Figure 1

Trace lines for question 13. From this plot it can be seen that option D is the correct response. The most common incorrect response is dependent on which part of ability space is being considered. The item parameters used to make this plot were taken from Table 3 in the Appendix. Below the figure, please find question 13 and the response options that correspond to the trace lines. FCI 13) A boy throws a steel ball straight up. Consider the motion of the ball only after it has left the boy’s hand but before it touches the ground, and assume that forces exerted by the air are negligible. For these conditions, the force(s) acting on the ball is (are):

a downward force of gravity along with a steadily decreasing upward force.

a steadily decreasing upward force from the moment it leaves the boy’s hand until it reaches its highest point; on the way down there is a steadily increasing downward force of gravity as the object gets closer to earth.

an almost constant downward force of gravity along with an upwards force that steadily decreases until the ball reaches its highest point; on the way down there is only a constant downward force of gravity.

an almost constant downward force of gravity only.

none of the above. The ball falls back to ground because of its natural tendency to rest on the surface of the earth.

Figure 2

FCI question 14 [1]. A plane travels to the right with a velocity of $\overrightarrow{v}$ and releases a bowling ball, which it was carrying. Options (A)–(E) indicate potential paths the bowling ball could take while it fall from the plane. The proposed Newtonian ordering for this question is given as $\mathrm{E}<\mathrm{A}<\mathrm{B}<\mathrm{C}<\mathrm{D}$.

Figure 3

FCI Question 15 [1]. A car is pushing on a truck and both accelerate to the right. This questions asks students about how the force from the car on the truck relates to the force from the truck on the car. The proposed Newtonian ordering for this question is given as $\mathrm{E}<\mathrm{D}<\mathrm{B}<\mathrm{C}<\mathrm{A}$.

the amount of force with which the car pushes on the truck is equal to that with which the truck pushes back on the car.

the amount of force with which the car pushes on the truck is smaller than that with which the truck pushes back on the car.

the amount of force with which the car pushes on the truck is greater than that with which the truck pushes back on the car.

the car’s engine is running so the car pushes against the truck, but the truck’s engine is not running so the truck cannot push back against the car. The truck is pushed forward simply because it is in the way of the car.

neither the car nor the truck exert any force on the other. The truck is pushed forward simply because it is in the way of the car.

Figure 4

FCI Question 17 [1]. An elevator is lifted up at a constant speed by a cable. This question asks the students about how the force exerted by the cable on the elevator is related to the force of gravity on the elevator and/or the force due to the air. The proposed Newtonian ordering for this question is given as $\mathrm{C}<\mathrm{E}=\mathrm{D}<\mathrm{A}<\mathrm{B}$.

the upward force by the cable is greater than the downward force of gravity.

the upward force by the cable is equal to the downward force of gravity.

the upward force by the cable is smaller than the downward force of gravity.

the upward force by the cable is greater than the sum of the downward force of gravity and a downward force due to the air.

none of the above. (The elevator goes up because the cable is being shortened, not because an upward force is exerted on the elevator by the cable).

Figure 5

Trace lines for question 17. From this plot it can be seen that option B is the correct response, with option A being a strong distractor. The item parameters used to make this plot were taken from Table 3 in the Appendix.

Figure 6

Plots comparing the results for the FCI using dichotomous scoring and the proposed partial credit scoring. (a),(b) Partial credit total scores vs the dichotomous total scores for students on the FCI pretest and post-test, respectively. (c),(d) Partial credit’s vs the dichotomous Hake gain and normalized gains, respectively. The red lines in all of the plots are a slope equals 1 line to be used for reference.

Figure 7

Average item scores for questions 1–15 pre and post-test. Averages from dichotomous scoring are in red and the partial credit scoring item averages are in blue.

Figure 8

Average item scores for questions 16–30 pre and post-test. Averages from dichotomous scoring are in red and the partial credit scoring item averages are in blue.