Large Language Models (LLMs) have achieved remarkable performance across a wide range of mathematical benchmarks. However, concerns remain as to whether these successes reflect genuine reasoning or superficial pattern recognition. Existing evaluation methods, which typically focus either on the final answer or on the intermediate reasoning steps, reduce mathematical reasoning to a shallow input–output mapping, overlooking its inherently multi-stage and multi-dimensional cognitive nature. Inspired by P’olya’s problem-solving theory, we propose SMART, a benchmark that decomposes mathematical problem-solving into four cognitive dimensions: **S**emantic Understanding, **M**athematical Reasoning, **A**rithmetic Computation, and **R**eflection Refinemen**T**, and introduces dimension-specific tasks to measure the corresponding cognitive processes of LLMs. We apply SMART to 22 state-of-the-art open- and closed-source LLMs and uncover substantial discrepancies in their capabilities across dimensions. Our findings reveal genuine weaknesses in current models and motivate a new metric, the All-Pass Score, designed to better capture true problem-solving capability.

In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple features to measure the relevance between examples. We argue that these features are not sufficient to reflect the intrinsic connections between examples. In this study, we propose a curriculum ICL strategy guided by problem-solving logic. We select demonstration examples by analyzing the problem-solving logic and order them based on curriculum learning. Specifically, we constructed a problem-solving logic instruction set based on the BREAK dataset and fine-tuned a language model to analyze the problem-solving logic of examples. Subsequently, we selected appropriate demonstration examples based on problem-solving logic and assessed their difficulty according to the number of problem-solving steps. In accordance with the principles of curriculum learning, we ordered the examples from easy to hard to serve as contextual prompts. Experimental results on multiple benchmarks indicate that our method outperforms previous ICL approaches in terms of performance and efficiency, effectively enhancing the complex reasoning capabilities of LLMs. Our project will be publicly available subsequently.