### Developing conceptual understanding of instantaneous change while utilizing physical knowledge in the solution of the catwalk problem.

PurposeLesson activity
DescriptionDuring a two-week Summer Institute, occurring after the completion of 11th grade, a group of students work together to solve the Catwalk Problem. From a sequence of 24 pictures of a cat in motion, students were challenged to find the speed of the cat in frame 10 and frame 20. “The pictures, photographed by E. Muybridge (1830-1904), were taken in time intervals of 0.031 seconds against a backdrop of 5-centimeter lines, where every 10th line was heavy” (Halien, 2011, p. 1-2).

In this analytic, we focus on the physical knowledge acquired during solution process of the Catwalk Problem. Physical knowledge in the context of the Catwalk is defined as “the motion of the cat in pictures and the perceived motion of the cat as recreated by the students” (Halien, 2011, p.16). During the onset of the investigation, students interpret characteristics of the movement of the cat, to include the total elapsed time, total distance the cat traveled and speed of the cat between consecutive frames. As discussions continue between students, new representations of the cat’s movement emerge.

This new organization sparks not only conversations about the cat’s movement, but also a framework which expands into a larger scale model the students can physically experience. Consequently, the first attempt at creating a scaled model of the cat’s movement is 10 times larger than the actual distance traversed by the cat. The students travel through the model with the goal of stepping on each marked distance in sync with a steady beat. The students express that this model lacks physical information about the speed of the cat because the distances were too close for students to witness any drastic changes in velocity.

Therefore, several members of the class create a new line in the hallway that is 50 times the original distance the cat traveled between frames. The students mimic the process of the library line and adjust their perceptions of the movement of the cat. The students use physical knowledge acquired from the hallway line activity to correspond with previously generated graphical representations of the cat’s motion.

As the students work on answering questions posed by researchers in the Catwalk activity, the usage of physical knowledge appears in multiple instances. “The students discussed and discovered the motion of the cat in two different ways: First by discussing what they could interpret of the cat’s movements as observed in the photographs and second by what they experienced in the tape line experiments” (Halien, 2011, p.66). The students must make implications of movement that is not explicitly provided between frames.

The problem-solving sessions, which occurred in July of 1999, are part of Rutgers longitudinal study in Kenilworth, New Jersey. In 1989, the study began with a class of 18 first grade students. The students participating in this two-week Summer Institute at Brearley High School in Kenilworth were not limited to those who have been involved in the longitudinal study. The included students could have been part of the Kenilworth focus group or could have traveled to the institute from outside of the school district. (Halien, 2011)

The Catwalk Problem
Eadward Muybridge (1830-1904) was a photographer that developed a way of taking pictures at split second intervals. One of the animals that Mr. Muybridge captures on film was a cat in motion.

The 24 pictures were taken in time intervals of 0.031 seconds against a backdrop of 5-centimeter lines, every 10th line was heavy.
Based on information you gather from the photographs:
1. How fast is the cat moving in Frame 10?
2. How fast is the cat moving in Frame 20?

(Halien, 2011, p.1-2)

References

Halien, W.B. (2011) Tracing Students’ Understanding of Instantaneous Change (Unpublished Doctoral Dissertation), Rutgers, New Brunswick, NJ
Created on2019-07-28T14:38:44-0400
Published on2019-10-28T11:27:48-0400
Persistent URLhttps://doi.org/doi:10.7282/t3-2c25-h858