The bimodal test and the retake demand

Start with the shape of the distribution, not the mean. A bimodal split that falls exactly along section lines is almost never an ability finding. It is a finding about opportunity to learn.

• Opportunity to learn: the afternoon section lost two lessons and was never given them back. The morning group had 100% of the teaching; the afternoon group had roughly 90%. The test did not control for that.
• Construct and curriculum alignment: Section C required three-step calculations practised only in end-of-chapter exercises, which many students never reach independently. If the test samples material the taught curriculum barely covered, the score measures exposure as much as understanding.
• Marking reliability: 90 scripts in one evening produces fatigue effects, halo effects from handwriting, and inconsistent application of a mark scheme that may not exist in written form. A single total score with no rubric is not auditable.
• Feedback timing: returned after 11 days, with no comments, the test cannot function as feedback. It functions as a verdict.

The student factor cannot be ruled in until the other three are ruled out. That is the order of the investigation.

Decide on validity grounds, not leniency grounds. An assessment that a group had unequal opportunity to prepare for, that sampled beyond the taught scope, and that was marked without a rubric is not a defensible measure. Re-testing restores the measure; it does not lower the standard.

The decision:

• Re-teach the two lost lessons and the three-step calculation to the afternoon section first. No retake before re-teaching - otherwise you are re-testing the same gap.
• Retake covers Section C only, same mark scheme, within ten school days.
• Recorded as 'most recent, original retained'. Be explicit that this is a school decision, written down, because the next parent will ask.
• Blind re-mark a sample of 15 scripts against a written rubric and check the variance before any grade is published. If variance is high, re-mark all 90.
• Offer the same retake route to any student in any section below 50, so the policy is not a favour to one family.

To the parent: show the diagnosis, not the concession. 'The section lost lessons that were never made up. We are re-teaching and then re-testing. Your daughter is not being given a pass; she is being given a fair test.'

To the colleague: the fairness argument cuts the other way - a test whose conditions differed between groups is unfair to the students who revised, because their score is not comparable to a score earned under different conditions.

Write the mark scheme before the test is written, with the acceptable methods for Section C named. A rubric is what makes 90 scripts markable by more than one person.

Change the turnaround, not just the effort. Eleven days is long enough that students have stopped thinking about the work. Target five working days. Achieve it by marking less per script, not by marking faster: two specific comments against the success criteria, plus a whole-class feedback sheet that names the three common errors with a worked correction.

Build feedforward time into the next lesson. Fifteen minutes where students act on the comments - redo the flagged question, correct the calculation, write the next step. Feedback without that time is decoration.

Use live marking during independent practice for the six or seven students whose errors are predictable, so the script marked in the evening is smaller and later.

Moderate. One sample of five scripts per teacher, marked blind, at the start of each unit. Cheaper than re-marking 90, and it catches drift before it reaches a report card. Then write the assessment policy, because a system that depends on individual heroism will fail again in the same week next term.