The Bimodal Test and the Pressure to Curve
Mr. Adjei teaches mathematics to a JHS 2 class of 48 learners in a public school. On the 50-item end-of-term test, 18 learners scored below 10, 20 scored between 35 and 45, and 10 scored between 20 and 30. The mean is 24 and the median is 27. School-based assessment marks are unusually high because most tasks were group work. The headteacher, under pressure from parents, asks Mr. Adjei to 'curve' the test so that no learner records a failing grade. Mr. Adjei has one week before results are due and can organise four 40-minute remedial sessions. He must also submit a class analysis to the district office. Some parents have threatened to complain if their children are labelled weak, while three learners in the low group have missed over 30 per cent of lessons.
1. Should Mr. Adjei curve the scores? Justify your decision using the distribution and principles of assessment.
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A blanket curve is not defensible here. The distribution is bimodal: a large low cluster below 10 and a high cluster between 35 and 45, with few learners in the middle. The mean of 24 is pulled downward by the low cluster, while the median of 27 is more representative of the typical learner. Curving every score upward would hide two different problems: basic skill gaps in the low group and possible ceiling effects or inflated school-based assessment in the high group. The unusually high SBA, built mainly on group work, weakens its comparability with the individual test. Before adjusting anything, Mr. Adjei should conduct item analysis to check whether low scores reflect faulty items, poor instructions, or genuine gaps. If the test is valid and reliable, scores should be reported against stated criteria, not forced into a normal curve. He may add a clearly documented retest opportunity after remediation, but should not label learners as failures or inflate marks to avoid parental complaints.
2. Design a defensible remediation and reporting plan for the one week and the following term.
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First, diagnose rather than reteach the whole class. Mr. Adjei should use a short diagnostic task on prerequisites such as place value, fractions, and word-problem comprehension to group the 18 low scorers by specific gap. The four 40-minute sessions should target two or three high-leverage skills, using worked examples, guided practice, and immediate feedback; the high group can work on extension problems, and the middle group on error correction. Keep the three learners with over 30 per cent absence in a separate attendance and catch-up plan rather than treating absence as a mathematical deficit. For reporting, present criterion-referenced levels for each strand, not only a total mark, and explain to parents what the learner can do and what comes next. Reassess after remediation with equivalent but not identical items and record both scores. The class analysis to the district should note the bimodal pattern, item quality, SBA limitations, and actions taken. This approach protects validity, avoids labelling, and gives parents concrete information instead of a manipulated grade.