Jonathan Kropko

Bryan R Christ, Jonathan Kropko, Thomas Hartvigsen

Math word problems are critical K-8 educational tools, but writing them is time consuming and requires extensive expertise. To be educational, problems must be solvable, have accurate answers, and, most importantly, be educationally appropriate. We propose that language models have potential to support K-8 math education by automatically generating word problems. However, evaluating educational appropriateness is hard to quantify. We fill this gap by having teachers evaluate problems generated by LLMs, who find existing models and data often fail to be educationally appropriate. We then explore automatically generating educational word problems, ultimately using our expert annotations to finetune a 70B language model. Our model, MATHWELL, is the first K-8 word problem generator targeted at educational appropriateness. Further expert studies find MATHWELL generates problems far more solvable, accurate, and appropriate than public models. MATHWELL also matches GPT-4's problem quality while attaining more appropriate reading levels for K-8 students and avoiding generating harmful questions.

Bryan R. Christ, Zack Gottesman, Jonathan Kropko et al.

Math reasoning is an active area of Large Language Model (LLM) research because it is a hallmark of artificial intelligence and has implications in several domains, including math education. However, few works have explored how math reasoning is encoded within LLM parameters and if it is a skill that can be isolated within models. Doing so could allow targeted intervention to improve math performance without altering non-math behavior and foster understanding of how models encode math reasoning. We introduce Math Neurosurgery (MathNeuro), a computationally efficient method we use to isolate math-specific parameters in LLMs using only forward passes. MathNeuro builds on existing work by using weights and activations to calculate parameter importance, but isolates math-specific parameters by filtering out those important for general language tasks. Through pruning parameters MathNeuro identifies, we delete a LLM's math reasoning ability without significantly impacting its general language ability. Scaling the identified parameters by a small constant improves a pretrained or instruction-tuned LLM's performance by 4-17% on GSM8K and 5-35% on MATH while leaving non-math behavior unaltered. MathNeuro is also data efficient: most of its effectiveness holds when identifying math-specific parameters using a single sample. MathNeuro highlights the potential for future work to intervene on math-specific parameters.

Bryan R. Christ, Penelope Molitz, Jonathan Kropko et al.

Math word problems (MWPs) are critical K-12 educational tools, and customizing them to students' interests and ability levels can increase learning outcomes. However, teachers struggle to find time to customize MWPs for each student given large class sizes and increasing burnout. We propose that LLMs can support math education by generating MWPs customized to student interests and math education standards. To this end, we use a joint human expert-LLM judge approach to evaluate over 11,000 MWPs generated by open and closed LLMs and develop the first teacher-annotated dataset for standards-aligned educational MWP generation. We show the value of our data by using it to train a 12B open model that matches the performance of larger and more capable open models. We also use our teacher-annotated data to train a text classifier that enables a 30B open LLM to outperform existing closed baselines without any training. Next, we show our models' MWPs are more similar to human-written MWPs than those from existing models. We conclude by conducting the first study of customized LLM-generated MWPs with grade school students, finding they perform similarly on our models' MWPs relative to human-written MWPs but consistently prefer our customized MWPs.