mlsanityData to 7 Oct 2026

MDToC: Metacognitive Dynamic Tree of Concepts for Boosting Mathematical Problem-Solving of Large Language Models

arXiv 2512.18841 ↗First posted 21 Dec 2025cs.CLcited by 2

On the map: LLM reasoning → Mathematical reasoning

Abstract (arXiv)

Despite advances in mathematical reasoning capabilities, Large Language Models (LLMs) still struggle with calculation verification when using established prompting techniques. We present MDToC (Metacognitive Dynamic Tree of Concepts), a three-phase approach that constructs a concept tree, develops accuracy-verified calculations for each concept, and employs majority voting to evaluate competing solutions. Evaluations across CHAMP, MATH, and Game-of-24 benchmarks demonstrate our MDToC's effectiveness, with GPT-4-Turbo achieving 58.1% on CHAMP, 86.6% on MATH, and 85% on Game-of-24 - outperforming GoT by 5%, 5.4%, and 4% on all these tasks, respectively, without hand-engineered hints. MDToC consistently surpasses existing prompting methods across all backbone models, yielding improvements of up to 7.6% over ToT and 6.2% over GoT, establishing metacognitive calculation verification as a promising direction for enhanced mathematical reasoning.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Mathematical reasoning, one of 17 directions in LLM reasoning. Builds on 9 of its 23 references that are in the map. First posted on arXiv 21 Dec 2025.

Builds on

9 of 23 references.

Closest ancestors · 1

Same direction, newest first

  1. 2024CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities13 Jan

Other references · 8

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,601
  3. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,203
  4. 2022Large Language Models are Zero-Shot Reasonerscited by 4,323
  5. 2021Are NLP Models really able to Solve Simple Math Word Problems?cited by 861
  6. 2023Large Language Model Guided Tree-of-Thoughtcited by 218
  7. 2023Universal Self-Consistency for Large Language Model Generationcited by 198
  8. 2023Beyond Chain-of-Thought, Effective Graph-of-Thought Reasoning in Language Modelscited by 51

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Metacognition in LLMs: Foundations, Progress, and Opportunitiescited by 1
  2. 2026Metacognition as Reward: Reinforcing LLM Reasoning via Knowledge and Regulation Signalscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Survey on Large Language Models for Mathematical Reasoning
  2. 2024MetaRuleGPT: Recursive Numerical Reasoning of Language Models Trained with Simple Rules
  3. 2024Mathador-LM: A Dynamic Benchmark for Mathematical Reasoning on Large Language Models
  4. 2025JT-Math: A Multi-Stage Framework for Advanced Mathematical Reasoning in Large Language Models
  5. 2025A Survey on Feedback-based Multi-step Reasoning for Large Language Models on Mathematics
  6. 2026Mathematical Reasoning in Large Language Models: Benchmarks, Architectures, Evaluation, and Open Challenges
  7. 2024ConceptMath: A Bilingual Concept-wise Benchmark for Measuring Mathematical Reasoning of Large Language Models
  8. 2024Benchmarking Large Language Models for Math Reasoning Tasks