Reporting a Multiple-Select Item Without Masking a Misconception
An eighth-grade team writes a four-item quiz on linear functions after a unit on slope-intercept form. Item 3 is a multiple-select item in the Milestones format: 'Select all statements that are true for y = −2x + 5.' The options are (A) the graph has a slope of −2; (B) the graph passes through (0, 5); (C) the graph decreases from left to right; (D) the y-intercept is −2; (E) the graph passes through (2, 1). The correct selections are A, B, C, and E. Of 31 students, 24 selected A, B, C, and D; 9 selected only A, B, and C; and 17 selected E. At the data meeting one teacher proposes awarding half credit for three of four correct selections, while another argues the item should count only when all four are selected. The team must report item data to the principal and plan the opener for the next unit.
1. Recommend a scoring policy for Item 3 and justify it. Address what each policy would do to the team's picture of student understanding.
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Report the item as all-or-nothing for the mastery record, and keep partial-credit patterns as instructional notes rather than as points.
The reason is that the item measures one construct: distinguishing slope from y-intercept while checking several representations at once. The 24 students who added D did not make a random slip. They correctly found the slope and correctly described the decreasing graph, then attached the −2 coefficient to the intercept, which is a coherent but wrong rule. Under partial credit, that student earns three-quarters of the item and the class average suggests near-mastery of a skill the student does not have. The team would then enter the next unit, systems of equations, with a misconception intact and invisible.
All-or-nothing also produces honest item data for the principal: 7 of 31 correct is a low p-value, but it is a true p-value for the full construct. The teacher who wants partial credit is not wrong about fairness in the abstract, but fairness to the student means accurate information, not gentler numbers. If the team wants partial credit for practice or homework, keep it out of the grade that drives the reteach decision.
2. Design one follow-up item that would separate the slope and intercept misconception from a computation error, and state the decision rule you would use for reteaching.
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Follow-up item: 'A pool drains at a steady rate. After 2 minutes it holds 46 gallons; after 6 minutes it holds 34 gallons. Find the rate of change and the starting amount, then write the equation and explain in words what each number means in the pool.'
This item separates the two problems. A student with the slope-intercept confusion will likely write the rate as the y-intercept, or report the starting amount as the slope coefficient, and the written explanation exposes the reversal directly. A student who simply slipped on the multiple-select item will compute both quantities correctly here. Requiring the explanation in words matters, because a correct equation with a wrong description still reveals the misconception.
Decision rule: 24 of 31 students (about 77 percent) attached the coefficient to the intercept, so the default is whole-class reteach, not a pull-out group. Whole-class reteach is two 15-minute tasks: matching equations to graphs with intercepts that are visibly not equal to the coefficient, and a card sort labeling slope and intercept in context problems. If the follow-up shows 22 or more students correct with sound explanations, replace the reteach with a 10-minute opener and move on.