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AdaTutor: Adaptive Tutoring through Pedagogical Strategy Selection

Rajeev Bhatt Ambati, Shashank Srivastava, Snigdha Chaturvedi

arXiv:2610.34659v1cs.AIcs.CLcs.LG

TL;DR

Tutors must choose not only what information to provide, but also which form of assistance fits a student’s progress. CPS trains a tutor to compare strategy-specific feedback and adapt its choices; after five turns, it outperforms fixed-strategy tutors across three datasets.

  • Problem

    Tutors must balance instructional support with opportunities for independent problem solving, while the appropriate assistance can vary as students progress.

    Source: §1 · p. 1

  • Method

    CPS compares feedback from different pedagogical strategies at the same tutoring context and uses the highest-scoring strategy-feedback pair as supervision for an adaptive tutor.

    Source: §3.3 · p. 3

  • Results

    After five turns, CPS improves final accuracy over the strongest fixed-strategy tutors by 6.3, 2.6, and 10.1 percentage points on GSM8K, SVAMP, and ScienceQA, respectively.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The findings support adapting the form of assistance to the current tutoring context rather than retaining one strategy throughout a session.

    Source: §7 · p. 8

    The experiments provide an efficient testbed for comparing strategies with simulated students, but do not demonstrate human learning.

    Source: Limitations · p. 9

Abstract

from arXiv · show

Effective tutoring requires determining not only what information to provide, but also which form of assistance to deliver. A tutor may address the same student error using various pedagogical strategies, adapting its approach as the interaction progresses. We introduce Comparative Pedagogical Supervision (CPS), a training framework to learn to select the optimal strategy and feedback for student learning. We evaluate CPS on math and science reasoning datasets. After five tutoring turns, CPS outperforms the strongest fixed-strategy baselines. The learned tutor transfers across datasets, and its strategy selection can also inform a separate API-based tutor.

1 Introduction

Tutors must balance instructional support with independent problem solving, and the assistance a student needs can change as they progress. CPS trains AdaTutor to select a pedagogical strategy and feedback for the tutoring context, outperforming fixed-strategy tutors after five turns.

1 Introduction

  • Tutors must balance instructional support with opportunities for independent problem solving, while the appropriate assistance can vary with student progress and remaining difficulties.For example, a student who understands a relationship but cannot apply it may benefit from a worked example, whereas one who applies it correctly may need only a hint.Source: §1 · p. 1
  • CPS adapts strategy to student progress and difficulties by training AdaTutor on strategy–response pairs selected using simulated student outcomes.AdaTutor generates a strategy-tagged response sequence in one call; the strategy tag supports interpretability and avoids candidate selection at inference.Source: §1 · p. 2
  • After five turns, CPS improves final accuracy over the strongest fixed-strategy tutors by 6.3, 2.6, and 10.1 percentage points on GSM8K, SVAMP, and ScienceQA, respectively.CPS also transfers across datasets, and its learned strategy selection improves final accuracy by 7.3 percentage points over the strongest fixed-strategy API tutors on a GSM8K subset.Source: §1 · p. 2

2 Previous Work

Prior work covers pedagogical dialogue and remediation as well as training tutors to select actions or prompts. AdaTutor instead compares strategy-specific responses by their effects on subsequent student outcomes.

2 Previous Work

  • Pedagogical dialogue datasets and objectives support instructional response generation, while error-remediation work grounds feedback in student reasoning.Examples include MathDial (Macina et al., 2023), Pedagogical Alignment (Sonkar et al., 2024b), SocraticLM, and stepwise verification (Daheim et al., 2024).Source: §2 · p. 2
  • AdaTutor differs by comparing responses from each pedagogical strategy according to their impact on subsequent student outcomes.Its training supervision uses alternative strategy feedback at the same tutoring context, then trains a tutor to jointly generate a strategy and feedback at each turn.Source: §2 · p. 2
  • Other approaches evaluate candidate responses, use multi-turn reinforcement learning, or learn tutoring actions and prompts from student or topic information.These include Scarlatos et al. (2025), TutorRL (Dinucu-Jianu et al., 2025), Nam et al. (2025), Learning to Prompt (Chang et al., 2026a), and LEAP.Source: §2 · p. 2

3 Method

CPS compares strategy-specific feedback at a tutoring context and uses student outcomes to supervise an adaptive tutor. Across turns, it revisits strategy choices as the dialogue changes.

3.1 Problem Setup

  • The tutoring context includes the problem, reference solution, and public dialogue history; an interaction ends when the student answers correctly or reaches the tutor-turn budget.The student also provides a public reply and a separate answer to the original problem, which is checked against the reference answer.Source: §3.1 · p. 2

3 Method

  • CPS samples feedback for each strategy at the same tutoring context and uses independent student attempts to identify strategy-feedback pairs that outperform alternatives.The selected pair provides a supervised target, while a separate exploration policy determines which strategy continues the multi-turn interaction.Source: §3 · p. 2, Figure 2 · p. 3

3.2 Pedagogical Strategies

  • The six strategies span different levels of assistance: hints, step scaffolds, explicit explanations, worked examples, self-explanations, and contrastive feedback.They address different sources of misconceptions and reflect the assistance dilemma.Source: §3.2 · p. 3

3.3 Comparative Pedagogical Supervision

  • CPS scores each strategy’s feedback by the fraction of independent attempts that answer correctly and retains a target when one strategy has a positive score strictly higher than all others.The target is the strategy tag followed by its feedback.Source: §3.3 · p. 3
  • For multi-turn supervision, CPS explores strategies to collect updated tutoring contexts but still uses the highest-scoring strategy as the training target; at inference it generates a strategy tag and feedback in one call.After the student replies, the tutor uses the updated dialogue to choose the next strategy.Source: §3.3 · pp. 3–4

4 Implementation Details

The implementation uses a stateful LLM-based student simulator to compare alternative tutor responses from a shared dialogue and recorded knowledge state. Separate dataset-specific tutors are trained and evaluated under a five-turn interaction protocol.

4 Implementation Details

  • A stateful LLM-based student simulator separates knowledge updates from response generation so alternative tutor responses can be compared from the same dialogue and recorded knowledge state.The design addresses cases where prompted LLM students may abandon an assigned misconception after feedback that does not address it.Source: §4 · p. 4
  • Student profiles track mastered, unmastered, or misconceived knowledge components, with the state updated after feedback before generating the student’s answer and public reply.The knowledge-component library is built from training problems and reference solutions and remains fixed during tutoring.Source: §4 · p. 4
  • Experiments use Qwen2.5-32B-Instruct for students and Qwen2.5-7B-Instruct for tutors, with at most five tutor turns per interaction.CPS scores candidate responses with 10 independent student attempts, uses ε = 0.5 for exploratory continuation, and trains a separate LoRA tutor for each dataset.Source: §4 · p. 4

5 Experiments

The experiments evaluate CPS on math and science reasoning tasks against fixed-strategy and strategy-selection tutors, using cumulative accuracy and correction rate to assess tutoring outcomes.

Datasets and student profiles

  • Evaluation covers GSM8K and SVAMP math reasoning and ScienceQA questions across natural, social, and language sciences.Each dataset uses 15 student profiles spanning three student types.Source: §5 · p. 4

Baselines and evaluation metrics

  • Baselines include six fixed-strategy tutors, PROMPT SELECTOR, SocraticLM, and TutorRL.PROMPT SELECTOR receives all six strategies and is prompted to choose the most appropriate one for the context.Source: §5 · pp. 4–5
  • Cumulative accuracy measures the fraction of student–problem pairs solved by turn t, while correction rate measures initially incorrect pairs solved within five turns.Appendix F also evaluates student-state updates and tutor response quality.Source: §5 · p. 5

6 Results and Analysis

After five tutoring turns, CPS outperforms the strongest fixed-strategy tutors on all three datasets. Analyses examine strategy choices, dialogue context, component contributions, qualitative behavior, transfer, and response quality.

6.1 Main Tutoring Performance

  • 72.7%, 82.5%, and 64.1% final accuracy on GSM8K, SVAMP, and ScienceQA; CPS beats strongest fixed strategies by 6.3, 2.6, and 10.1 percentage points, respectively.WORKED EXAMPLE is strongest on GSM8K and SVAMP, while CONTRASTIVE FEEDBACK is strongest on ScienceQA; CPS also outperforms PROMPT SELECTOR.Source: Table 1 · p. 5, §6.1 · p. 5

6.2 Which Strategies does CPS select?

  • CPS improves on the strongest fixed tutor in 8/9 student-type comparisons, while the student-type oracle matches the global fixed strategy but not CPS.Choices shift across turns: WORKED EXAMPLE declines on GSM8K, while HINT becomes most frequent by turn five on ScienceQA.Source: Table 2 · p. 5, §6.2 · pp. 5–6, Figure 3 · p. 6

6.3 Does Context Help Strategy Selection?

  • Adjacent tutor turns switch strategies in 54.3–62.3% of comparisons; dialogue effects vary by dataset, with ScienceQA favoring problem-only over full history.Among sessions reaching at least two tutor turns, 67.3–84.9% include a strategy change; dialogue helps on both arithmetic datasets, and the best context amount differs by dataset.Source: Table 4 · p. 6, §6.3 · p. 6

6.4 What Does CPS Learn?

  • With fixed-strategy feedback, CPS improves first-turn correction over PROMPT SELECTOR by 34.1, 33.8, and 13.8 points on GSM8K, SVAMP, and ScienceQA.CPS’s own feedback adds 2.1, 3.5, and 7.9 points, respectively; the difference associated with strategy selection is larger than the further response-generation improvement.Source: Table 5 · p. 7, §6.4 · p. 7

6.5 Qualitative Examples

  • Qualitative examples show CPS changing strategy after unresolved errors and targeting remaining confusion more precisely than a fixed-strategy tutor.In one example both tutors use STEP SCAFFOLD, but only CPS addresses confusion between accumulated amount and earned interest.Source: §6.5 · p. 7, Figure 4 · p. 8

6.6 Transfer Across Datasets and Tutors

  • Transfer is strongest between GSM8K and SVAMP: the SVAMP-trained tutor reaches 75.5% on GSM8K, while the reverse-direction tutor trails in-domain and the strongest fixed strategy.Transfer between arithmetic and ScienceQA yields lower accuracy; the authors relate stronger GSM8K–SVAMP transfer to shared student needs.Source: Table 6 · p. 7, §6.6 · p. 7
  • With CPS strategy choices, GPT-4.1-mini reaches 89.9% final accuracy, at least 7.3 points above every fixed-strategy tutor on the 247-example GSM8K study.Against API PROMPT SELECTOR, the final gain is 2.0 points with a 95% confidence interval of [−2.0, 6.1].Source: §6.6 · pp. 7–8, Table 7 · p. 8

6.7 Response Quality Evaluation

  • Tutor responses were judged 95.0% mathematically correct, and student-state updates raised accuracy on new same-KC problems from 5.0% to 67.7%.Human agreement was 84.0% for student-KC judgments and 95.0% for tutor strategy and correctness judgments.Source: §6.7 · p. 8

7 Conclusion

The conclusion presents CPS as a tutor that adapts its strategy to student work and dialogue, trained by comparing feedback strategies. Across three datasets it improves tutoring over the strongest alternative after five turns, and learned strategy choices also improve tutoring with GPT-4.1-mini.

7 Conclusion

  • After five turns, CPS significantly improves tutoring over the strongest alternative on GSM8K, SVAMP, and ScienceQA.First-turn comparisons show contributions from both learned strategy choices and feedback generation.Source: §7 · p. 8
  • CPS trains strategy choices by comparing feedback from different strategies at the same point in a tutoring session.The selected strategy and feedback supervise a tutor that chooses a strategy and generates its response in one call.Source: §7 · p. 8
  • Learned strategy choices also improve tutoring with GPT-4.1-mini over fixed strategies.The conclusion supports adapting assistance to the current tutoring context rather than retaining one strategy throughout a session.Source: §7 · p. 8

Limitations

The experiments compare pedagogical strategies with simulated students and do not demonstrate human learning. Strategies represent different forms of assistance, with context-specific content, rather than a prescribed sequence or fixed mapping to student types.

Limitations

  • The experiments provide an efficient testbed for comparing pedagogical strategies with simulated students, but do not demonstrate human learning.This limits the reported evidence to simulated-student comparisons.Source: Limitations · p. 9

A Pedagogical Strategies

  • The strategies identify primary forms of assistance, while their specific content varies by tutoring context.Table 8 defines and illustrates six strategies using the same tutoring context.Source: A Pedagogical Strategies · p. 10
  • The strategies are alternatives, not a prescribed sequence or fixed mapping from student types to instructional responses.Source: A Pedagogical Strategies · p. 10

B Stateful Student Simulator

The stateful simulator creates controlled synthetic student conditions using knowledge components, screened misconceptions, student profiles, and sequential LLM calls. It checks aspects of response and state consistency but is not intended to model the full behavior of human students.

B Stateful Student Simulator

  • The simulator combines a KC library, screened misconceptions, synthetic student profiles, and a two-call LLM interaction to create controlled conditions rather than model full human behavior.Source: B Stateful Student Simulator · p. 10

KC library and misconception construction

  • Knowledge components are built from training-solution reasoning steps by clustering similar steps, proposing and merging candidates, retaining recurring KCs, and annotating problems.The library is reviewed before problem annotation.Source: B Stateful Student Simulator · p. 10, Figure 6 · p. 12
  • Misconceptions are retained only when students follow the intended incorrect belief and perform worse than a mastered control on problems requiring that KC.Malformed, duplicate, and overly specific candidates are removed before testing.Source: B Stateful Student Simulator · p. 10

Student profiles

  • Profiles assign KCs as mastered, unmastered, or misconception; relevant states shape responses to a problem and persist during the interaction and into the next problem’s initialization.Source: B Stateful Student Simulator · p. 10

Student responses

  • Two sequential LLM calls separate state updating from response generation; only the public response enters the tutor dialogue, while the original-problem answer is checked separately.The runtime checks required fields and state labels but does not execute equations, recover answers from public responses, or repair model mathematics.Source: B Stateful Student Simulator · pp. 10, 12, Figure 5 · p. 11

Simulator checks

  • Simulator checks assess adherence to active KC states, agreement between public response and returned answer, and whether state changes are supported by tutor feedback.The checks are presented as supporting a controlled synthetic testbed.Source: B Stateful Student Simulator · p. 12

C Experimental Setup

The experimental setup pairs problems with student profiles containing relevant knowledge gaps or misconceptions and evaluates tutoring over up to five turns. It specifies the models, training and decoding configuration, baselines, and metrics used for comparison.

Datasets and student profiles

  • Evaluation uses five knowledge-gap, five misconception, and five mixed profiles, each assessed on 200 problems involving an assigned deficit; GSM8K and SVAMP share KCs and profiles.Mixed profiles contain two gaps and two misconceptions; the other profile types contain four affected KCs each.Source: C Experimental Setup · p. 12, Table 9 · p. 13

Models and Interaction Protocol; Data Collection and Training

  • The setup separates student state updates from public-response generation and reports training records, decoding temperatures, and CPS fine-tuning configuration in Tables 10–12.The two-call simulator uses separate decoding settings for state updating and response generation.Source: C Experimental Setup · p. 12, Table 10 · p. 13, Table 11 · p. 13

Data Collection and Training

  • Dataset checkpoints are selected using final accuracy in five-turn validation interactions, while collection and training configuration is selected through GSM8K validation experiments.Source: C Experimental Setup · pp. 12–13

Baselines and evaluation metrics

  • Fixed-strategy tutors retain one strategy while adapting response content; the PROMPT SELECTOR chooses among the same six strategies at each turn.TutorRL and SocraticLM use released 7B checkpoints with native prompts; the GSM8K comparison gives SocraticLM the reference answer and solution analysis.Source: C Experimental Setup · p. 13
  • The study reports accuracy by turn, final accuracy A5, gain over initial accuracy A5 − A0, and correction rate, with gains in percentage points and accuracy and correction rates in percentages.Cumulative accuracy is the fraction of evaluated student–problem pairs solved by turn t; turn zero is the initial attempt.Source: C Experimental Setup · p. 13

E Collection and Training Ablations

The ablations compare sequential collection and training choices on shared GSM8K validation interactions. Direct completion produces the strongest downstream tutoring accuracy among the outcome-construction approaches and requires fewer model requests.

E Collection and Training Ablations

  • The ablations use the same 297 GSM8K validation problem assignments and initial student responses, evaluate five-turn interactions, and proceed sequentially across design choices.Figures 7–9 show valid strategy-tag distributions by turn among still-active interactions on GSM8K, SVAMP, and ScienceQA.Source: E Collection and Training Ablations · p. 13, Figure 7 · p. 14, Figure 8 · p. 14

E.1 Outcome Construction

  • Direct completion estimates each strategy-conditioned response by testing whether the student solves the original problem across ten independent attempts.The alternatives insert an intermediate student response, either followed by ten completion probes or evaluated through ten sampled responses and paired probes as needed.Source: §E.1 · p. 14
  • 88.55% validation accuracy with direct completion, versus 70.37% and 71.72% for the two alternatives, using identical initial student responses.Direct completion also yields more unique positive winners and fewer tied maxima, while requiring fewer model requests.Source: §E.1 · pp. 14–15

E.2 Exploratory Trajectory Continuation

Exploration during collection produces the highest observed validation accuracy in its comparison, while the ablations favor retaining unique positive winners, observed strategy distributions, and interaction-based checkpoint selection. The response-quality evaluation audits student and tutor outputs using an LLM judge, with selected human ratings for agreement assessment.

E.2 Exploratory Trajectory Continuation

  • 90.24% validation accuracy, 1.68 percentage points above greedy continuation, is the highest observed result among evaluated configurations.At ε = 0.5, collection yields 1,048 supervised examples, compared with 773 under greedy continuation, by exposing additional histories after nonwinning responses.Source: §E.2 · p. 15

E.3 Supervised Targets and Sampling

  • 86.20% validation accuracy with positive ties (1,399 examples) trails the 90.24% result with unique positive winners (1,048 examples); margins of 0.2 and 0.5 yield 89.56% and 86.53%.The default retains comparisons with a unique positive maximum; the alternatives include a seeded positive tie or require a winner margin.Source: §E.3 · p. 15
  • 90.24% validation accuracy with ordinary shuffled sampling exceeds strategy-balanced sampling at 79.80% and strategy-and-turn-balanced sampling at 75.42%.The results favor training on the observed distribution of unique positive winners, preserving the contextual distribution of successful strategy-conditioned responses.Source: §E.3 · p. 15

E.4 Interaction-Based Checkpoint Selection

  • 91.92% validation accuracy with interaction-based checkpoint selection exceeds 88.55% with minimum validation loss; mean five-turn accuracy is 87.81% versus 85.72%.The selected checkpoint is step 220, compared with step 120 for minimum validation loss.Source: §E.4 · p. 15

F Response Quality Evaluation

  • The GSM8K response-quality audit uses an LLM judge on 270 initial student replies, 180 tutoring replies, and 180 fixed-strategy tutor responses, with human ratings on selected subsets.The human-rated subsets assess agreement with the judge on the same examples.Source: F Response Quality Evaluation · p. 15

F.1 Student Response Quality

  • Among 31 tutoring replies with recorded knowledge-state changes, the judge supports 29 changes (93.5%) and finds 30 restricted to the appropriate knowledge component (96.8%).The percentages use only turns with an actual change.Source: §F.1 · p. 16, Table 14 · p. 16

F.2 Tutor Response Quality

  • The tutor audit evaluates 180 responses, checking strategy appearance and prominence, mathematical correctness, and disclosure of the original problem’s correct final answer.The sample includes 30 responses per strategy and 36 per tutoring turn across turns one through five.Source: §F.2 · p. 16

F.3 Human Evaluation

This section documents the procedures, prompts, tutoring strategies, and auditing criteria used to construct and evaluate tutoring interactions. It covers student-state simulation and strategy selection, as well as human agreement with Luna, changes in simulated students’ knowledge states, and transfer to new problems.

F.3 Human Evaluation

  • Human majorities judged 21 of 31 reached KCs consistent with assigned knowledge (67.7%); Luna-human agreement was 84.0% on resolved student-KC labels and 95.0% on tutor strategy and correctness.Agreement was 91.7% for judgments about support for state changes, while human pairwise agreement on student-KC labels was 41.8%. Luna and humans saw different information, and neither saw private student reasoning.Source: §F.3 · pp. 16–17

F.4 Response to Different Feedback

  • Only relevant feedback changes the targeted KC state; answer revelation raises immediate accuracy to 82.5%, but accuracy falls to 7.5% when the answer is removed.Of 40 target-state changes, 39 mark the KC as mastered and one does not; an LLM judge considers all 40 supported and local to the target KC. Across 240 responses, consistency is 90.4% over affected KCs and 88.9% over KCs reached during reasoning, while structured answers agree with public responses in 100.0% of cases.Source: §F.4 · p. 17, Table 18 · p. 18

F.5 Transfer to New Problems

  • Relevant feedback raises accuracy on new problems from 5.0% to 67.7%, a 62.7-percentage-point improvement over irrelevant feedback.Accuracy rises from 0.0% to 70.0% for knowledge-gap students and from 10.0% to 65.3% for misconception students; the test covers four KCs, with model parameters fixed.Source: §F.5 · p. 18, Table 19 · p. 18

G Prompt Templates

  • The prompt set covers KC construction, student simulation, tutor feedback, and response evaluation, while withholding private student information from tutors and reference solutions from students.Source: G Prompt Templates · p. 18

G.1 Knowledge Component Construction

  • KC construction extracts atomic reasoning observations, groups them into reusable capability families, and finalizes leaf KCs by semantic capability while separating distinct goals and inverse directions.The procedure generalizes input/output roles and treats contextual objects and units as instances rather than separate KCs.Source: §G.1 · pp. 18–19
  • Knowledge-component records include a definition, applicability conditions, and a contrast field.Source: §G.1 · p. 19

G.2 Problem Annotation

  • Problem annotation maps each authored solution line to zero or more atomic reasoning steps, assigns each step one supplied knowledge-component name or “unmatched,” and records non-reasoning or failed lines.Annotators must not invent knowledge-component names or add dependencies, equations, numerical results, or solution steps absent from the supplied material.Source: §G.2 · p. 20

G.3 Misconception Construction

  • Misconstructions are designed as distinct, coherent, reusable novice beliefs that produce distinguishable reasoning rather than random mistakes or vague claims.Math beliefs include a worked numerical example and a symbolic rule where possible; beliefs for other subjects include a worked example and a predictably wrong answer on typical multiple-choice questions.Source: §G.3 · p. 20

G.4 Stateful Student Simulator

  • After tutor feedback, one call updates the student’s knowledge-component state and another generates a reply using that state.For an initial attempt, separate calls generate private reasoning and the public student reply.Source: §G.4 · p. 21
  • The simulator updates a capability from public feedback only when a valid method is supplied or derived; rejected misconceptions without a usable replacement may become unmastered.Praise, retry requests, irrelevant feedback, requests for the missing method, and final answers alone leave the state unchanged.Source: §G.4 · p. 22
  • Student replies reflect current understanding: students stop before unavailable methods and apply believed methods naturally, even when those methods are misconceptions.The simulator is instructed not to repair or replace the student’s reasoning, and to preserve the resulting answer, even if wrong.Source: §G.4 · p. 22

G.5 Comparing Pedagogical Strategies During Training

  • For GSM8K strategy comparisons, each strategy’s feedback receives one student reply; incorrect replies trigger ten further attempts used for comparison but excluded from dialogue and supervised examples.Source: §G.5 · p. 23

G.6 Screening Student Knowledge

  • Knowledge screening asks the student to solve the original problem using their own reasoning and return concise work and its answer, without assigned difficulties.Source: §G.6 · p. 23

G.7 Tutor Instructions and Dialogue

  • Tutor instructions call for addressing one unresolved subgoal per response, using the reference solution only to ensure mathematical correctness and not revealing the complete solution or final answer.Source: §G.7 · p. 23
  • G.7 directs tutors to assess the learner’s actual work, adapt unhelpful explanations, and stop before giving the original problem’s final answer.Tutors should not attribute unobserved errors or repeat explanations verbatim when they have not helped.Source: §G.7 · pp. 23–24

G.8 Six Pedagogical Strategies

  • A minimal hint gives one brief question pointing to what the learner should notice or determine next, while leaving the operation and calculation to them.The instructions limit the response to one question of at most 20 words and prohibit explaining the underlying rule or naming an operation.Source: §G.8 · p. 24
  • A step scaffold supplies an explicit operation, unevaluated equation, or ordered procedure for one next subgoal, then asks the learner to carry it out.It leaves execution and the final answer to the learner.Source: §G.8 · p. 25
  • Explicit explanation teaches the single conceptual or mathematical relationship at the learner’s impasse through declarative sentences, not next-step instructions or a full solution.It should explain what the relationship means, when it applies, and why it fits the learner’s situation.Source: §G.8 · p. 26
  • For explicit explanation, the private plan derives its mathematical basis from the reference solution, then fills the strategy fields and student-facing response.Only the response is shown to the student, and it must naturally explain the planned relationship, when it applies, and why it fits.Source: §G.8 · p. 26
  • A worked example demonstrates relevant reasoning on a short analogous problem, with a completed calculation and result connected to the learner’s problem without solving it.The analogous problem uses different objects and values from the learner’s problem.Source: §G.8 · p. 26
  • Self-explanation asks exactly one concise question about the meaning or justification of the learner’s visible reasoning, without supplying the relationship or correcting the step.If the learner has not shown a justification, the question should address their current or intended approach.Source: §G.8 · p. 27
  • For either strategy, the private instructional plan derives its mathematical basis from the reference solution rather than assuming the learner’s intermediate values are correct.Only the planned response is shown to the student, and it should elicit reasoning rather than merely request the next result.Source: §G.8 · p. 28
  • Contrastive feedback states a concrete incorrect relationship, contrasts what it represents with what the problem requires, and asks the learner to revise it without giving the final answer.The response should identify the incorrect relationship before the contrast and should not substitute praise for either part.Source: §G.8 · p. 28
  • Contrastive feedback attributes an error to the learner only when it appears in the dialogue; otherwise, it presents a genuinely incorrect relationship as hypothetical.The alternative must be a concrete wrong relationship or procedure, not simply an omission of the correct one.Source: §G.8 · p. 28
  • An example correction contrasts adding group count to group size with repeating group size, then asks the learner to revise the setup to represent that repetition.Source: §G.8 · p. 29

G.9 Prompt Selector and AdaTutor

  • The Prompt Selector chooses a strategy before generating feedback, whereas AdaTutor generates the strategy tag and feedback together; strategy use is constrained by visible learner reasoning or error.The tag is retained for analysis and removed before the response is shown to the student.Source: §G.9 · p. 29

G.10 TutorRL and SocraticLM

  • TutorRL is instructed to withhold the answer while guiding understanding, while SocraticLM guides problem solving with heuristic questions.TutorRL guidance is intended to help students understand and improve their solution, even when they can already solve the problem.Source: §G.10 · pp. 29–30

G.11 LLM Evaluation of Student and Tutor Responses

  • The student-response audit checks capability fidelity and justified, local state changes, while the tutor audit classifies actions from response content rather than inferred instructions.Tutor responses may realize multiple actions; the evaluator records the dominant action and the realized strategies.Source: §G.11 · pp. 30–31
  • The rubric distinguishes contrastive error feedback from minimal hints and step scaffolds, and classifies complete solved analogies as worked examples.It treats a substantive wrong-versus-right comparison as contrastive error feedback, even when paired with explanation or a request for a step.Source: §G.11 · p. 31
  • Correctness is judged against the private solution, while gold-answer leakage requires stating, confirming, or calculating the actual final answer.An incorrect proposed answer is not leakage, though it may be mathematically incorrect.Source: §G.11 · p. 31
  • The audit hides system identity and strategy names, judges only transcript-visible behavior, checks mathematics against a private reference solution, and codes each hypothesis independently.For true codes, evaluators provide exact teacher quotes and, when relevant, student quotes; false codes require null evidence and a brief rationale.Source: §G.11 · pp. 31–32
  • Positive mechanism codes cover targeting visible errors, giving immediately executable guidance, and adapting progression to learner responses rather than merely rewording requests.Source: §G.11 · p. 31
  • Other positive codes assess valid closure through the requested answer or appropriate termination, and correct grounding of quantities, units, entities, and reference quantities.Source: §G.11 · p. 31
  • Failure codes flag unadapted repetition, incorrect or misleading teacher content, off-target help, answer revelation without derivation, inconsistent reasoning, and defects in the benchmark itself.Benchmark defects are coded for both trajectories because they characterize the problem, answer choices, or reference solution rather than either tutor.Source: §G.11 · p. 31
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