# DB5 - Collision? What Collision?

## Outline? What Outline?

I. The PDD - The Problem Decomposition Diagnostic

II. The Background - How the PDD was administered.

III. The Items - PDD items involving collisions.

IV. The Results - What the students did.

## I. The Problem Decomposition Diagnostic

The Problem Decomposition Diagnostic, or PDD, is an instrument being developed at the Ohio State University. It is intended to examine the ability of students to:

1. Break multi-part mechanics problems into sub-problems that they are better able to solve.
2. Identify student approaches to solving these sub-problems.
The PDD was administered to a number of small groups before being given to classes in Autumn 1998. The data presented in this talk concern only the first aspect of the test, specifically student ability to identify collision sub-problems.

## II. Background

During Autumn Quarter 1998 at The Ohio State Unversity, three groups of students were tested using the Problem Decomposition Diagnostic. All three were taking some version of PHYS 131, the introductory calculus-based mechanics course.

• "Regular" Calculus-based physics course: PHYS 131 (N = 52)
• Honors 131 for Physics Majors: PHYS H131 (N = 41)
• Honors 131 for Engineering Majors (Gateway): PHYS 131E (N = 93)
All students in H131 and 131E were tested. Due to scheduling constraints (specifically, finding time to administer both the PDD and the FCI), not all students in 131 were tested.

## III. The Items

Two items on the PDD were designed with collisions as part of them. The first was the "Pendulum Box Bash," where a pendulum swings down and strikes a box, which then slides along a table until stopped by friction. Students were presented with the simplified version in which the pendulum stops after hitting the box:

COLLISION ONE

The second item was a "Block Catcher" in which a block slid along a frictionless surface until it hit another block attached to a spring. The two blocks would stick together and the spring would be compressed:

COLLISION TWO

### Student Exposure To Items

131

The regular 131 students performed a lab using the Pendulum Box Bash setup seen in Collision One. They worked in groups to solve the problem, and had their work assessed by the lab instructor. They had no special exposure to a Block Catcher problem.

H131

Honors H131 students had no specific exposure to collisions in either context, Pendulum Box Bash or Block Catcher.

131E

Gateway 131E students had no specific exposure to either setup. However, they did receive treatment regarding internal energy conservation in collisions, using a variety of demos applied by Xueli Zou during Large Group meetings. Poster BK33 by Xueli Zou at the San Antonio meeting covered this treatment.

## Criteria For Success

Before scoring the students on performance, it was necessary to determine what constituted a correct response. The following criteria were established:

1. The student's test sheet must contain a response that indicates something was happening at the time of the collision. In other words, the student must identify a sub-problem that could potentially be the collision.
2. The student's classification of the sub-problem could not rule out the possibility that the student saw the sub-problem as a collision.
The second criterion turned out to be redundant in this case, as all students who met the first criterion also met the second. It is worth noting that this is a very lenient scoring scheme. The intention was to mark as wrong only those responses which were clearly wrong, beyond reasonable doubt. As a result the percentages which will be reported later in this paper are likely to be greater than the "real" percentage of the students who would have identified the collision. In addition, because many students would not have broken the problem up without being told to do so, there is an additional group of potential "false positives."

## IV. Results

 COLLISION ONE Class Percent Correct 131 40% H131 35% 131E 78% COLLISION TWO Class Percent Correct 131 19% H131 14% 131E 71%
As you can see, the regular and honors physics classes have virtually identical performance in both collisions. Oddly, performance overall was poorer on the obviously inelastic collision than on the partially elastic collision, a result that suggests further research is needed on student concepts of collisions.
Most dramatic, of course, is that a rather minor treatment (only about an hour of contact time or less) produced large improvements in student performance. One possibility is that once a student recognizes what's going on in a collision, they're more likely to recognize a collision as a nontrivial step.

## Concluding Remarks

In classes without specific instruction, students may not view collisions as important parts of a complex problem. This may lie in an assumption that kinetic energy is conserved.

Even limited treatment (see poster BK33) can be very effective in reducing student difficulty in recognizing the relevance of collisions.