A Unit Test That Most of the Class Fails
Mr. Lindqvist gives a 25-question multiple-choice unit test on linear equations to his 9th-grade algebra class. The class average is 58%, and 14 of 30 students score below 60%. Item analysis shows that Questions 4, 9, and 17 were missed by more than 80% of students. Question 4 asks students to solve an equation with variables on both sides; Question 9 uses the phrase "find the value of x when the expression is undefined"; Question 17 requires interpreting a graph of a line and identifying its slope from a context. In class, Mr. Lindqvist had taught variables on both sides for two days and had used graphing mainly as a check. Several students tell him the test was "unfair." He has one week before the next unit begins and is deciding whether to curve the scores, reteach, or move on.
1. Distinguish between a test-design problem and an instruction problem in this scenario, using the item data.
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The item data suggest both, and they require different responses.
Likely test-design problems: Question 9 is missed by over 80% of students and uses the phrase "undefined" in a way that may not match the vocabulary students were taught. High miss rates concentrated on a single oddly worded item often indicate a construct-irrelevant barrier -- students may know the mathematics but not the phrasing. That is a validity problem in the item, not evidence of poor learning.
Likely instruction problems: Questions 4 and 17 were missed by most students and correspond to content the teacher describes as lightly covered -- two days on variables on both sides and graphing used mainly as a check. If instruction allocated little time and practice to these skills, the low scores reflect an opportunity-to-learn gap.
What the data do not support: concluding the class is simply weak, or that the test was uniformly unfair. A blanket curve would erase the distinction between items that were badly written and content that was under-taught.
2. Recommend a course of action for the coming week and justify each element.
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A defensible plan combines several moves rather than choosing one:
- Audit the items before assigning blame. Have a colleague or reread Questions 9 and 17 against the taught vocabulary and the standard. If an item tested untaught phrasing or an untaught representation, revise or drop it and rescore. This is a validity correction, not a favor.
- Reteach the under-taught skills, not the whole test. Use the item data to target variables on both sides and slope interpretation from context. A full reteach of the unit wastes time on content students already know.
- Do not apply a flat curve. A curve applied to all students masks which items were flawed and removes the information the teacher needs. If any adjustment is warranted, base it on the rescored, revised items.
- Build in a reassessment opportunity on the targeted skills so the original low scores are not the final word on those objectives.
- Change the instructional plan for the next unit -- more guided practice and earlier formative checks on multi-step equations and graph interpretation -- so the same gap does not recur.
Justification: the response should follow the evidence. Where the evidence points to item problems, fix the instrument; where it points to instruction, fix instruction; and preserve the assessment's usefulness as information rather than converting it into a negotiation over points.
3. Students say the test was unfair. How should Mr. Lindqvist respond in a way that is honest about the data without undermining the assessment?
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He should neither dismiss the complaint nor simply agree. An honest response separates the parts: "Part of your concern is justified -- a couple of questions used wording we did not practice, and I am reviewing those. Part of the result reflects that we did not spend enough time on two skills, and that is on me, so we will reteach them. And part of it reflects skills you will need to demonstrate, so we will reassess those directly."
This preserves the assessment's credibility because the teacher is modeling that evidence drives decisions, not student sentiment. It also avoids two failure modes: defending every item as if tests are infallible, and capitulating by curving everything, which teaches students that a low score is grounds for renegotiation rather than information about what to learn next.