Assessing the impact of representational and contextual problem features on student use of right-hand rules

Students in introductory physics struggle with vector algebra and these challenges are often associated with contextual and representational features of the problems. Performance on problems about cross product direction is particularly poor and some research suggests that this may be primarily due to misapplied right-hand rules. However, few studies have had the resolution to explore student use of right-hand rules in detail. This study reviews literature in several disciplines, including spatial cognition, to identify ten contextual and representational problem features that are most likely to influence performance on problems requiring a right-hand rule. Two quantitative measures of performance (correctness and response time) and two qualitative measures (methods used and type of errors made) were used to explore the impact of these problem features on student performance. Quantitative results are consistent with expectations from the literature, but reveal that some features (such as the type of reasoning required and the physical awkwardness of using a right-hand rule) have a greater impact than others (such as whether the vectors are placed together or separate). Additional insight is gained by the qualitative analysis, including identifying sources of difficulty not previously discussed in the literature and revealing that the use of supplemental methods, such as physically rotating the paper, can mitigate errors associated with certain features.

Figure 1

Overview of the problem features identified from the literature and used in this study as predictors of performance. Individual features are in light blue (single quotations in text), with the variations beneath in white (italics in text). The features are grouped into larger categories (dark blue) to facilitate discussion in the text. See Table 1 for the hypothesized impact of each feature on performance.

Figure 2

Examples of Nonphysics (row 1), Magnetic Field (row 2), and Magnetic Force (row 3) questions where the problem involves working Forward (column 1) and working Backward (columns 2 and 3). Problem statements for rows 2 and 3 have been abbreviated for space.

Figure 3

The same orientation, $(+\widehat{y})\times (-\widehat{x})=+\widehat{z}$, with the vectors Head to tail, Tail to tail, Together, and Separate.

Figure 4

All possible cross product combinations for on-axis, perpendicular vectors ($\overrightarrow{A}\times \overrightarrow{B}$). The green orientations were the five orientations with the lowest average ranking for physical awkwardness (Easy orientations) and the blue orientations were those with the highest average ranking for physical awkwardness (Awkward orientations).

Figure 5

Examples of physically awkward orientations in the $xy$ and non-$xy$ planes.

Figure 6

Examples of one orientation, $(+\widehat{y})\times (-\widehat{x})=+\widehat{z}$, with the vectors presented as Perpendicular and Nonperpendicular (with both acute and obtuse angles).

Figure 7

Examples of the variation in physics features. The ‘Sign’ of the charge, which was varied between the positive and negative charges in (a) and the current-carrying wires in (b). The ‘Shape’ of the current-carrying wire in (b) was also varied between straight and circular. Finally, the representation of magnetic ‘Field’ was varied between a vector or arrow representation and a bar magnet representation, shown in (c).

Figure 8

Graphical depiction of method codes and subcodes. Those in green are discussed in the text and in Table 5.

Figure 9

Graphical depiction of error codes and subcodes. Codes in green are discussed in the text and described in Table 6.

Figure 10

The number of RHR: Order errors by the type of reasoning required. Backward problems are separated by the type of answer required, i.e., $A$ means that the first vector in the cross product was required, $B$ means the second vector was required, and $q$ means that all vectors were provided and the sign of the charge was required.

Figure 11

A magnetic field problem that requires reasoning backward to find the first vector in the cross product.

Figure 12

An example problem where the given vectors are in the non-$xy$ plane.

Figure 13

Interaction of rotation and orientation: (a) fraction of RHR errors on physically easy and awkward problems with and without rotation; (b) fraction of RHR errors on problems in the $xy$ and non-$xy$ planes with and without rotation.