Testing alternative explanations for common responses to conceptual questions: An example in the context of center of mass

In physics education research it has been common to interpret student errors on conceptual questions in topic-specific ways, rather than in terms of general perceptual or reasoning difficulties. This paper examines two alternative accounts for responses to questions related to the concept of center of mass. In one account, difficulties are said to be perceptual in nature; in the other, difficulties are said to be tightly linked to the concepts in question. Hypotheses derived from the former perspective are tested in studies conducted among university students in introductory physics courses. The results do not provide strong support for the perceptual hypothesis; in fact, there is evidence that performance on perception tasks may be influenced by subjects’ ideas about the physical scenario. While the results do not provide general support for one perspective versus the other, the paper serves as an illustration of the type of investigation needed to develop the kind of rich representation of student thinking that will allow instructional resources to be most effectively targeted.

Figure 1

Figure used in the bat version of the mass comparison task. Students were told that the bat is balanced on the finger. They are asked (1) if the center of mass of the bat is to the left of, to the right of, or at point $P$ and (2) if the mass of the piece to the left of point $P$ is greater than, less than or equal to the mass to the right of point $P$. The bat is stylized in order to make it easier for students to gauge the location of the c.m. of each piece by eye.

Figure 2

A figure (Fig. 3) from Sattizahn et al. [11]. Subjects were shown a series of such shapes on a touch-screen device and asked to locate the center of gravity with a stylus. The original figure caption states that the red circle indicates the correct answer while the green circle is the average of all responses.

Figure 3

Figure used in the c.m. location task. Students were told that a bat has been cut into two pieces. They were asked (1) if the center of mass of the left piece is closest to point $A$, $B$, or $C$, and (2) if the center of mass of the right piece is to the left of, to the right of, or at point $X$. They were told that points $C$ and $X$ are the same distance from the break. In both cases, students were given the option “there is not enough information.”

Figure 4

Figure used in the shaded bar version of the mass comparison task. Students were told that the bar is made of two pieces of different material and that it is balanced on a frictionless pivot and will remain at rest when released. They were asked if the mass of the unshaded (left) piece is greater than, less than, or equal to the mass of the shaded (right) piece.

Figure 5

Figure used in the $T$-shaped object task. Dimensions are given on the diagram. Students were told that the density of the shaded part is twice that of the unshaded part. They were asked if the center of mass of the object is located to the left of, to the right of, or at point $R$.