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TrussTutor-Bench: Benchmarking large language models on solution accuracy, sycophancy, and error detection in statics

Evangelos Apostolakis, Erfan Hamdi, Sara Jahedazad, Emma Lejeune

arXiv:2610.38917v1cs.CYcs.AIcs.LG

TL;DR

Existing LLM benchmarks largely test final-answer accuracy, leaving tutoring-relevant confirmation and error detection less examined. TrussTutor-Bench evaluates thirteen models on verified truss problems and generated student work; models differ most in how they respond when students doubt correct work. The authors conclude that further work should examine learning outcomes and human–AI interaction.

  • Problem

    Existing benchmarks focus mainly on final-answer accuracy, not whether models confirm correct work under doubt or identify errors in flawed work.

    Source: §1 · p. 3

  • Method

    TrussTutor-Bench pairs 200 verified two-dimensional truss problems with automatically generated student solutions to evaluate thirteen LLMs on solving, confirmation under pushback, and error detection.

    Source: §1 · p. 3, §2.3 · p. 6

  • Results

    Models generally solved nearly all problems and detected nearly all injected errors, while reliability diverged sharply when students insisted correct work was wrong.

    Source: §1 · p. 3, §3 · p. 7, §4 · p. 12

  • Takeaways & Limitations

    For leading models on these truss problems, technical problem-solving is no longer the apparent limiting factor; open questions concern learning and human–AI interaction.

    Source: §4 · p. 12

    The detection findings may not generalize to authentic student work because benchmark solutions are synthetic and typeset, with at most one injected error.

    Source: §3.3 · p. 12, §4 · p. 12

Abstract

from arXiv · show

Large language models (LLMs) have rapidly become a default source of help for students in science and engineering courses. In foundational engineering mechanics courses such as statics, students routinely use these tools to check answers, work through partial solutions, and ask for explanations. Effective tutoring in this setting requires more than a correct final answer. A model must also confirm correct work when a student doubts it, and identify errors in flawed work. Existing benchmarks evaluate LLMs primarily on final-answer accuracy, so it is unclear whether models that can solve mechanics problems also have the other technical capabilities that tutoring depends on. Here we introduce TrussTutor-Bench, a benchmark of 200 verified two-dimensional truss problems paired with automatically generated student solutions, and use it to evaluate thirteen LLMs on solution accuracy, sycophancy, and error detection. Baseline accuracy ranged from 64.5% to 97.0%. Every model detected nearly all injected errors in synthetic flawed student work (90.4% to 100%), so error detection did not distinguish models under these clean conditions. Sycophancy did. When a student insisted that correct work was wrong, models rejected correct solutions to problems they had themselves solved in 1.6% to 50.0% of cases. These results show that performance varies widely across models: the leading models solve, check, and defend student work nearly perfectly, while others are far less reliable, particularly when a student doubts correct work. TrussTutor-Bench provides a verified, extensible standard for determining which models are technically reliable enough to put in front of students. Follow-up work must now focus on teaching rather than technical capability, drawing on learning science to determine whether LLM help leads students to understand the material or simply to reach the right answer.

1 Introduction

Students increasingly use LLMs for statics, but existing benchmarks largely assess final-answer accuracy rather than the judgment and error-localization needed for tutoring. TrussTutor-Bench evaluates these capabilities alongside problem-solving and finds sharp model differences in response to student pushback.

Student use and attitudes

  • In a Boston University statics course, weekly LLM use rose from 37% to 51% during Spring 2026, while students’ never-use share fell from 33% to 6%.At semester end, 84.2% agreed they could evaluate whether an AI-generated mechanics solution was correct.Source: §1 · pp. 2–3

Study contribution

  • TrussTutor-Bench evaluates thirteen LLMs on 200 verified two-dimensional truss problems paired with automatically generated student solutions.It assesses solution accuracy, confirmation of correct work under doubt, and identification of errors in flawed work.Source: §1 · p. 3

Motivation

  • Existing benchmarks primarily measure correct answers, leaving untested whether models confirm doubted correct work and locate errors in flawed student work.Truss problems have exact answers and canonical solution steps that allow errors to be localized.Source: §1 · pp. 2–3

Key findings

  • Leading models solve nearly all truss problems and detect nearly all injected errors, but models differ sharply in whether they defend correct work under student pushback.Some reject correct solutions to problems they had solved in up to half of cases, and problem-solving accuracy only partly predicts this behavior.Source: §1 · p. 3

2 Methods

The methods construct verified truss tasks, generate correct and flawed worked solutions, and evaluate models’ answers in baseline and formative workflows. Thirteen multimodal models with structured-output support are assessed under practical API and budget constraints.

2 Methods

  • Thirteen LLMs were evaluated in baseline and formative workflows, with formative responses judged on correctness and first-error step against verified references.The explanation text was not graded.Source: §2 · p. 3, Figure 2 · p. 4

2.1 Benchmark tasks

  • The 200 two-dimensional statically determinate truss tasks span four archetypes and draw on six textbooks and original problems.Original problems include handwritten tasks and computer-prepared figures in 30 drawing styles.Source: §2.1 · pp. 3, 5

2.2 Benchmark task verification

  • Each task was retained only after symbolic and direct-stiffness solutions agreed within 10^-4 for every solved member and a human reviewer confirmed solvability and the answer.Tasks also had to be statically determinate, geometrically stable, and conform to the answer schema.Source: §2.2 · p. 5

2.3 Automatic generation of worked solutions

  • Worked solutions were generated from verified traces; flawed versions injected a right-hand-rule error or reversed tension/compression labels, with error steps recorded.Posture 2 applies to 163 tasks and Posture 3 to 52 tasks; the framework can extend to other errors by modifying solver operations.Source: §2.3 · pp. 5–6

2.4 LLM API calls and evaluation protocol

  • Models received up to four runs, and formative scoring required both the correctness judgment and first erroneous step to match; explanations were not scored.Posture 1 pairs correct work with pressured student wording, but no neutral-question run was included to separate deference from general doubt.Source: §2.4 · p. 6

2.5 Models

  • Models had to accept text and images, return structured JSON, and be publicly API-accessible within the study’s access and budget constraints.These criteria excluded some capable models, so the set is not exhaustive and results should not be read as a ranking of all available LLMs; API settings also differed across models.Source: §2.5 · pp. 6–7

3 Results and Discussion

Across the three tutoring capabilities, baseline problem-solving and error detection were strong for many models, but models differed sharply in whether they defended correct work under student pushback. Baseline accuracy only partly predicted that response, while error-detection scores were near ceiling under the benchmark’s controlled conditions.

3.1 Baseline technical performance

  • Baseline accuracy ranged from 64.5% (GPT-5.6 Luna) to 97.0% (GPT-6 Astra) across 200 tasks.Six models solved more than 90% of tasks; the three open-weight models scored between 65.0% and 74.0%.Source: §3.1 · pp. 7, 9, Figure 3 · p. 8

3.2 Sycophancy sensitivity

  • Posture 1 accuracy ranged from 46.5% (GLM-5.3-Flash) to 98.5% (Gemini 4 Argon), and rankings shifted substantially from baseline.Four models confirmed correct work in more than 90% of cases; the supplied figure compares textbook and original tasks and plots Posture 1 against baseline accuracy.Source: §3.2 · p. 9, Figure 4 · p. 10
  • Among tasks proprietary models had solved, they rejected correct work under pushback on 1.6%–25.5%; open-weight models did so on 20.0%–50.0%.Raw Posture 1 accuracy also counts failures on tasks a model could not solve, so it overstates sycophancy for weaker models.Source: §3.2 · p. 11

3.3 Auditing work in progress

  • Posture 2 accuracy ranged from 91.4% to at least 95.7% for eleven models, while Posture 3 accuracy ranged from 90.4% to 100%.Mean accuracy was 97.4% in Posture 2 and 95.7% in Posture 3; the figure scores error identification and naming the erroneous step.Source: Figure 5 · p. 11, §3.3 · pp. 11–12
  • In Posture 2, 27 of 55 failures called the work correct; in Posture 3, 26 of 29 flagged the work but named the wrong step.Errors were always at step 1 in Posture 2 and at step 2 in 49 of 52 Posture 3 tasks, so these scores do not establish localization at arbitrary positions.Source: §3.3 · p. 12
  • Posture 2 and 3 scores are an upper bound on real-world error detection because benchmark solutions are cleanly typeset, stepwise, and contain at most one injected error.The authors call for naturalistic benchmarks using authentic student work; each model was also run only once per task at its default temperature.Source: §3.3 · p. 12

4 Conclusion

TrussTutor-Bench evaluates thirteen LLMs on 200 verified two-dimensional truss problems, finding that leading models solve and detect injected errors well while resistance to student pushback separates models. The authors identify limits in the synthetic evaluation and call for studies of learning outcomes using authentic student work.

4 Conclusion

  • Resistance to incorrect student pushback separated models: some rarely rejected correct work, while others did so frequently, and problem-solving accuracy only partly predicted which.Open-weight models were less reliable under pushback on average, though reliability varied within both open-weight and proprietary groups.Source: §4 · p. 12
  • Every model detected nearly all injected errors, but the student solutions were synthetic and typeset, with at most one of two error types.The authors say detection results may not generalize to authentic student work.Source: §4 · p. 12
  • Posture 1 used one pushback wording and no neutral-question control, so its rejection rate cannot separate deference from rejection under neutral questioning.Source: §4 · p. 12
  • Future work should examine how students’ use of LLMs affects learning and should evaluate explanations, since identifying the correct step does not ensure the model gave the correct reason.Source: §4 · p. 12
  • TrussTutor-Bench’s verified tasks, generated worked solutions, and extensible error-generation framework can be expanded to other error types and areas of engineering mechanics.Source: §4 · p. 12
  • The authors did not record model price or access conditions, leaving possible differences in feedback quality by access unmeasured.Source: §4 · p. 12

6 Additional Information

The authors provide code to reproduce the benchmark and five example problems, while withholding the remaining problems to prevent contamination and avoid copyright issues.

6 Additional Information

  • Code to reproduce TrussTutor-Bench and five example problems are available on GitHub.Source: §6 · p. 13
  • The remaining problems are not publicly released to prevent data contamination and avoid copyright issues with textbook-derived tasks.Source: §6 · p. 13
  • The authors say they are willing to share further details on request.Source: §6 · p. 13

A Task template

The task-template example defines the truss problem, its symbolic and numerical inputs, the solver workflow, and the requested structured answer; a rendered schematic accompanies the problem statement.

A Task template

  • Each task template specifies truss geometry, loads, supports, a problem statement, units, variables, and the required structured answer.Source: A Task template · p. 14
  • For TRUSS_0001, the example is an equilateral-truss method-of-joints problem, and the model receives its rendered schematic with the problem statement.Source: A Task template · p. 14, Figure 6 · p. 14
  • The example template defines nodes, member connectivity, symbolic variables, loads, and support conditions for the truss.Source: A Task template · pp. 14–15
  • Its problem schema asks for the maximum compression force and specifies units and numerical-variable settings.Source: A Task template · p. 15
  • The solution recipe initializes the truss, solves global reactions, applies a method-of-joints operation, and extracts the requested answer.Source: A Task template · p. 16
  • The template also includes drawing variables and a development block that runs the programmatic solution and renders the schematic.Source: A Task template · p. 17

B Example prompts

The appendix illustrates baseline and formative prompts, including the task schematic, generated student work, and the question used to assess it.

B Example prompts

  • Each API request combines a text prompt, one or more PNG images, and a JSON schema constraining the response; stored ground truth is withheld from the model.Source: B Example prompts · p. 17

B.1 Baseline problem solving

  • The baseline example includes the task schematic as an image.Source: §B.1 · p. 17
  • The appendix identifies a ground-truth answer for the baseline example, but the supplied text does not fully state its value.Source: §B.1 · p. 18

B.2 Formative assessment

  • In formative runs, the prompt places the problem statement before the student question.Source: §B.2 · p. 18
  • The formative prompt then includes the task schematic and generated student solution, with each free-body diagram preceding the step that uses it.Source: §B.2 · p. 18

B.3 Clean solution, pressured question

  • The clean-solution, pressured-question example marks the work as correct and specifies no error step.Source: §B.3 · p. 20

B.4 Right-hand rule error

The work is marked incorrect, with the error at step 1.

B.4 Right-hand rule error

  • The work is marked incorrect, with the error at step 1.Source: §B.4 · p. 22

B.5 Tension/compression error

This example uses a method-of-sections truss problem adapted from Osgood et al., with a schematic and a student asking whether their work is correct.

B.5 Tension/compression error

  • The example uses task TRUSS_0003, a method-of-sections problem adapted from Osgood et al..Task TRUSS_0001 has no method-of-sections step; the schematic is reproduced from Osgood, Cameron, and Christensen.Source: §B.5 · p. 22, Figure 7 · p. 22
  • The problem asks for the magnitudes and tension-or-compression status of forces in members D, E, and F, given 60.0 kN and 80.0 kN downward loads and a 20.0-degree bottom-chord slope.The top chord has bay lengths of L.Source: §B.5 · p. 22
  • The student asks, “Is my work correct?”, and the ground truth marks the work incorrect at step 2.Source: §B.5 · pp. 22–23
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