📄 Experimental Identification of the Use of Hedges in the Simplification of Numerical Expressions

Summary

The paper looks at how numbers in text, especially proportions, can be rewritten so that readers with weak numeracy understand them. It focuses on hedges, the small words that signal approximation or its direction, such as "about" or "just over". The authors took sentences from the NUMGEN corpus, which holds 110 newspaper and scientific texts that state the same facts in different ways. They asked 34 numeracy experts (school maths teachers and adult numeracy tutors) to simplify the bracketed percentages in a SurveyMonkey questionnaire with three tasks: rewrite without percentages, rewrite without decimals, and simplify freely. Each answer was coded as a pair of original and simplified expression. The coding recorded the mathematical form used (fraction, ratio or percentage), a relative error measuring lost precision, and whether a hedge appeared. Simplified forms carried hedges slightly more often than not. Hedge use depended on the task type, the chosen form and the precision lost, but there was no clean overall link between hedging and error. The resulting guidelines and the parallel original/simplified corpus are meant to support automatic simplification of numbers.

Key points

• Data came from the NUMGEN corpus: 10 topic sets with 110 texts in total. Three sets of eight sentences were chosen, one with only decimal percentages and two mixing whole-number and decimal percentages. Values ranged from near 0 to near 1.
• Participants were 34 native-English mathematics teachers and adult numeracy tutors. Some did not finish the survey.
• The authors tested five hypotheses. These linked hedge use to the chosen strategy, to whether the value is central (0.2–0.8) or extreme, and to precision loss. One hypothesis predicted that writers skip hedges when no precision is lost.
• Precision loss was measured as a relative error, (simplified − original) / original.
• Three hedges appeared in all three tasks: "about", "just over" and "over". Ratios were hedged differently from fractions and percentages. In the no-decimals task, hedges were mostly attached to rounded percentages (113 counted uses, against 42 with fractions and 28 with ratios).

Interesting ideas

• I1. Each rewrite is coded as a triple of target form, measured relative error and hedge yes/no, which turns vague advice about simplifying into features a system can choose among.
• I2. Hedges come in two kinds: some only say the value is approximate ("about"), while others also give the direction ("just under", "over").
• I3. Constraining rewrites by reader type (no percentages, no decimals, free) shows how one fact gets re-expressed in each case, much like the NUMGEN design of the same facts in many forms.
• I4. The authors noticed that experts restate numbers that are being compared on a common base. This suggests simplifying the whole sentence's set of numbers together rather than each number separately.
• I5. The authors plan to check inter-rater agreement before treating a hedge as the right choice.

For Mova

How these ideas could serve Mova, our small open language model — its files, stages and tests:

• I1 (back): When generation verbalises a quantity from the meaning graph, it could pick a form and attach a hedge whenever the rounding error is non-zero, and log that error so the choice stays explainable.
• I2 (world): Quantities in the world of the text could keep a value plus an approximation flag and a direction, so that "just over half" becomes a bounded interval instead of a fixed 0.5.
• I3 (answer): Maths word-problem readers could be tested on paraphrased number forms of the same problem (fractions, ratios, hedged percentages) to check that the extracted quantity and answer stay stable.
• I4 (frames): Comparison frames could link their numeric arguments so later normalisation or verbalisation treats them jointly and keeps the comparison intact.
• I5 (learn): Hedge or rounding choices from several LLM teachers could count as silver data only when they agree, with disagreements kept as hard cases.