5.3 Force Law Domain
Force Law questions on the final version of the NGCI test the common misapplications of the scientific model
documented in Williamson and Willoughby (2012) while also gauging students’ understanding of the
proportionality of both mass and distance in determining gravitational force. For example, Table 6 shows how
Item 4 on the final version of the NGCI probes student understanding of the role of distance by asking students to
implement proportional reasoning when thinking about a changing Earth-Moon distance. Student interviews
indicate that the most effective distractor is that which represents the misconception that distance, rather than
distance squared, is inversely related to gravitational force. Table 6 also shows how the development of this
question was informed by earlier versions, which, as evidenced by Figures 1 and 2, led to an item of appropriate
difficulty and good discriminatory power. One can see that Version 2 of the question used a proportionality
factor of two, and Version 1 used a factor of ten. In Version 1, the factor of ten was overly large. It was originally
5.3 Force Law Domain
Force Law questions on the final version of the NGCI test the common misapplications of the scientific model
documented in Williamson and Willoughby (2012) while also gauging students’ understanding of the
proportionality of both mass and distance in determining gravitational force. For example, Table 6 shows how
Item 4 on the final version of the NGCI probes student understanding of the role of distance by asking students to
implement proportional reasoning when thinking about a changing Earth-Moon distance. Student interviews
indicate that the most effective distractor is that which represents the misconception that distance, rather than
distance squared, is inversely related to gravitational force. Table 6 also shows how the development of this
question was informed by earlier versions, which, as evidenced by Figures 1 and 2, led to an item of appropriate
difficulty and good discriminatory power. One can see that Version 2 of the question used a proportionality
factor of two, and Version 1 used a factor of ten. In Version 1, the factor of ten was overly large. It was originally
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