DICE-Bench: A Benchmark for Intervention-Aware AI Tutoring

DICE-Bench is a mathematical tutoring benchmark introduced in DICE: Decoupling Capability from Intervention Necessity in LLM Tutoring (NeurIPS 2026).

Most conversational tutoring datasets focus on what a tutor should say next. DICE-Bench addresses a complementary question: When does a student actually need intervention, and when should the tutor allow them to continue independently?

The benchmark combines skill-preserving math problem variants, turn-level pedagogical action annotations, and counterfactual Intervention Value (IV) estimates.

It supports research on selective tutoring, intervention calibration, student progress, and efficient multi-turn teaching.

Dataset Overview

Component	Size	Purpose
Math problem triplets	10,273	Evaluate tutoring across increasing difficulty
Individual problem variants	30,819	Easy, source, and hard problems
Tutoring evaluation subset	250 triplets	Reproduce the paper's tutoring evaluations
Policy annotations	20,477	Train and evaluate pedagogical action-selection models
IV estimates	7,379 states	Study the marginal value of tutoring interventions

Each problem triplet consists of:

• Easy: A simplified version requiring the same underlying mathematical skill.
• Source: The original math word problem.
• Hard: A more complex version that preserves the target skill.

This structure enables evaluation of tutoring decisions across related problems with different levels of reasoning complexity.

Dataset Configurations

DICE-Bench provides three Hugging Face configurations: default, policy, and iv.

1. default — Skill-Preserving Problem Triplets

Split	Triplets	Description
triplets_all	10,273	Complete benchmark
triplets_250	250	Evaluation subset used in the paper

The evaluation subset is contained within the full benchmark and was selected using seed 42.

Source composition

Source	Full benchmark	Evaluation subset
GSM8K	7,973	197
MAWPS	2,300	53
Total	10,273	250

The same 250 triplets support two evaluation settings:

• Single-problem tutoring: 750 individual problems (250 easy, 250 source, 250 hard), each evaluated independently with an 8-turn limit.
• Session-level tutoring: 250 complete triplets, each evaluated sequentially under a shared 20-turn budget.

Load the data

from datasets import load_dataset

# Evaluation triplets
eval_data = load_dataset(
    "chocokiddo/DICE-Bench",
    "default",
    split="triplets_250"
)

# Complete benchmark
full_data = load_dataset(
    "chocokiddo/DICE-Bench",
    "default",
    split="triplets_all"
)

2. policy — Pedagogical Action Annotations

This configuration contains 20,477 cleaned tutoring decision points used for training and evaluating the DICE action-selection policy.

Split	Instances	Source problems
Train	16,383	452
Validation	2,048	54
Test	2,046	56
Total	20,477	562

The official split uses seed 42 and groups instances by source problem ID, keeping related states and difficulty variants together within each split.

Each instance is annotated with one of six pedagogical actions:

Action	Meaning
accept_and_advance	Acknowledge progress and move to the next step
arithmetic_repair	Address an arithmetic error
conceptual_hint	Provide guidance for a conceptual misunderstanding
handle_question	Respond to a student clarification
ask_for_justification	Request additional reasoning
refocus_subgoal	Redirect attention to the current learning objective

Annotations originate from two settings:

• observed_multi_dialogue: Decision points extracted from SocraTeach dialogues involving source problems.
• synthetic_step_variant: Decision points generated from the subgoal structure of easier and harder problem variants.

Load the policy dataset

from datasets import load_dataset

policy = load_dataset(
    "chocokiddo/DICE-Bench",
    "policy"
)

train = policy["train"]
validation = policy["validation"]
test = policy["test"]

The _row_id field can be used to associate policy instances with their corresponding IV estimates.

3. iv — Counterfactual Intervention Value

This configuration provides estimates of Intervention Value (IV), which measures whether a pedagogical action improves expected student progress relative to accepting and allowing the student to continue.

[ IV(x,a)=\mu(x,a)-\mu(x,a_0) ]

Here, (a_0) represents accept_and_advance, and (\mu) denotes expected student progress estimated through controlled simulated continuations.

• Positive IV: Intervention improves expected progress.
• Zero IV: No estimated marginal benefit.
• Negative IV: Intervention performs worse than the non-intervention alternative.

Available splits

Split	States	Description
target_observed	6,091	Source-dialogue states used for the main IV audit and policy weighting
easy_synthetic	479	Easy-variant synthetic states
hard_synthetic	809	Hard-variant synthetic states

Key fields include:

Field	Description
mu_action	Estimated progress under the annotated action
mu_accept_and_advance	Estimated progress under the non-intervention reference
intervention_value	Difference between the two estimates
action_eval_json	Per-rollout evaluation details for the annotated action
accept_eval_json	Per-rollout evaluation details for the reference action

The rollout-detail fields are stored as JSON strings.

Load the IV estimates

from datasets import load_dataset

iv = load_dataset(
    "chocokiddo/DICE-Bench",
    "iv",
    split="target_observed"
)

Key finding from the paper: Among 2,367 annotated active interventions in the target-observed subset, 44.4% had zero or negative estimated Intervention Value, suggesting that many prescribed tutoring interventions offer little or no marginal benefit over allowing the student to continue.

This finding is specific to the evaluated intervention subset, student simulator, and progress-scoring procedure.

Dataset Construction

DICE-Bench builds on mathematical word problems and structured tutoring dialogues from SocraTeach, which draws on GSM8K and MAWPS.

Construction involves three main stages:

1. Difficulty augmentation: Generate easier and harder variants while preserving the original mathematical skill and validating solution correctness.
2. Policy annotation: Convert dialogue and subgoal-level tutoring states into explicit pedagogical action labels.
3. Intervention Value estimation: Compare simulated student progress following an annotated action against a non-intervention reference using controlled rollouts.

The resulting benchmark provides both problem-level structure for evaluating tutoring sessions and turn-level supervision for studying intervention decisions.

Original SocraTeach dialogue dumps are not redistributed as part of this release.

Intended Use and Limitations

DICE-Bench is intended for research on:

• Intervention-aware AI tutoring and pedagogical action prediction.
• Mathematical reasoning across difficulty levels.
• Counterfactual evaluation of tutor interventions.
• Multi-turn tutoring and intervention efficiency.

Limitations: The benchmark focuses on English mathematical word problems and uses synthetic difficulty variants, model-generated annotations, and simulated student continuations. IV estimates depend on the simulator and evaluation rubric and should not be interpreted as direct measurements of learning outcomes in human students.

The benchmark is not intended to replace educational evaluations involving real learners.

Related Resources

• Paper: DICE: Decoupling Capability from Intervention Necessity in LLM Tutoring (NeurIPS 2026)
• Code: Sayantan-world/DICE
• Trained policy: chocokiddo/DICE-Policy
• Source tutoring dataset: SocraticLM / SocraTeach
• GSM8K: openai/gsm8k
• MAWPS: Original repository

Citation

If you use DICE-Bench, please cite the DICE paper:

@misc{pal2026dicedecouplingcapabilityintervention,
      title={DICE: Decoupling Capability from Intervention Necessity in LLM Tutoring},
      author={Sayantan Pal and Kaiyi Ji and Rohini K. Srihari},
      year={2026},
      eprint={2610.04825},
      archivePrefix={arXiv},
      primaryClass={cs.AI},
      url={https://arxiv.org/abs/2610.04825},
}

Please also cite the original GSM8K, MAWPS, and SocraticLM/SocraTeach publications where applicable.

License and Attribution

The DICE dataset release is designated MIT. DICE's independently created annotations, generated variants, and analysis artifacts are released under the project's stated terms. Underlying source materials remain subject to any applicable original licensing and attribution requirements.

Please preserve appropriate attribution to DICE and the original source datasets when redistributing or building upon this work.