Multiple-Choice Distractors That Diagnose Misconceptions, Not Just Wrong Answers

Build multiple-choice distractors from mistakes you can investigate with a written step or a second question. A wrong option can be linked to a misconception, a skipped step or an overgeneralised rule. But the selected option is evidence to investigate, not a mind-reading device: a learner might have guessed or used an unexpected route to the same number.

This guide focuses on what to do after drafting a clear question. It uses a fractions example to show how to source distractors from real work, map each choice to a possible explanation, read class patterns and revise the item. For a broader stem-and-option checklist, see our guide to writing good multiple-choice questions. The purpose here is a better teaching decision after the quiz.

Start with written errors before creating options

Suppose your class is learning to add unlike fractions. Collect a few anonymised solutions to 1/2 + 1/4 from practice work. Some students may write 2/6 by adding numerators and denominators. Others may write 2/4, perhaps by converting the half incorrectly. The correct sum is 3/4. These observed answers give you a better starting point than inventing two random fractions that merely look different.

Write down the reasoning you think each answer may represent, but keep it tentative. 2/6 is consistent with adding both parts directly. 2/4 could mean several things: a faulty common denominator, copying the denominator, or guessing. If you have not actually seen that error, do not present your theory as a fact about your students. The goal is to build a question that separates likely misunderstandings enough to guide a follow-up.

A study developing MCQ distractors from learner responses used observed misconceptions as the basis for plausible wrong alternatives. Its assessment context is not your classroom, so it does not validate the particular fractions above. It supports the practical direction: start with errors learners make, then test whether those options are informative in your own setting.

This table is a hypothesis sheet, not an answer key for students. Keep it beside the item when you interpret results. You may decide to replace 2/4 after hearing students’ explanations because it is too hard to map to one useful error.

Keep the stem and options fair

For the diagnostic item above, use: “What is 1/2 + 1/4? Choose one answer, then show how you found the denominator.” Do not add “in simplest form” to the options 3/4, 2/6 and 2/4: only the correct option is simplified, so that instruction would create an unintended clue. If simplifying is the target, use a separate question with fair options or ask for a written answer.

A separate ambiguity arises if you display both 6/8 and 3/4: they have the same value, so a single-choice question asking only for the sum would have two defensible answers. Remove the equivalent duplicate rather than silently rejecting a correct value. For formal assessment, pilot the complete item with a colleague who cannot see your key.

Give options the same format. Do not make the correct answer the only simplified fraction while wrong choices use awkward mixed numbers. Avoid “none of the above” as a shortcut: it can turn the task into a test of elimination. Add another option only when it represents an error you can identify and address. Three sound choices are preferable to five with two impossible fillers.

A study of nonfunctioning distractors and item-writing flaws describes clues such as grammatical mismatch and an unusually long correct answer in medical-education tests. The percentages from that setting should not become a rule for younger learners. Use the findings as a reminder to remove unintentional hints before you trust the results.

Add one explanation prompt to test the hypothesis

After a student selects a fraction, ask a brief open question: “Show the step that gave you that denominator.” This does not need to become a long proof. A few words or a drawing can reveal whether 2/6 came from the error you expected. When time is short, ask a sample of students to explain their reasoning orally or use a second, carefully changed item. Do not label someone as having a persistent misconception based on one click.

The Education Endowment Foundation’s feedback evidence stresses that teachers need to understand the gap and decide how learners can move forward. In this example, that means choosing a representation or worked example that targets the actual confusion. A score report without that response is an incomplete feedback loop.

If the option 2/6 is common, compare 1/2 and 1/4 on strips of the same length. Ask students to point to one half as two quarters before adding. If 2/4 is common but explanations vary, do not teach a single presumed mistake to everyone; show two worked solutions and let students diagnose which step failed. If nearly all answer correctly, introduce a transfer item such as 1/3 + 1/6 to see whether the method generalises.

Read class patterns carefully

Look at results by question and by option, not only the average score. A distractor selected by no one may have been too easy to eliminate, or the class may genuinely have mastered the idea. A distractor selected by many may reveal a real misunderstanding, but it may also signal a broken stem or answer key. Check the item first, then interpret the learners. One small class is not enough to set a universal statistical cut-off.

Compare the response pattern with your hypothesis sheet. If 2/4 is chosen by learners who explain different methods, change or retire that option. If the explanation prompt reveals that some correct answers were guessed, add an application question before concluding mastery. Our diagnostic quiz guide explains how to use these patterns at the start of a unit; the same care applies after teaching.

In Skolina, build a short quiz with the closed item and a separate open response, then share it by link or QR code. Closed choices can be marked automatically after you verify the key. Read the open explanations yourself. The question-bank workflow shows how to record the item, its version and the misconception it targets so it can be improved later. Check the current plan limits if you intend to keep multiple quiz versions active.

Worked response analysis: the same wrong fraction can hide different errors

Imagine a fictional class of 28: 15 select 3/4, seven select 2/6, four select 2/4 and two leave the item unanswered. That is 15 correct selections out of 26 submitted choices, or about 58%; it is 15 out of 28, about 54%, if the denominator includes the whole class. Neither percentage explains the wrong reasoning. Keep the two missing responses visible rather than silently counting them as a particular misconception.

Read a few written steps before deciding what to teach. The following are constructed responses, not results from a Skolina class.

This comparison changes the follow-up: the seven selections of 2/6 are a reason to investigate direct addition, while the four selections of 2/4 are not yet one teachable category. Where advanced per-question reporting is needed in Skolina, check Starter, Pro or eligible institution access on the plans page before the activity. A teacher-maintained tally can also support this small review; it is not an automatic analysis of written reasoning.

Check the correction with a new denominator pair

After modelling equal-sized parts, ask 1/3 + 1/6 without showing the first answer. The worked check is 1/3 = 2/6, so 2/6 + 1/6 = 3/6 = 1/2. Accept 3/6 if the question asks for the value and does not require simplification. Direct addition would give 2/9; ask the learner to compare that result with the first addend, since adding a positive fraction should increase it. One successful follow-up supports a next teaching decision; it does not establish that the misconception has disappeared in every context.

Make a teaching decision and revise the item

Before publishing, write a simple if-then plan. If many choose 2/6, model equal-sized parts; if they choose 2/4 for different reasons, inspect a few written steps; if most succeed, move to a new denominator pair. These are decisions for a specific class, not claims that a certain percentage always demands reteaching. After the follow-up, ask a new question to check whether the explanation helped.

Then edit the item itself. Keep a distractor only if it remains clearly wrong, plausible and informative. Record why you changed it, and correct any live quiz that contains an incorrect key. If an AI tool drafted the options, treat them as unverified suggestions: polished wording does not prove they reflect your students’ actual errors.

To test the method, create a Skolina teacher account, start with one question from your learners’ recent work and attach a one-sentence explanation prompt. Use the explanations to choose the next example and revise any option that produces ambiguous evidence.