by Bruno Lopez Orozco, Jesus Tadeo Cruz Soto, Miguel Angel Peñaloza Pérez

Language models have made tremendous progress in their ability to solve mathematical problems, but how do we really know how well they're doing? It's not enough to just check if the final answer is correct; we need to understand how they got there and where they're falling short.

What Others Have Discovered

Recent research has revealed fascinating patterns about these models' limitations:

The Weaknesses of Current Models

Burnham (2025) conducted an in-depth analysis of the Grok 4 model and discovered something interesting: while the model can solve complex high school-level problems, it has a clear weakness in spatial intuition. Problems requiring abstraction and creativity remain its Achilles' heel.

Three Common Types of Errors

Parra et al. (2024) identified three fundamental error categories when working with models like GPT-3.5 and Bard:

Construction errors: The model doesn't correctly represent geometric elements on the plane
Conceptual errors: Applies properties without verifying necessary conditions, mixes units of measurement, or omits crucial information
Contradictions: The reasoning steps contradict each other

Structured Step-by-Step Evaluation

Wang et al. (2025) proposed a more systematic approach with five evaluation dimensions: final answer correctness, step completeness, step validity, intermediate calculation accuracy, and problem comprehension. Their main findings: models tend to omit key steps, fail at unit conversions, misinterpret concepts, and make basic arithmetic errors.

Liu et al. (2025) went further, modeling the evaluation process according to human cognitive stages: problem understanding, problem solving, and problem summarization. Their nine evaluation dimensions capture everything from linguistic details to mathematical conceptual mastery.

Our Approach: Five Core Criteria

For this evaluation, we developed a system based on five key constructs, each assessed on a Likert scale from 1 (deficient) to 4 (excellent):

Evaluation Dimensions
Criteria	Level 4 Excellent (4 points)	Level 3 Adequate (3 points)	Level 2 Insufficient (2 points)	Level 1 Deficient (1 point)
Reasoning and Justification	Presents coherent and well-founded, solid arguments, outlining intermediate steps and demonstrating deep understanding of logic and justification in behaviors and decisions.	Presents adequate reasoning,

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