Item Analysis: Acceleration at the Top of a Toss
A district midterm includes this multiple-choice item: 'A ball is thrown straight upward and moves freely. At the highest point of its flight, what is the ball's acceleration? A) zero B) 9.8 m/s² downward C) 9.8 m/s² upward D) changing from upward to downward.' In a class of 28, 17 students choose A, 6 choose B, 3 choose C, and 2 choose D. The item's discrimination index is 0.05. In think-aloud interviews, students who choose A say 'at the top it stops, so acceleration is zero'; students who choose C say 'gravity acts upward on the way up.' The department requires items aligned to a standard on net force and acceleration and wants to keep the item if possible. The next unit is forces and Newton's laws. The teacher has 10 minutes of class time for a response.
1. Interpret the distractor distribution and discrimination index. What does this pattern suggest about student thinking and about the item?
Read the worked answer
The distribution is diagnostic. If students understood that only gravity acts after release, B would dominate. Instead, 17 of 28 choose A. The interviews show a velocity–acceleration conflation: students infer zero acceleration from zero velocity at the apex. The 3 students choosing C reveal an 'upward force on the way up' model, and D treats acceleration as changing direction rather than as a constant downward vector.
The discrimination index of 0.05 is low, meaning high and low scorers are almost equally likely to choose A. That does not necessarily make the item invalid; a widespread misconception can depress discrimination. But it does mean the item is currently providing little information about who can apply Newton's second law. The item is aligned to the net-force/acceleration standard only if students must reason from forces, not recall a fact about the top of flight.
2. Decide whether to reteach, revise the item, or both, and justify with the standard. If you revise, write a revised item or scaffold.
Read the worked answer
Reteach first, then keep and strengthen the item. The misconception is central to the standard, not an item flaw to be papered over. The item should not be discarded simply because it produced a low discrimination index; that would remove evidence of a real instructional need. However, the wording can be improved: state 'ignore air resistance' explicitly, and add a second tier that asks students to justify the acceleration with a force diagram or v-t graph.
A revised two-part item: 'A ball is thrown straight upward. At the highest point, (a) its velocity is ___ and (b) its acceleration is ___.' Students select from zero, 9.8 m/s² down, 9.8 m/s² up for each, then draw the free-body diagram at the apex. This separates the velocity and acceleration ideas and requires application rather than recall.
3. Design a 10-minute instructional move that uses the item's data and a v-t graph to confront the misconception.
Read the worked answer
Use a 10-minute v-t graph confrontation. Project a velocity–time graph for a ball tossed upward: a straight line with slope −9.8 m/s² crossing zero at the apex. Ask students to compute the slope between t = 0.9 s and t = 1.1 s around the apex, then between 1.0 s and 1.1 s. The slope remains −9.8 m/s² even though v = 0 at the instant. Connect to the free-body diagram: the only force is weight, mg downward, at every point, so a = F_net/m = g downward, including at the top.
Then show a slow-motion toss or a spark-tape interval pattern and have students mark the apex. Exit ticket: 'At the top, v = ___, a = ___; explain in one sentence.' Use the item's own distractor A as the discussion prompt, not as a gotcha.