Why a submitted solution cannot stand in for the work
The worry behind the paper is specific: generative AI may let students hand over exactly the mathematical thinking a task was designed to elicit. The authors note that this claim is usually tested through outcomes such as submitted solutions, test scores, or survey responses. Those outcomes, they argue, speak at most to the move from working with an LLM to the final product, not to the work that preceded it.
Their alternative is to treat the chat itself as evidence. They followed 23 first-year linear algebra students at a teacher education college in Israel as those students solved three differently designed homework tasks with LLMs. Each assignment included one problem explicitly designated for LLM use, and students had to submit screenshots of their complete dialogues alongside their solutions. The analysis covered 429 prompts and compared 59 chatlogs with the solutions students submitted.
Two regulatory spaces organize the study. The first is the exchange with the LLM, where students choose the mathematics, the toolkit, the roles assigned to the LLM, and the standards for judging its output. The second is the transition from that exchange to the submitted product, where students decide how to adopt, adapt, or abandon what the LLM produced. Offloading in one space need not imply offloading in the other.
Prompts clustered into five structures, not one habit
The researchers read each prompt as a trace of a regulatory event, drawing on self-regulated learning and on a model of choice-affluent environments in which an LLM becomes a source of knowledge the student can question. Prompts formed five structures, which cast the LLM mainly as a solver, an explainer, or a validator.
The mix of structures shifted across the three tasks, and the tasks were designed to pull in different directions. Task 1 asked students to prove or disprove whether non-zero 3×2 and 2×3 matrices can multiply to the zero matrix, with students told to lead the mathematical work and given minimal guidance. Task 2 asked for proofs about decomposing matrices into sums of special types and supplied a pool of learning-promoting prompts, such as asking the LLM to break a problem into simpler subproblems. Task 3 gave students a step-by-step proof that AB is invertible if and only if A and B are invertible and asked them to use the LLM as a dialogic partner to explain why each step is valid.
The variation was not only between tasks. Ten of the 15 students who completed all three tasks changed their dominant prompt structure at some point. That matters for interpretation: a single chatlog captures one configuration of choices, not a fixed trait of the student.
Most submissions stayed close to what the LLM produced
The central result concerns the second regulatory space. Most final submissions stayed close to LLM output. Crucially, this held even for submissions that followed exchanges in which students had explained their own reasoning, offered conjectures, and checked their own ideas.
That combination is what breaks the shortcut from product to process. If close copying of LLM output occurred after visibly engaged exchanges, then the same surface feature — a solution resembling the model's answer — can accompany quite different amounts of student mathematical work. The authors therefore conclude that an LLM-aided submission is not a trustworthy marker of offloading.
The paper's recommendation follows from this comparison rather than from a general caution: offloading should be examined in each regulatory space and part by part, not judged for the assignment as a whole. A student might regulate actively during the chat and still adopt the model's wording at submission, or the reverse.
What the chatlogs can and cannot record
The evidence is bounded by what a chatlog contains. The authors state that their inferences about regulation are limited to what the recorded exchanges show, so unrecorded thinking, notes, or work outside the chat is invisible to the analysis.
The sample is also narrow. The study took place in a single course with two dozen consenting students, all prospective secondary mathematics teachers, whose prompting may reflect a professional interest in explanation that other undergraduates do not necessarily share. Participation varied by assignment: 19, 21, and 19 of the consenting students submitted chatlogs for Tasks 1 to 3, because some did not submit an assignment.
Two further conditions shape how the prompt structures should be read. The chatlogs were a required part of the submission and students knew their teacher would read them, which may have shaped their prompting; the authors note that "Solve this problem" appeared in most chatlogs, which suggests the logs were not merely curated to display learning-oriented use, but they cannot rule out curation. And the three tasks were given in a fixed order with different mathematical content, so variation attributed to task design may partly reflect when in the semester each task fell and what it covered.
Engaged prompting may reflect understanding rather than build it
The relationship between prompting and submission is correlational. Students who understood the mathematics better may have been both more inclined to share their ideas with the LLM and more motivated to revise what it returned. In that reading, prompting reflects mathematical understanding rather than shaping it.
This caveat does not undo the main negative claim. Whether engaged prompting causes better regulation or merely signals prior understanding, the practical point stands: a submission that resembles LLM output cannot by itself tell an instructor which case they are looking at.
A smaller measurement issue also qualifies the chat data. The right-to-left direction of Hebrew scrambled the mathematics in some LLM replies, so some minor revisions were corrections of rendering rather than of the mathematics. Revisions counted as mathematical regulation should be read with that in mind.
Where evidence of offloading should be sought
The paper's priority is a shift in the unit of judgment. Rather than asking whether an assignment was offloaded, an instructor or researcher should ask which parts of the work were handed over and in which space. The two spaces give a concrete split: the exchange, where the five prompt structures and the roles assigned to the LLM are visible, and the transition to submission, where adoption, adaptation, or abandonment of LLM output becomes visible.
The task design results add a second, narrower lesson. Because the mix of structures shifted across tasks and most students who completed all three changed their dominant structure, a judgment based on one assignment describes that assignment's configuration of choices, not the student's stable approach.
The most decision-relevant finding remains the mismatch between engaged exchanges and close-to-output submissions. For anyone tempted to treat a polished LLM-assisted solution as proof of offloading, this study shows the marker fails in the cases that matter most: submissions that followed students explaining, conjecturing, and checking their own ideas.
Sources used in this answer
What the submission does not show: Complexifying cognitive offloading in students' mathematical work with LLMs
Most final submissions stayed close to LLM output, including those following exchanges where students explained, conjectured, and checked their own ideas, so an LLM-aided submission is not a trustworthy marker of cognitive offloading.