Private Universe Project Video 6: Problems and Possiblities

The final video demonstrated a 2 week summer institute for 18 students who all participated in the Rutgers study in one way or another. They were provided a problem called the Cat Walk. This consisted of a cat moving in a series of 24 pictures. The pictures had a background so the distance of the cat could be measured and the students were provided a time. They were then tasked with trying to identify the speed of the cat in the 10Th frame and the 20Th frame. Their methods for solving this problem as in previous videos slowly developed and improved as they went. They were able to present their ideas to their peers and the researchers allowing for student discovery and collaboration. The video demonstrated how students need opportunity to build personal representations in order to understand the standard scientific representations and that mathematical knowledge grows from personal and real life experiences. The students were all able to graph their time and velocity of the movement of the cat and they did this in several ways. They were also able to take these graphs and representations and put them into a real life experience. They expanded the distances first to 10 times and then to 50 times the original distance. This allowed them to visualize, feel and live the actual accelerations of the cat. They were then able to identify the motions of the cat and where it was at certain points and relate it to their graphs. They were then given a scenario that a CEO of a company had the opportunity to bet on the speed of the cat in the 10Th frame. The students were to tell the CEO if he should place the bet. The three groups presented and decided that the CEO should not place a bet on this because their were to many variables. This final video really demonstrated how their mathematical problem solving abilities had grown and as a student stated in the video "The Rutgers way the students present ideas and get to show the others what they discovered and a regular class would never do that."