Item Analysis After the Second Terminal Mathematics Examination
Anita Gurung teaches Grade 10 mathematics at an aided secondary school in Pokhara. After the second terminal examination (75 marks, 40 students), she tabulated item-level results. Item 14, a two-step unitary-method problem about filling a water tank, was correct for only 9 of 40. Item 15, a one-step percentage-increase calculation, was correct for 31 of 40. Item 18, a discount problem requiring the same percentage idea but embedded in a shop context, was correct for 12 of 40. The class mean was 41 out of 75. Many scripts left word problems blank or wrote 'not understood'. The principal wants a revision schedule for the SEE in ten weeks and advises her to 'just do past papers from now on'. Anita has six periods a week, a class set of one textbook, and no photocopier; she writes on the board or dictates. Several strong students are bored by revision and have started missing morning classes.
1. Interpret the three items. What can and cannot be concluded about the students' difficulties, and what further diagnostic evidence should Anita collect before teaching?
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What the pattern supports
Item 15 (31 of 40 correct) shows the percentage procedure itself is largely secure. Item 18 (12 of 40) uses the same procedure but hides it inside a shop context. The drop from 31 to 12 cannot be explained by inability to calculate percentages; it points to representation and comprehension - identifying what the unknown is, what operation the words imply, and which quantity is the base. Item 14 (9 of 40) adds a second layer: two operations must be chained, so it requires planning, not just decoding.
Three plausible causes that the data cannot yet separate
- Conceptual: percentage not understood as a comparison to a base.
- Linguistic: terms such as discount, marked price, rate, per unit are not understood, in either the Nepali or English medium.
- Strategic: students stop at the first unfamiliar word, which matches the blank answers and 'not understood'.
Diagnostic to run before reteaching A 15-minute, no-mark task on four items: (a) draw a diagram for a discount problem, (b) say in one sentence what is being asked, (c) solve a bare percentage calculation, (d) solve one two-step problem aloud to a partner while she listens to six students across the bands. Also check whether errors are in setting up or in arithmetic by requiring the setup line separately. Without this, past-paper drilling will simply reproduce the same failure.
2. Design a three-week reteaching plan that addresses the diagnosis and keeps the high scorers engaged. State your success criteria.
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Week 1 - representation before calculation Every problem begins with a bar model or a two-column table (quantity / value / base). Students translate ten short scenarios into diagrams and into one setup line, without solving. Teacher models aloud, then fades: first full model, then last step missing, then setup only. This targets the comprehension gap directly.
Week 2 - chaining and unitary method Worked examples that show the two steps explicitly, then 'spot the difference' pairs (one-step versus two-step versions of the same story). Students write their own two-step problem for a partner to solve; writing the problem is the strongest test of whether the structure is understood.
Week 3 - mixed and spaced Mixed set of percentage, unitary method and discount items, interleaved with earlier topics. Error journal: each student records two errors, the type of error (read, setup, calculate), and the correction.
High scorers Not extra drill. They take a parallel challenge set (reverse problems, multi-step with a distractor), serve as explainers for ten minutes twice a week, and prepare one board solution with justification. This addresses the boredom and absenteeism risk.
Success criteria On a parallel 4-item quiz at the end of week 3: at least 28 of 40 correct on the discount-type item and at least 20 of 40 on a two-step unitary item, with fewer than six blank scripts. If the blank rate does not fall, the problem is comprehension of instructions, and the plan must shift to language work.
3. How should Anita respond to the principal's instruction to 'just do past papers'? Give the substance of her reply and the compromise she can defend.
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Acknowledge the valid part. Past papers are useful: they reveal the paper's format, timing, and the weighting of topics, and familiarity reduces examination anxiety. The disagreement is about sequencing, not about whether to use them.
Present evidence, not opinion Show the item table: 31 of 40 can do the percentage procedure and only 12 of 40 can apply it in context. Then make the argument plainly - a student who cannot set up the problem will practise setting it up wrongly for ten weeks and consolidate the error. Past papers used as the only method measure the problem; they do not fix it.
Defensible compromise
- Weeks 1–3: reteaching of representation and two-step problems, with one short past-paper section each week used as a diagnostic, not as practice volume.
- Weeks 4–7: two full timed past papers, each followed by item analysis and a targeted repair lesson keyed to the errors found.
- Weeks 8–10: revision by weak items across years, plus formula and method summaries.
- Ask for one extra period or an agreed morning slot for the timed papers, since six periods and no photocopier make full papers expensive in class time; write papers on the board or dictate in sections.
Record it Put the schedule and item data in a short note to the principal so that the plan is shared and reviewable. This converts a directive into a monitored agreement and protects the students from an unstructured ten weeks of paper-solving.