Private Universe Project in Mathematics: Thinking Like a Mathematician video 4

This video introduced a mathematician who demonstrated some of the real world uses for her skills. I also liked that she did not really enjoy mathematics until she entered the 9Th grade (Algebra) and the abstract concepts pulled her in.
The video then went on to classroom instruction and the students were introduced to the Towers of Hanoi. They began problem solving and were attempting to figure out how many moves it would take for 100 discs. They began small and worked up from a few discs to more and more discs. They began to identify patterns and this was the key for them to solve the problem because they were able to use the patterns to solve the problem. After figuring out how many moves it would take for 100 discs they were then tasked with determining how many seconds and how many years it would take to accomplish that task. Their ability to come up with and identify the patterns was pretty impressive and the students figured out it would take about 2 billion years to move 100 discs.
Next the video cut to a high school teacher and her methods of instructing students. She "encouraged her students to think." She did not force feed students answers but allowed them to investigate and problem solve. She also demonstrated to her students that it was acceptable to have different strategies to solve problems. She developed a community of students who accepted each others methods and strategies.
Finally, the video went back to the original core of students and demonstrated how they went back to previous problems and expanded upon them and how their strategies used to solve these problems evolved.