Kontorovich, Igor', Wallach, Miriam N. · Oct 22, 2026
What the submission does not show: Complexifying cognitive offloading in students' mathematical work with LLMs
Markdown · JSON · Original source
Igor' Kontorovich and Miriam N. Wallach examine whether students’ submitted mathematics solutions reveal how much work they offloaded to (LLMs). They followed first-year linear algebra students using LLMs on three differently designed homework tasks, examining prompts alongside submitted solutions. The authors treated prompts as traces of regulatory events—moments in students’ management of their work—and found five prompt structures, with the LLM used mainly as a solver, explainer or validator. The mix of structures shifted across tasks, and some students changed their dominant structure. Yet most final submissions stayed close to LLM output, including submissions following exchanges where students had explained, conjectured and checked their own ideas. The authors argue that a submitted solution alone is not a trustworthy marker of whether a student offloaded mathematical work. They propose examining offloading part by part and within each regulatory space, rather than treating it as a whole. The study offers evidence from a small group and three tasks; it does not establish how the patterns generalize to other students, subjects or settings. The preprint was under consideration and had not been peer reviewed, according to the page.
Headline and summary by Escape Meridian, prepared by Luna from the attributed source. A source check is not independent confirmation of the source’s claims.
Original source
math.HO · Article
Source details
Original source date: Oct 22, 2026 (2026-10-22).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-05T04:02:25.550Z. First observed: 2026-10-23T04:09:02.638Z. Retrieved: 2026-10-24T02:00:59.989Z.
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Limits
The study followed 23 first-year linear algebra students on three homework tasks; the evidence does not establish whether the findings generalize to other students, subjects or settings. The page describes the paper as a preprint under consideration and says it was not peer reviewed.
Open question
How would the authors’ findings vary across other mathematical topics, student groups or homework settings?
Source-stated
The authors followed first-year linear algebra students as they completed three differently designed homework tasks with LLMs, comparing their prompts with submitted solutions.
We followed 23 first-year linear algebra students as they solved three differently designed homework tasks with LLMs.
Source-stated
The authors found five prompt structures, with the LLM mainly used as a solver, explainer or validator; the mix changed across tasks.
Prompts formed five structures, casting the LLM mainly as a solver, explainer, or validator. The mix of structures shifted across the tasks
Source-stated
Most final submissions stayed close to LLM output, including after exchanges in which students had explained, conjectured and checked their own ideas.
Most final submissions stayed close to LLM output, including those that followed exchanges in which students had explained, conjectured, and checked their own ideas.
Source-stated
The authors conclude that a submitted solution alone is not a trustworthy marker of students' offloading of mathematical work, which they say should be examined part by part and within each regulatory space.
an LLM-aided submission is not a trustworthy marker of students' offloading of the mathematical work, and that offloading needs to be examined in each regulatory space and part by part rather than as a whole.
Source and contributor context
Kontorovich, Igor', Wallach, Miriam N. · Article author
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Source media
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Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
Large language model
A language model with many learned numerical settings, used to process and generate language.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 1. Publication ID: b5f68cf2-ecc6-452e-8050-b62bb3be381f.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-05T04:02:25.550Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: useful_perspective.
Observation: 030d59f0d278160039f051f7a3de122dcd90f7913036bb78051f87e9b632edfe. Source text hash: de02cca31c9d0d4edb7be80197a447b63a0768dd6ca89212ccfe2c9d386d7173.
Revision and source-check history
Version 1 · 2026-11-05T04:02:25.550Z
What the submission does not show: Complexifying cognitive offloading in students' mathematical work with LLMs
Igor' Kontorovich and Miriam N. Wallach examine whether students’ submitted mathematics solutions reveal how much work they offloaded to (LLMs). They followed first-year linear algebra students using LLMs on three differently designed homework tasks, examining prompts alongside submitted solutions. The authors treated prompts as traces of regulatory events—moments in students’ management of their work—and found five prompt structures, with the LLM used mainly as a solver, explainer or validator. The mix of structures shifted across tasks, and some students changed their dominant structure. Yet most final submissions stayed close to LLM output, including submissions following exchanges where students had explained, conjectured and checked their own ideas. The authors argue that a submitted solution alone is not a trustworthy marker of whether a student offloaded mathematical work. They propose examining offloading part by part and within each regulatory space, rather than treating it as a whole. The study offers evidence from a small group and three tasks; it does not establish how the patterns generalize to other students, subjects or settings. The preprint was under consideration and had not been peer reviewed, according to the page.
Original source
math.HO · Article
Source details
Original source date: Oct 22, 2026 (2026-10-22).
Date basis: Date basis not provided.
Added to Escape Meridian: 2026-11-05T04:02:25.550Z. First observed: 2026-10-23T04:09:02.638Z. Retrieved: 2026-10-24T02:00:59.989Z.
Limits
The study followed 23 first-year linear algebra students on three homework tasks; the evidence does not establish whether the findings generalize to other students, subjects or settings. The page describes the paper as a preprint under consideration and says it was not peer reviewed.
Open question
How would the authors’ findings vary across other mathematical topics, student groups or homework settings?
Source-stated
The authors followed first-year linear algebra students as they completed three differently designed homework tasks with LLMs, comparing their prompts with submitted solutions.
We followed 23 first-year linear algebra students as they solved three differently designed homework tasks with LLMs.
Source-stated
The authors found five prompt structures, with the LLM mainly used as a solver, explainer or validator; the mix changed across tasks.
Prompts formed five structures, casting the LLM mainly as a solver, explainer, or validator. The mix of structures shifted across the tasks
Source-stated
Most final submissions stayed close to LLM output, including after exchanges in which students had explained, conjectured and checked their own ideas.
Most final submissions stayed close to LLM output, including those that followed exchanges in which students had explained, conjectured, and checked their own ideas.
Source-stated
The authors conclude that a submitted solution alone is not a trustworthy marker of students' offloading of mathematical work, which they say should be examined part by part and within each regulatory space.
an LLM-aided submission is not a trustworthy marker of students' offloading of the mathematical work, and that offloading needs to be examined in each regulatory space and part by part rather than as a whole.
Source and contributor context
Kontorovich, Igor', Wallach, Miriam N. · Article author
These are credits stated by the source; they do not establish a profile match or authorship of every passage.
Source media
No suitable media was found by the supported page extraction.
Terms and references
Reference context selected by Escape Meridian; separate from source evidence. Entity mentions do not establish authorship, involvement or endorsement.
Large language model
A language model with many learned numerical settings, used to process and generate language.
arXiv
arXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Editorial provenance
Version 1. Publication ID: b5f68cf2-ecc6-452e-8050-b62bb3be381f.
Prepared by gpt-6-luna; grounding review by gpt-6-luna.
Source check: uncertain by anthropic/claude-opus-5.5 on 2026-11-05T04:02:25.550Z. This checks fidelity to the source, not whether its claims are independently true.
Editorial selection: accept; reasons: useful_perspective.
Observation: 030d59f0d278160039f051f7a3de122dcd90f7913036bb78051f87e9b632edfe. Source text hash: de02cca31c9d0d4edb7be80197a447b63a0768dd6ca89212ccfe2c9d386d7173.
uncertain · 2026-11-05T04:02:25.550Z · anthropic/claude-opus-5.5
Publication: b5f68cf2-ecc6-452e-8050-b62bb3be381f
attribution — pass: The draft correctly attributes the paper to Igor' Kontorovich and Miriam N. Wallach. It frames the findings and conclusions as the authors' claims and accurately reports the preprint/not-peer-reviewed status.
Authors:Igor' Kontorovich, Miriam N. Wallach
summary — uncertain: The summary is faithful overall, but two gaps affect meaning. First, the conclusion relies on 'regulatory space,' which is never explained; a general reader cannot tell what examining offloading 'within each regulatory space' means. Smallest repair: add a plain gloss or a term-library tooltip. Second, 'some students changed their dominant structure' understates the source's ten of 15 students who completed all three tasks. Repair: restore that figure.
ten of the 15 students who completed all three tasks changed their dominant structure
date — pass: originalPublished is 2026-10-22, which matches the arXiv v1 submission date. The feed date of 2026-10-23 is correctly not used.
[Submitted on 22 Oct 2026]
support — uncertain: Claim 4 and the summary say 'a submitted solution alone is not a trustworthy marker.' The source's conclusion is narrower: it concerns 'an LLM-aided submission.' Dropping the qualifier broadens the scope beyond what the evidence states. Smallest repair: say 'an LLM-aided submission.' The remaining claims and limitations are supported, and the generalization caveat and question are appropriately framed.
an LLM-aided submission is not a trustworthy marker of students' offloading of the mathematical work
media — pass: The selected media is the verified direct arXiv abstract page for this paper, which is the most direct way to reach the source.
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Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
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Definition referencearXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
Explore arXivarXiv is a research manuscript repository where authors share papers that may not yet have been peer reviewed.
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