Proof Scripts and Proof Comprehension

Definitions and mathematical statement

A proof script, in the supplied record, is a dialogue written around a mathematical proof. The intended subject is students' comprehension of proofs; the record does not give an operational definition or measurement of that comprehension.

The supplied conjecture is: "Proof scripts provide an excellent vehicle for investigating and enhancing proof comprehension." Its accompanying question asks whether proof scripts provide an effective method both for investigating students' proof comprehension and for improving it. These are distinct diagnostic and educational claims.

This is a qualitative mathematics-education research question. A precise quantified mathematical or statistical assertion cannot be extracted from the supplied formulation: it specifies neither the student population, the proofs and dialogues involved, the instructional setting, a comparison condition, a measure of comprehension, nor a criterion for effectiveness or excellence. No universal quantifier, effect size, or causal interpretation is specified. These qualifications remain unresolved; the conjecture is retained without imposing such choices.

Short English statement

The question asks whether dialogues written around mathematical proofs help assess and improve students' understanding of proofs. The supplied record leaves the population, intervention, assessment, and standard of effectiveness unspecified, so it does not determine a precise mathematical theorem or statistical hypothesis.

Sources

• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $30002749$, title Proof Scripts and Proof Comprehension, source code catalogue entry; supplied complete source record. No individual proposer is identified; the proposed year is recorded as 2014.
• Supplied report citation: Mathematics in Undergraduate Study Programs: Challenges for Research and for the Dialogue between Mathematics and Didactics of Mathematics (2015), Oberwolfach Reports, pp. 3103--3175, DOI 10.4171/owr/2014/56. https://doi.org/10.4171/owr/2014/56. The supplied background describes Oberwolfach Reports as records of mathematical workshops and their open-problem discussions.
• Supplied literature reference: Zazkis, proof scripts report. https://ems.press/content/serial-article-files/46547.
• Supplied literature reference: Zazkis and Zazkis, proof-comprehension study. https://doi.org/10.1007/s10763-014-9595-0.
• Supplied literature reference: 2023 systematic review of proof research. https://doi.org/10.1007/s11858-023-01518-y.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem partially solved and states that several primary studies support proof scripts as a useful diagnostic and pedagogical tool, while the stronger conjecture that they generally enhance proof comprehension remains unverified. This is supplied dated curation derived from the OWR material, not an independently verified assessment; its time-sensitive status and cited claims require independent checking.
• The supplied statement status is corrected_verified. Its verification note reports that the official Oberwolfach passage was checked directly and the question, definitions, and notation restored without strengthening the claim. This is a source-record assertion, not verification performed for this draft.