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

arXiv: https://arxiv.org/abs/2512.18841 · HTML: https://mlsanity.com/paper/2512.18841/

## Key facts

- Cited by 2 papers in the map (data through 14 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.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 9 of 9)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [Beyond Chain-of-Thought, Effective Graph-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2305.16582/) (2023)
- [CHAMP: A Competition-level Dataset for Fine-Grained Analyses of LLMs' Mathematical Reasoning Capabilities](https://mlsanity.com/paper/2401.06961/) (2024)

## Built on by (most cited first, 2 of 2)

- [Metacognition in LLMs: Foundations, Progress, and Opportunities](https://mlsanity.com/paper/2607.11881/) (2026)
- [Metacognition as Reward: Reinforcing LLM Reasoning via Knowledge and Regulation Signals](https://mlsanity.com/paper/2605.23384/) (2026)

## 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.