Inserted in the clip is a description of the solution to the problem by mathematician Fern Hunt. The episode returns to show the students' problem solving. Working from simpler cases, they notice a pattern for the number of moves up to five rings that is shared by Michelle as 31; for six rings, by Brian as 63; and for 10 rings by Ankur as 1023. The students offer conjecture for the number of moves for 100 rings and offer as a conjecture 2 to the 100th power as a solution for the number of moves. In dealing with larger moves, the students struggle with the algebra of exponents. Inserted in the clip is an interview that took place seven years later. It was conducted by mathematician Gary Davis and former student, Matt, who viewed the video, revisited the problem, and reflected on the students’ problem solving. Matt comments on the remainder of the video that shows the exploration of the students guided by researcher Robert B. Davis. ; Transcript is also available. ; Smithsonian Astrophysical Observatory. (1993).PUP Math Towers of Hanoi [video]. ; Resource vailable in QuickTime and Flash digital video formats.
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Keyword:
6; 6-8; Algebra; Classroom; Communication; Connections; Considering a simpler problem; Critical thinking in children--New Jersey--Case studies; Direct reasoning; Function tables; Learning; Manipulatives (Education)--Case studies; Mathematics education; Mixed; Number and operations; Physical models; Problem solving; Psychology of--Case studies; Public school; Reasoning and proof; Recognizing a pattern; Recursive reasoning; Representation; Representations; Student view; Teacher view; Towers of Hanoi; Towers of Hanoi (game); Work view
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URL: http://hdl.rutgers.edu/1782.1/rucore00000001201.Video.000062052
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