Paper Summary
Title: Investigating Large Language Models in Diagnosing Students’ Cognitive Skills in Math Problem-solving
Source: arXiv (0 citations)
Authors: Hyoungwook Jin et al.
Published Date: 2025-04-01
Podcast Transcript
Hello, and welcome to paper-to-podcast, where we take academic papers from the dusty halls of academia and turn them into something you can listen to while pretending to fold laundry or jog a marathon. Today, we're diving into a paper that might just make you question whether artificial intelligence is as smart as it thinks it is. The paper is titled "Investigating Large Language Models in Diagnosing Students’ Cognitive Skills in Math Problem-solving," and it was penned by Hyoungwook Jin and colleagues, published on April Fool's Day 2025. But I assure you, this is no joke—though it might be a little funny.
Let's get into it. Picture this: artificial intelligence, the whiz kid of the digital world, has been tasked with grading math skills. You'd think it would be a walk in the park for AI, right? I mean, we’re talking about machines that can beat chess grandmasters, write almost-convincing love letters, and even compose music that makes your cat purr with delight. But when it comes to assessing students' math skills, these models are about as effective as a chocolate teapot.
The researchers discovered that even the most advanced large language models are struggling with this task. How bad is it? Well, in terms of F1 score, which is a measure of a model’s accuracy, all the models scored below 0.5. In other words, their performance was pretty dismal. Imagine a teacher grading papers blindfolded and armed with a magic eight ball—that gives you an idea of how reliable these models are at the moment.
Now, here's a twist that might knock your socks off: these models are not just inaccurate; they are overconfidently inaccurate. The study found a strong correlation, with a coefficient of 0.62 between a model's accuracy and its tendency to be overconfident. It's like that one friend who's absolutely sure they know the way to the restaurant, only to lead you into a swamp. The more confident these AI models were, the more they were likely to make mistakes. So, if you've ever been misled by someone who seemed really sure of themselves, now you know machines can be just as bad.
On the brighter side, there was a positive correlation between model size and performance, with a correlation coefficient of 0.77. Bigger models tend to do better. It's like discovering that eating more chocolate does indeed make you happier—expected, but still delightful to confirm.
The study also explored how different inputs and reasoning capabilities affect the models' performance. Incorporating multimodal inputs, like images of student responses, had a subtle impact on improving results. But it wasn't enough to make these models the Einstein of math diagnostics.
Interestingly, models specifically designed for reasoning did not always outperform the standard ones. Some, like the model charmingly named DeepSeek-R1, did better. Others? Not so much. It’s like having a fancy kitchen gadget that promises to make cooking easier, but you still end up burning the toast.
When it came to specific skills, none of the skill categories achieved a maximum F1 score above 0.5. Even for "Compute" skills, which involve evaluating the correctness of calculations and should be straightforward, the models only achieved moderate performance. So, if you're relying on these models for math help, maybe keep that calculator handy.
Surprisingly, there was no significant performance gap between "Knowing" and "Applying" cognitive skills, even though "Knowing" skills are generally seen as easier. It's like expecting to ace a quiz on your favorite TV show and finding out you know as much as your pet goldfish.
The paper suggests that current AI models are not quite ready for high-stakes diagnostic tasks. With low recall and high overconfidence, these models might overlook students' misconceptions, which is a big deal when the goal is to identify and correct them.
But fear not! The researchers propose some solutions. Before unleashing these AI models on the world, practitioners should evaluate their performance on small, verified samples. This can help expose any limitations and allow for adjustments in how the models make decisions. Model developers are also encouraged to train these AI tools to be a bit more humble and evidence-based.
In summary, while large language models hold promise for evaluating cognitive skills, they're not quite ready to replace human judgment when it comes to math assessments. There's still a lot of work to be done, especially in handling messy student responses and vague notations that leave even the smartest machines scratching their virtual heads.
Now, let’s chat about the methods that brought us these enlightening, albeit slightly disappointing, findings. The researchers crafted a benchmark dataset called MATHCOG, featuring 639 student responses to 110 expertly curated math problems. These responses were annotated based on a cognitive skill checklist from the TIMSS 2019 framework. The study evaluated 16 different large language models, both open and closed, to see how well they could classify student responses.
The task was set up as a single-label classification problem, where models had to match a checklist item to one of four verdict categories: "Evident Yes," "Vague Yes," "Evident No," or "Vague No." The models received input in the form of OCR-transcribed student responses and, sometimes, the original handwritten images. Chain-of-Thought prompting was used to guide the models systematically through each checklist item.
Now, let's talk strengths and limitations. The research shines in its innovative approach, using a novel dataset and collaborating with education experts to ensure accuracy and validity. They even measured inter-rater agreement to keep things consistent.
However, the study has its limitations. Due to data-sharing restrictions, the dataset is not publicly available outside of Korea, which means other researchers can't directly replicate the work. The dataset also focuses primarily on arithmetic problems, which might not cover all the diverse mathematical concepts out there. Plus, the study relies on machine-translated inputs and OCR technology, which could lead to errors, especially with students' handwriting that looks like ancient hieroglyphics.
So, what's the silver lining here? Despite the current shortcomings, the research has potential applications in educational settings. Imagine automated tutoring systems that provide real-time feedback to students, helping them correct misconceptions on the fly. This could be especially useful in large-scale online courses where personalized feedback is often a pipe dream.
The research could also enhance educational assessment tools, offering more nuanced evaluations beyond traditional grading. By diagnosing cognitive skills, teachers can gain insights into students' thought processes and provide targeted support to improve their understanding.
Finally, the approach could be used in teacher training programs to demonstrate effective diagnostic techniques, boosting educators' abilities to support students' cognitive development in math.
And there you have it, folks! While we're not quite ready for AI to take over math grading duties, this research points the way to more personalized and effective learning experiences in the future. You can find this paper and more on the paper2podcast.com website. Thanks for tuning in!
Supporting Analysis
The paper investigates how well large language models (LLMs) can diagnose students' cognitive skills in math. It turns out that even the state-of-the-art LLMs struggle with this task, which is quite surprising given their prowess in other areas. All the LLMs scored below 0.5 in F1 score, which indicates they are not very accurate when it comes to assessing cognitive skills in math problem-solving. This means that the models often make mistakes in their evaluations, and they are not very reliable. One surprising finding is the tendency of these models to be overconfident in their incorrect judgments. The study reports a strong correlation (rs = .617) between a model's accuracy and its tendency to be overconfident. This means that the more accurate models were, the more likely they were to make incorrect judgments with high confidence. This is concerning because it could mislead teachers and students who rely on these assessments for feedback. Another interesting result is the correlation between model size and performance. The study found that the size of the model positively correlates with its diagnostic performance (rs = .771). Larger models tend to perform better, which is expected, but the correlation is quite strong, indicating that simply using bigger models could lead to better results in diagnosing cognitive skills. The study also explored the influence of multimodal inputs, reasoning capabilities, and model size on the models' performance. It was found that multimodal input, such as providing images of student responses in addition to text, had a subtle impact on improving performance. However, it wasn't enough to significantly change the results. Interestingly, reasoning-oriented LLMs did not always outperform the standard models. For some reasoning models, like DeepSeek-R1, performance was better, but others did not show clear advantages. This suggests that while reasoning capability is important, it doesn’t automatically translate to improved cognitive skill diagnosis. The analysis of skill-specific performance reveals that no skill category achieved a maximum F1 score above 0.5. Even for skills like "Compute," which involves evaluating the correctness of mathematical procedures and calculations and is similar to traditional grading tasks, the models only achieved moderate performance. This indicates that LLMs have difficulty verifying correct computation in constructed student responses. Contrary to expectations, there was no substantial performance gap between the "Knowing" and "Applying" cognitive skills. The models performed comparably on both types, which is surprising since "Knowing" skills are generally seen as more surface-level and should be easier for LLMs. The study's findings imply that current LLMs are not yet suitable for high-stakes cognitive skill diagnosis. The models’ low recall and high overconfidence suggest they might frequently overlook students’ misconceptions. This is problematic as the main goal of automated assessment is to identify and address these misconceptions, potentially compromising trust in automated systems. The paper suggests that to responsibly integrate LLMs into real-world assessment settings, practitioners should start by evaluating their performance on small, ground-truth samples. This process helps expose limitations and allows for the fine-tuning of model judgments and confidence levels for different math topics and student populations. Model developers are also encouraged to mitigate overconfidence during training by promoting more conservative, evidence-based decision-making. Overall, while LLMs show promise for nuanced evaluation of students’ cognitive skills, they currently fall short of providing reliable and accurate assessments. There’s a lot of room for improvement, especially in handling non-linear, spatially scattered student responses and ambiguous notations that current models struggle with. Future work could involve developing richer representations of math responses that capture high-level semantic intent beyond surface-level cues.
The research aimed to evaluate how well large language models (LLMs) can diagnose students' cognitive skills in mathematics. The researchers developed a benchmark dataset called MATHCOG, which includes 639 student responses to 110 expertly curated middle school math problems. Each response was annotated with detailed teacher diagnoses based on a cognitive skill checklist from the TIMSS 2019 framework, covering skills like knowing, applying, and reasoning. The study examined 16 different LLMs, both open and closed, from various vendors, evaluating them based on their ability to classify student responses into specific cognitive skill categories. The task was set up as a single-label classification problem, where models had to match a checklist item to one of four verdict categories: "Evident Yes," "Vague Yes," "Evident No," or "Vague No." The models received input in the form of OCR-transcribed student responses and, in some cases, the original handwritten images to assess the impact of multimodal input. Chain-of-Thought prompting was used to guide the models in systematically addressing each checklist item. The performance was measured using macro F1 scores, accuracy, and overconfidence/underconfidence metrics.
The most compelling aspect of the research is its innovative approach to evaluating cognitive skills in math problem-solving using large language models (LLMs). The researchers constructed a novel benchmark dataset, MATHCOG, which consists of expertly curated middle school math problems and annotated student responses. This dataset allows for a detailed diagnosis of cognitive skills, offering insights into students' thinking processes beyond merely grading their answers. The researchers followed best practices by collaborating with education experts and middle school teachers to ensure the diagnostic checklists were comprehensive and valid. They addressed potential biases by involving multiple teachers in the diagnosis process and measuring inter-rater agreement to ensure consistency. Additionally, the researchers explored various configurations of LLMs, including model size and input types, to thoroughly understand their impact on cognitive skill diagnosis. By comparing the performance of different LLMs, the study provides a robust evaluation of current AI capabilities in educational settings. The systematic exploration of multimodal input and reasoning capabilities further highlights the comprehensive and methodical nature of their approach.
Possible limitations of the research include the dataset constraints, as the original math problems and student responses cannot be publicly released outside Korea due to data-sharing restrictions. This limits the ability for other researchers to directly replicate or build upon the work. The dataset currently focuses on a narrow range of problem types, primarily arithmetic equation solving, which may not fully represent the diversity of mathematical concepts and reasoning skills across different areas like geometry. The research also primarily examines zero-shot settings, which may not capture the potential of few-shot or test-time compute prompting that could enhance diagnostic accuracy. Additionally, the study relies on machine-translated inputs, which could introduce errors or nuances lost in translation, potentially affecting model performance. Lastly, the reliance on OCR for digitized inputs may lead to transcription errors, especially with unconventional student handwriting or layouts, which could impact the models' ability to accurately diagnose cognitive skills. These limitations suggest a need for more comprehensive datasets, diverse problem types, and exploration of advanced prompting techniques to strengthen future research.
The research on diagnosing students' cognitive skills in math problem-solving using large language models (LLMs) could be applied in several educational contexts. One potential application is in automated tutoring systems, where LLMs could provide real-time feedback to students on their problem-solving approaches, helping them identify and correct misconceptions without waiting for a human grader. This could be particularly beneficial in large-scale online courses or environments with high student-to-teacher ratios, such as MOOCs, where personalized feedback is often limited. Additionally, the research could be implemented in educational assessment tools to offer more nuanced evaluations beyond traditional grading systems. By diagnosing cognitive skills, educators can gain insights into students' thought processes and provide targeted interventions to improve their understanding and application of mathematical concepts. Finally, the approach could be utilized in teacher training programs to demonstrate effective diagnostic techniques and enhance educators' abilities to assess and support students' cognitive development in mathematics. Overall, the integration of LLM-based diagnostic tools into educational systems holds the promise of fostering more personalized and effective learning experiences.