Central distractors in Force Concept Inventory data

The Force Concept Inventory was designed to poll the Newtonian conception of force. While there are many in-depth studies analyzing response data that look at the structure of the correct answers, we believe that the incorrect answers also carry revealing information about the students’ worldview. The inventory was originally designed so that the “distractors” in each question reflected commonly held misconceptions, and thus the rate at which students guess the correct answer is very low. Students select incorrect answers that correspond to the misconception that they hold and there are very few responses which appear obviously wrong to students. A side effect of this approach is that the incorrect responses reflect the non-Newtonian worldviews held by students. These non-Newtonian worldviews are coherent and robust, and this, at least in part, helps to explain why these misconceptions are so resistant to instruction. In this study we focus once more on the misconception data in Force Concept Inventory responses, particularly on the linkages between these misconceptions. We hypothesize that there are distinct groupings of distractor items formed by the strength of the association between these items. The two largest groupings are associated with the “impetus” world view in which the motion of an object is determined by the quantity of impetus which that object contains. We find that certain central items hold particularly important places in these groupings and also that individual groupings may be connected to each other by “connector” items. We finally suggest that, on the basis of this study, that these non-Newtonian worldviews might best be dismantled by addressing these key central and connector items.

Figure 1

The network of all FCI questions is shown. The strength of connection between questions is based on Cramér’s V statistics, with a minimal threshold of 0.05. The thicker the lines, the stronger the association between questions.

Figure 2

A small, undirected, nonweighted graph for demonstrating selected centrality measures. It is apparent that node 4 must score high on several centrality measures as it has the most connections. However, nodes 6 and 7 are also important as they form the single link connecting two subnetworks ($\{1,2,3,4,5,6\}$ and $\{7,8,9\}$) together. Their betweenness score should capture this property.

Figure 3

The network structure of factor 1 items is plotted in a circular distribution. The stronger the correlation the thicker the connecting line, and the colors black and blue represent positive and negative correlations, respectively. For sake of transparency, connections with absolute value less than 0.1 are omitted. While there are connections with strong correlation they only seem to form binary groups, e.g., 6A and 7A, rather than larger cliques. There are, perhaps, two items (10D and 30E), which could play some central role and provide cohesive force for the other items. Otherwise this circular graph seems to be connected in a balanced manner, i.e., lots of items are connected relatively weakly to lots of other items.

Figure 4

The network structure of factor 2 items is plotted in a circular distribution. The clockwise ordering of items represents their natural order in the inventory. The stronger the correlation the thicker the connecting line, while the colors black and blue express positive and negative correlations, respectively. For sake of transparency connections with absolute value less than 0.35 are omitted. Item 7D seems to be the central item as it is connected to several other items. Some items, e.g., 8D, seem to hang alone meaning that their connection to factor 2 is quite weak.

Figure 5

The network structure of all thirty correct, Newtonian items is plotted in a circular distribution. The clockwise ordering of items represents their natural order in the inventory. The stronger the correlation the thicker the connecting line. For sake of transparency, connections with absolute value less than 0.1 are omitted.